research article sliding mode variable structure control...
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Research ArticleSliding Mode Variable Structure Control andReal-Time Optimization of Dry Dual Clutch Transmissionduring the Vehiclersquos Launch
Zhiguo Zhao Haijun Chen and Qi Wang
School of Automotive Studies Tongji University Shanghai 201804 China
Correspondence should be addressed to Zhiguo Zhao zhiguozhaotongjieducn
Received 19 September 2013 Revised 5 November 2013 Accepted 5 November 2013 Published 2 February 2014
Academic Editor Hui Zhang
Copyright copy 2014 Zhiguo Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
In order to reflect driving intention adequately and improve the launch performance of vehicle equipped with five-speed drydual clutch transmission (DCT) the issue of coordinating control between engine and clutch is researched which is based onthe DCT and prototype car developed independently Four-degree-of-freedom (DOF) launch dynamics equations are establishedTaking advantage of predictive control and genetic algorithm target tracing curves of engine speed and vehicle velocity areoptimally specified Slidingmode variable structure (SMVS) control strategy is designed to track these curvesThe rapid prototypingexperiment and test are respectively conducted on the DCT test bench and in the chassis dynamometer Results show that thedesigned SMVS control strategy not only effectively embodies the driverrsquos intention but also has strong robustness to the vehicleparameterrsquos variations
1 Introduction
Based on the automated mechanical transmission (AMT)if remodelling its transmission mechanism (including inputshaft positions of gear pairs and intermediate shaft) andadding a set of dry friction clutch and corresponding actuatordry dual clutch transmission (DCT) can be constructed Theproblem of traction interruption while gear shifting canalso be resolved effectively through the coordinating controlbetween two clutches and engine So the quality of shiftingand the power performance of vehicle can also be improved
As to the launch process of vehicle equipped with dryDCT single or double clutches can be adopted to launchLaunching with double clutches aims at balancing the slidingfriction work of twin clutches and lengthening their servicelife [1 2] but dual clutches participation mode can easilylead to power cycling inside the DCT so its feasibilityrequires further investigation By contrast when single clutchis involved the launch dynamics model and control logic ofDCT are the same as the AMTrsquos because the launch mod-elling and controlling of vehicle equipped with AMT have
been studied widely and profoundly Two degree-of-freedom(DOF) dynamics model has been set up and the optimalclutch engaging control law via minimum principle has beenfounded [3 4] Quadratic optimal launch controller has beendesigned and equivalent damping of AMT transmission hasalso been taken into account [5 6] Six-DOF launch dynamicsequations and clutchrsquos hydraulic actuator model have beenestablishedThe correspondingmodelrsquos parameters have beenalso obtained through experiments [7] Five-DOF launchmodel has been established and simplified and engine speeddecoupling control strategy has also been put forward [8]In addition fuzzy logic control method for the launchingprocess of AMT based on experience has been studied largelyand fuzzy input variables could be the accelerator pedalopening and its changing rate [9] or the deviation and itschanging rate between engine speed and target speed relatedto accelerator pedal [10] or the rotary speed differencebetween clutch driving plate and driven plate [11] Generallyoutput variables could be clutch engaging speed geneticalgorithm has been further used to optimize the fuzzy ruleset [12] Moreover in the aspect of launch control for vehicle
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 494731 18 pageshttpdxdoiorg1011552014494731
2 Mathematical Problems in Engineering
I
1st gears
2nd gears4th gears
3rd gears
5th gears
Clutch 1
Clutch 2
Reverse gears
(solid shaft)
Synchronizer 1
Synchronizer 2
Synchronizer 3
Synchronizer 4
Engine
Intermediate shaft
(hollow shaft)
Output shaft
Vehiclei4
i5
120596c1
Tc1
Ic1
bc1
120596c2
Tc2
Ic2bc2
120596e
Te
Ie
be
120596m
TsmIm
bs
120596s
Tf
iabm
Ig1
Ig2
Ig3
Ig4
Ig5
Igr
i1
i2
i3
Tmc1
Tmc2
Tcm1 or Tcm2
Tms
Input shaft NO1
Input shaft NO2
Figure 1 Five-speed dry DCT dynamic model
equipped with DCT clutch optimal engaging control lawhas been introduced by utilizing minimum principle andsynthetically taking shock intensity sliding friction workand engine output torque into consideration [13] Linearquadratic optimal control has been applied to simulate clutchengaging pressure in the launching process [14 15] Launchfuzzy intelligent control algorithm has been designed andoptimized by using accelerator pedal opening and its chang-ing rate clutch relative slip rate and engine speed differenceto describe the driving intention clutch engaging states andengine working condition respectively [16] Comparativelydouble-layer fuzzy intelligent control architecture has beenpresented by setting up clutch engaging fuzzy control rulesand real car chassis dynamometer test has been conducted[17]
But the above stated studies only focus on the control ofclutch engaging control rules rarely taking consideration ofthe issue of coordinating control between engine and clutchduring the vehiclersquos launch process and let alone the qualifi-cation of driverrsquos intention
Taking the factors such as driverrsquos intention enginecondition clutch state and shock intensity into account theissue of coordinating control between engine and clutch isinvestigated in the paper which is based on the DCT andprototype car developed independently Four degrees of free-dom (DOF) launch dynamics equations are established Thecomputational formulas of engine speed and clutch transfertorque in the launching process have also been quantifiedand given Taking advantage of predictive control and geneticalgorithm target tracing curves of engine speed and vehiclevelocity are optimally specified Sliding mode variable struc-ture (SMVS) control strategy has been designed to track thesecurves Based on the MatlabSimulink software platform andthe hardware-in-the-loop test bench the launch performanceof prototype car equipped with dry DCT has been simulatedunder different driving conditions and the rapid prototyping
experiment and test are respectively conducted on the DCTtest bench and in the chassis dynamometer
2 Mathematical Models
21 Five-Speed Dry DCT Dynamic Model The five-speeddry DCT described in the paper is made up of dry dualclutch module and its actuator four synchronizers and theiractuators and single intermediate shaft gear transmissionmechanism In order to study the dynamic characteristic ofsingle clutch in the launching process and develop relevantcoordinating control strategy the following assumptionsshould be made before modeling (1) Both wheelsrsquo momentof inertia and vehiclersquos translation quality are converted intothe transmission output shaftThe engine output shaft and theinput shaft intermediate shaft and output shaft of transmis-sion are regarded as rigid body with distributed parametersand concentrated inertia and the friction damping loss isconsidered respectively (2)Thedynamic process of the clutchactuator and the synchronizers as well as the heat fade of theclutch are not the focus of this paper (3)Neglect the elasticitybetween bearing and its block as well as the elasticity and gapin gear engagement Finally the established dynamicmodel offive-speed dry DCT after simplification is shown in Figure 1
In Figure 1 parameters and variables are defined asfollows
119868119890 equivalent moment of inertia of engine crankshaft
(including flywheel) and clutch driving plate1198681198881 Equivalent moment of inertia of clutch 1 driven
plate transmission NO1 input shaft (solid part) andrelevant odd number gears1198681198882 equivalent moment of inertia of clutch 2 driven
plate transmissionNO2 input shaft (hollowpart) andits relevant even number speed gears
Mathematical Problems in Engineering 3
119868119898 equivalent moment of inertia of transmission
intermediate shaft its relevant gears and final drivedriving part
119868119904 equivalent moment of inertia of final drive driven
part differential gears axle shafts wheels and com-plete vehicle which are equally converted into trans-mission output shaft
1198681198921 1198681198923 119868119892119903 moment of inertia of 1st 3rd and reverse
driven gears
1198681198922 1198681198924 1198681198925 moment of inertia of 2nd 4th and 5th
driving gears
1198941sim 1198945 119894119886 forward gear ratios and final drive ratio
119887119890 rotating viscous damping coefficient of engine
output shaft
1198871198881 rotating viscous damping coefficient of transmis-
sion NO1 input shaft
1198871198882 rotating viscous damping coefficient of transmis-
sion NO2 input shaft
119887119898 rotating viscous damping coefficient of transmis-
sion intermediate shaft
119887119904 equivalent rotating viscous damping coefficient of
axle shafts and wheels which are equally convertedinto transmission output shaft
120596119890 angular speed of engine crankshaft
1205961198881 angular speed of clutch 1 driven plate (or trans-
mission NO1 input shaft)
1205961198882 angular speed of clutch 2 driven plate (or trans-
mission NO2 input shaft)
120596119898 angular speed of transmission intermediate shaft
120596119904 angular speed of transmission output shaft
119879119890 engine output torque
1198791198881 1198791198882 transfer torque of clutch 1 and clutch 2
1198791198881198981
1198791198881198982
torque of NO1 and NO2 input shaftsacting on intermediate shaft
1198791198981198881
1198791198981198882
torque of intermediate shaft reacting onNO1 and NO2 input shafts
119879119891 driving resistance torque which is equally con-
verted into transmission output shaft
22 Dynamics Equations for Five-Speed Dry DCT DCT canuse 1st speed gear or 2nd speed gear to start Take 1st speedgear launch for example Assuming that the engine is alreadyoperating in idle state the synchronizer 1 firstly engages tothe left gear (1st gear) Because the synchronizer engagingprocess does not belong to the research focus in this paperthe detailed analysis of synchronizer is neglected After theengagement of synchronizer the clutch 1 begins to engageto transmit the torque from the engine side until the end of
launching process During the launch process clutch 1 getsthrough four phases
Free Stroke Eliminating It is to eliminate the vacant distancebetween the clutch driving and driven plates
Slipping Friction before Half-Engaging The clutch begins toengage but the transmitted torque cannot overcome thevehicle resistance to move the vehicle
Sliding Friction after Half-Engaging The clutch is furtherengaged and the torque transmitted by clutch is able to forcethe vehicle to move
Full-Engaging after Synchronizing The engaging process andthe launching process finish
The first two phases have a small effect on the launchingquality and therefore the main research attention is focusedin the last two phases especially the third phase
The four-DOF dynamics equations on the phase of slip-ping friction after half-engaging can be expressed as follows
119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890
11986811988811198881= 1198791198881minus 1198791198981198881
minus 11988711988811205961198881
(119868119898+ 1198681198921
+ 11986811989221198942
2120578 + 11986811989241198942
4120578 + 11986811989251198942
5120578) 119898
= 1198791198881119898
minus 119879119904119898
minus 119887119898120596119898
119868119904119904= 119879119898119904
minus 119879119891minus 119887119904120596119904
(1)
where 119879119890= 119891(120572 120596
119890) 1198791198881198981
= 1198791198981198881
1198941120578 119879119898119904
= 119879119904119898119894119886120578 V = 120596
119904119877119882
1198791198881=
2
3(1198773
0minus 11987731
11987720minus 11987721
)1205831119865 (1199091) 1205961198881le 120596119890
1198791198711198881
1205961198881= 120596119890
(2)
119879119891= (
119862119889119860
2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898
119889V119889119905
)119877119882 (3)
120575 = 1 +1
119898
1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V
119877119882
(4)
Among above formulas 120572 is engine throttle opening119891(120572 120596
119890) denotes nonlinear function of engine output torque
120578 is transmitting efficiency of transmission shafts as well asfinal drive 120583
1is kinetic friction coefficient among friction
plates of clutch 1 1198770 1198771are internal and external radius of
friction plates of clutch 1 1199091is opening of clutch 1 119865(119909
1)
denotes positive pressure function of pressure plate of clutch1 1198791198711198881
is transfer torque after full-engaging of clutch 119898 isvehicle mass 119892 is gravity acceleration 119891 is rolling resistancecoefficient V is vehicle velocity 119862
119889is wind drag coefficient119860
is windward area 120579 is road slope 120575 is conversion coefficientof rotating mass 119877
119882is radius of wheel
For the sake of easily designing the controller furtherassumptions about motional relationship among the inputintermediate and output shafts of transmission should meetthe equations 120596
1199041198941198861198941= 1205961198981198941= 1205961198881 Then the DCT dynamic
model in Figure 1 can be simplified as that in Figure 2
4 Mathematical Problems in Engineering
Clutch 1
Clutch 2
Tc1
120596c2
Tc2120596e
Te
Iebe
120596s
Tf
120596c1
Tmsbo
Io
VehicleEngine
Figure 2 DCT dynamics model after simplification
Simplify formula (1) and then some two-DOF dynamicsequations are obtained
119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881
119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891
(5)
where parameters are defined as follows
119894119890= 11989411988611989411205782
119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + 11986811988811198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119900= 119887119904+ 1198871198981198942
119886120578 + 11988711988811198942
11198942
1198861205782
(6)
When the clutch is fully engaged 1198791198881
= 1198791198711198881 He clutch
transmitted torque 1198791198881is only determined by engine output
torque and driving resistance which satisfies
1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879
119891+ 119887119900120596119904) 1198681198901198941119894119886
119868119900+ 1198681198901198941198901198941119894119886
(7)
When the clutch is fully engages the vehicle is launchedin certain gear In this sense formula (5) can still be furthersimplified as a single-DOF dynamics equation
119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)
where
119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + (119868
1198881+ 119868119890) 1198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119889= 119887119904+ 1198871198981198942
119886120578 + (119887
1198881+ 119887119890) 1198942
11198942
1198861205782
(9)
Synthesizing formulas (5) and (8) the DCT launchdynamic model after eliminating the null distance of clutchcan be seen as a hybrid model namely including a two-DOF sliding frictionmodel and a single-DOF stably operatedmodel The switching condition between the two models is120596119890= 1205961198881 The controller will be designed on the basis of this
hybrid model in the following
3 Coordinating Control and Real-TimeOptimization for Dry DCT
31 Launch Control Objectives The control objectives of dryDCT in the launching process are as follows
(1) reflect the driverrsquos intention adequately to let thedriver have different driving feel according to accel-erator pedal opening and its changing rate
(2) under the condition of meeting the requirements ofshock intensity and sliding friction work to decreasethe slipping friction work as much as possible andguarantee the launch comfort (shock intensity is10ms3 in German standard [18])
(3) take the effect of launching on enginersquos working stateinto account to avoid the flameout of the engine in thelaunching process
32 Launch Controller Design Architecture A layered archi-tecture of launching control is used as shown in Figure 3Theupper layer controller is applied to determine the optimalclutch transfer torque and engine target speed (or torque)while the lower one is used to implement a servocontrol ofclutch torque and a closed-loop control of engine torque (orspeed) The upper controller can further be divided into twoparts according to the activation order the sliding controlbefore the speed synchronization and engaging control afterthe speed synchronization The sliding control is aiming atthe sliding friction after half-engaging phase and also thecore of the launching control Based on the two-DOF modelduring the sliding phase the driving intention the closed-loop control of engine speed and clutch torque and canbe realized Relatively based on the single-DOF model theengaging control is for the full-engaging after synchronizingphase and to make the clutch engage completely as quickly aspossible and prevent engaged clutch plates from falling intosliding state again due to the change of engine output torqueMeanwhile engine output torque is adjusted to match thedemand torque Even though the driving anddriven plates arealready synchronized the launch controller does not send outan accomplishment signal Only if the engine output torqueis equal to the demand torque it sends out the signal
33 Launch Sliding Friction Process Control The inputs oflaunch slipping friction process control include acceleratorpedal opening engine speed wheel speed and so forth Theoutputs contain Clutch 1 target engaging pressure and enginedemand torque They would be realized through the slidingmode variable structure tracing control algorithm
(1)Determine target control variables The target controlvariables include engine target speed and vehicle target shockintensity The engine target speed should be proportional tothe accelerator pedal opening and its changing rate in orderto partially reflect the driverrsquos intention Taking engine targetspeed and vehicle target shock intensity asmeasuring index ofdriverrsquos intention the DCT launch controller can be designedwithout considering the concrete physical characteristics ofclutch actuators thus improving the generality of launchcontroller
(2) Target tracing controller design Based on simplifiedmodels of engine and transmission sliding mode variable
Mathematical Problems in Engineering 5
Control of clutch engaging process after synchronizing
Calculation of driverdemand torque
Driver demandtorque Tde
t lt 998779tYes
Yes
No
No
Switch control ofdemand torque
Engine targetEngine model and itstorque control model
Lower control
Engine realtorque Te
Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing
pedal opening
d120573
dt
120573
Calculation ofequivalent acceleratorpedal opening
120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates
Clutch driven plate speed 120596c1
Engine real speed 120596e
Determination ofengine target speed
Engine target Sliding mode variablestructure tracingcontrol of engine speed
Engine targetEngine model and itstorque control model
Clutch model and itstorque control model
Engine realtorque Te
Clutch real Tc1transfer torque
Lower controlDeterminationof target shockintensity
Target shock Determination oftarget wheel speed
Target wheelSliding mode variablestructure tracingcontrol of wheel speed
Real wheel speed 120596s
Clutch target
Control of starting sliding friction process
120573
Accelerator
output torque Trefe
transfer torque Trefc1
output torque Trefe
speed 120596refs
speed 120596refe
intensities jp andjs
Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing
Figure 3 Design architecture of launch controller
structure controller is designed to track engine target speedand vehicle target shock intensity
331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows
(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell
(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area
(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905
119901 the engine target
speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch
driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref
119890is shown
120596refe
tp
120596e(0)
120596e(ts)
ts
120596c1
Spee
d120596
(rad
s)
Time t (s)
Figure 4 Determination of engine target speed
in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596 119905 lt 119905
119901
120596119890(119905119904) other
(10)
where 120596119890(119905119904) and 120596
119890(0) respectively denote engine target
speed postsynchronizing and idle speed 119905119901is linearly increas-
ing time of engine speed 119905119904is time elapsed until clutch driving
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
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Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
I
1st gears
2nd gears4th gears
3rd gears
5th gears
Clutch 1
Clutch 2
Reverse gears
(solid shaft)
Synchronizer 1
Synchronizer 2
Synchronizer 3
Synchronizer 4
Engine
Intermediate shaft
(hollow shaft)
Output shaft
Vehiclei4
i5
120596c1
Tc1
Ic1
bc1
120596c2
Tc2
Ic2bc2
120596e
Te
Ie
be
120596m
TsmIm
bs
120596s
Tf
iabm
Ig1
Ig2
Ig3
Ig4
Ig5
Igr
i1
i2
i3
Tmc1
Tmc2
Tcm1 or Tcm2
Tms
Input shaft NO1
Input shaft NO2
Figure 1 Five-speed dry DCT dynamic model
equipped with DCT clutch optimal engaging control lawhas been introduced by utilizing minimum principle andsynthetically taking shock intensity sliding friction workand engine output torque into consideration [13] Linearquadratic optimal control has been applied to simulate clutchengaging pressure in the launching process [14 15] Launchfuzzy intelligent control algorithm has been designed andoptimized by using accelerator pedal opening and its chang-ing rate clutch relative slip rate and engine speed differenceto describe the driving intention clutch engaging states andengine working condition respectively [16] Comparativelydouble-layer fuzzy intelligent control architecture has beenpresented by setting up clutch engaging fuzzy control rulesand real car chassis dynamometer test has been conducted[17]
But the above stated studies only focus on the control ofclutch engaging control rules rarely taking consideration ofthe issue of coordinating control between engine and clutchduring the vehiclersquos launch process and let alone the qualifi-cation of driverrsquos intention
Taking the factors such as driverrsquos intention enginecondition clutch state and shock intensity into account theissue of coordinating control between engine and clutch isinvestigated in the paper which is based on the DCT andprototype car developed independently Four degrees of free-dom (DOF) launch dynamics equations are established Thecomputational formulas of engine speed and clutch transfertorque in the launching process have also been quantifiedand given Taking advantage of predictive control and geneticalgorithm target tracing curves of engine speed and vehiclevelocity are optimally specified Sliding mode variable struc-ture (SMVS) control strategy has been designed to track thesecurves Based on the MatlabSimulink software platform andthe hardware-in-the-loop test bench the launch performanceof prototype car equipped with dry DCT has been simulatedunder different driving conditions and the rapid prototyping
experiment and test are respectively conducted on the DCTtest bench and in the chassis dynamometer
2 Mathematical Models
21 Five-Speed Dry DCT Dynamic Model The five-speeddry DCT described in the paper is made up of dry dualclutch module and its actuator four synchronizers and theiractuators and single intermediate shaft gear transmissionmechanism In order to study the dynamic characteristic ofsingle clutch in the launching process and develop relevantcoordinating control strategy the following assumptionsshould be made before modeling (1) Both wheelsrsquo momentof inertia and vehiclersquos translation quality are converted intothe transmission output shaftThe engine output shaft and theinput shaft intermediate shaft and output shaft of transmis-sion are regarded as rigid body with distributed parametersand concentrated inertia and the friction damping loss isconsidered respectively (2)Thedynamic process of the clutchactuator and the synchronizers as well as the heat fade of theclutch are not the focus of this paper (3)Neglect the elasticitybetween bearing and its block as well as the elasticity and gapin gear engagement Finally the established dynamicmodel offive-speed dry DCT after simplification is shown in Figure 1
In Figure 1 parameters and variables are defined asfollows
119868119890 equivalent moment of inertia of engine crankshaft
(including flywheel) and clutch driving plate1198681198881 Equivalent moment of inertia of clutch 1 driven
plate transmission NO1 input shaft (solid part) andrelevant odd number gears1198681198882 equivalent moment of inertia of clutch 2 driven
plate transmissionNO2 input shaft (hollowpart) andits relevant even number speed gears
Mathematical Problems in Engineering 3
119868119898 equivalent moment of inertia of transmission
intermediate shaft its relevant gears and final drivedriving part
119868119904 equivalent moment of inertia of final drive driven
part differential gears axle shafts wheels and com-plete vehicle which are equally converted into trans-mission output shaft
1198681198921 1198681198923 119868119892119903 moment of inertia of 1st 3rd and reverse
driven gears
1198681198922 1198681198924 1198681198925 moment of inertia of 2nd 4th and 5th
driving gears
1198941sim 1198945 119894119886 forward gear ratios and final drive ratio
119887119890 rotating viscous damping coefficient of engine
output shaft
1198871198881 rotating viscous damping coefficient of transmis-
sion NO1 input shaft
1198871198882 rotating viscous damping coefficient of transmis-
sion NO2 input shaft
119887119898 rotating viscous damping coefficient of transmis-
sion intermediate shaft
119887119904 equivalent rotating viscous damping coefficient of
axle shafts and wheels which are equally convertedinto transmission output shaft
120596119890 angular speed of engine crankshaft
1205961198881 angular speed of clutch 1 driven plate (or trans-
mission NO1 input shaft)
1205961198882 angular speed of clutch 2 driven plate (or trans-
mission NO2 input shaft)
120596119898 angular speed of transmission intermediate shaft
120596119904 angular speed of transmission output shaft
119879119890 engine output torque
1198791198881 1198791198882 transfer torque of clutch 1 and clutch 2
1198791198881198981
1198791198881198982
torque of NO1 and NO2 input shaftsacting on intermediate shaft
1198791198981198881
1198791198981198882
torque of intermediate shaft reacting onNO1 and NO2 input shafts
119879119891 driving resistance torque which is equally con-
verted into transmission output shaft
22 Dynamics Equations for Five-Speed Dry DCT DCT canuse 1st speed gear or 2nd speed gear to start Take 1st speedgear launch for example Assuming that the engine is alreadyoperating in idle state the synchronizer 1 firstly engages tothe left gear (1st gear) Because the synchronizer engagingprocess does not belong to the research focus in this paperthe detailed analysis of synchronizer is neglected After theengagement of synchronizer the clutch 1 begins to engageto transmit the torque from the engine side until the end of
launching process During the launch process clutch 1 getsthrough four phases
Free Stroke Eliminating It is to eliminate the vacant distancebetween the clutch driving and driven plates
Slipping Friction before Half-Engaging The clutch begins toengage but the transmitted torque cannot overcome thevehicle resistance to move the vehicle
Sliding Friction after Half-Engaging The clutch is furtherengaged and the torque transmitted by clutch is able to forcethe vehicle to move
Full-Engaging after Synchronizing The engaging process andthe launching process finish
The first two phases have a small effect on the launchingquality and therefore the main research attention is focusedin the last two phases especially the third phase
The four-DOF dynamics equations on the phase of slip-ping friction after half-engaging can be expressed as follows
119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890
11986811988811198881= 1198791198881minus 1198791198981198881
minus 11988711988811205961198881
(119868119898+ 1198681198921
+ 11986811989221198942
2120578 + 11986811989241198942
4120578 + 11986811989251198942
5120578) 119898
= 1198791198881119898
minus 119879119904119898
minus 119887119898120596119898
119868119904119904= 119879119898119904
minus 119879119891minus 119887119904120596119904
(1)
where 119879119890= 119891(120572 120596
119890) 1198791198881198981
= 1198791198981198881
1198941120578 119879119898119904
= 119879119904119898119894119886120578 V = 120596
119904119877119882
1198791198881=
2
3(1198773
0minus 11987731
11987720minus 11987721
)1205831119865 (1199091) 1205961198881le 120596119890
1198791198711198881
1205961198881= 120596119890
(2)
119879119891= (
119862119889119860
2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898
119889V119889119905
)119877119882 (3)
120575 = 1 +1
119898
1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V
119877119882
(4)
Among above formulas 120572 is engine throttle opening119891(120572 120596
119890) denotes nonlinear function of engine output torque
120578 is transmitting efficiency of transmission shafts as well asfinal drive 120583
1is kinetic friction coefficient among friction
plates of clutch 1 1198770 1198771are internal and external radius of
friction plates of clutch 1 1199091is opening of clutch 1 119865(119909
1)
denotes positive pressure function of pressure plate of clutch1 1198791198711198881
is transfer torque after full-engaging of clutch 119898 isvehicle mass 119892 is gravity acceleration 119891 is rolling resistancecoefficient V is vehicle velocity 119862
119889is wind drag coefficient119860
is windward area 120579 is road slope 120575 is conversion coefficientof rotating mass 119877
119882is radius of wheel
For the sake of easily designing the controller furtherassumptions about motional relationship among the inputintermediate and output shafts of transmission should meetthe equations 120596
1199041198941198861198941= 1205961198981198941= 1205961198881 Then the DCT dynamic
model in Figure 1 can be simplified as that in Figure 2
4 Mathematical Problems in Engineering
Clutch 1
Clutch 2
Tc1
120596c2
Tc2120596e
Te
Iebe
120596s
Tf
120596c1
Tmsbo
Io
VehicleEngine
Figure 2 DCT dynamics model after simplification
Simplify formula (1) and then some two-DOF dynamicsequations are obtained
119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881
119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891
(5)
where parameters are defined as follows
119894119890= 11989411988611989411205782
119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + 11986811988811198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119900= 119887119904+ 1198871198981198942
119886120578 + 11988711988811198942
11198942
1198861205782
(6)
When the clutch is fully engaged 1198791198881
= 1198791198711198881 He clutch
transmitted torque 1198791198881is only determined by engine output
torque and driving resistance which satisfies
1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879
119891+ 119887119900120596119904) 1198681198901198941119894119886
119868119900+ 1198681198901198941198901198941119894119886
(7)
When the clutch is fully engages the vehicle is launchedin certain gear In this sense formula (5) can still be furthersimplified as a single-DOF dynamics equation
119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)
where
119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + (119868
1198881+ 119868119890) 1198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119889= 119887119904+ 1198871198981198942
119886120578 + (119887
1198881+ 119887119890) 1198942
11198942
1198861205782
(9)
Synthesizing formulas (5) and (8) the DCT launchdynamic model after eliminating the null distance of clutchcan be seen as a hybrid model namely including a two-DOF sliding frictionmodel and a single-DOF stably operatedmodel The switching condition between the two models is120596119890= 1205961198881 The controller will be designed on the basis of this
hybrid model in the following
3 Coordinating Control and Real-TimeOptimization for Dry DCT
31 Launch Control Objectives The control objectives of dryDCT in the launching process are as follows
(1) reflect the driverrsquos intention adequately to let thedriver have different driving feel according to accel-erator pedal opening and its changing rate
(2) under the condition of meeting the requirements ofshock intensity and sliding friction work to decreasethe slipping friction work as much as possible andguarantee the launch comfort (shock intensity is10ms3 in German standard [18])
(3) take the effect of launching on enginersquos working stateinto account to avoid the flameout of the engine in thelaunching process
32 Launch Controller Design Architecture A layered archi-tecture of launching control is used as shown in Figure 3Theupper layer controller is applied to determine the optimalclutch transfer torque and engine target speed (or torque)while the lower one is used to implement a servocontrol ofclutch torque and a closed-loop control of engine torque (orspeed) The upper controller can further be divided into twoparts according to the activation order the sliding controlbefore the speed synchronization and engaging control afterthe speed synchronization The sliding control is aiming atthe sliding friction after half-engaging phase and also thecore of the launching control Based on the two-DOF modelduring the sliding phase the driving intention the closed-loop control of engine speed and clutch torque and canbe realized Relatively based on the single-DOF model theengaging control is for the full-engaging after synchronizingphase and to make the clutch engage completely as quickly aspossible and prevent engaged clutch plates from falling intosliding state again due to the change of engine output torqueMeanwhile engine output torque is adjusted to match thedemand torque Even though the driving anddriven plates arealready synchronized the launch controller does not send outan accomplishment signal Only if the engine output torqueis equal to the demand torque it sends out the signal
33 Launch Sliding Friction Process Control The inputs oflaunch slipping friction process control include acceleratorpedal opening engine speed wheel speed and so forth Theoutputs contain Clutch 1 target engaging pressure and enginedemand torque They would be realized through the slidingmode variable structure tracing control algorithm
(1)Determine target control variables The target controlvariables include engine target speed and vehicle target shockintensity The engine target speed should be proportional tothe accelerator pedal opening and its changing rate in orderto partially reflect the driverrsquos intention Taking engine targetspeed and vehicle target shock intensity asmeasuring index ofdriverrsquos intention the DCT launch controller can be designedwithout considering the concrete physical characteristics ofclutch actuators thus improving the generality of launchcontroller
(2) Target tracing controller design Based on simplifiedmodels of engine and transmission sliding mode variable
Mathematical Problems in Engineering 5
Control of clutch engaging process after synchronizing
Calculation of driverdemand torque
Driver demandtorque Tde
t lt 998779tYes
Yes
No
No
Switch control ofdemand torque
Engine targetEngine model and itstorque control model
Lower control
Engine realtorque Te
Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing
pedal opening
d120573
dt
120573
Calculation ofequivalent acceleratorpedal opening
120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates
Clutch driven plate speed 120596c1
Engine real speed 120596e
Determination ofengine target speed
Engine target Sliding mode variablestructure tracingcontrol of engine speed
Engine targetEngine model and itstorque control model
Clutch model and itstorque control model
Engine realtorque Te
Clutch real Tc1transfer torque
Lower controlDeterminationof target shockintensity
Target shock Determination oftarget wheel speed
Target wheelSliding mode variablestructure tracingcontrol of wheel speed
Real wheel speed 120596s
Clutch target
Control of starting sliding friction process
120573
Accelerator
output torque Trefe
transfer torque Trefc1
output torque Trefe
speed 120596refs
speed 120596refe
intensities jp andjs
Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing
Figure 3 Design architecture of launch controller
structure controller is designed to track engine target speedand vehicle target shock intensity
331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows
(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell
(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area
(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905
119901 the engine target
speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch
driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref
119890is shown
120596refe
tp
120596e(0)
120596e(ts)
ts
120596c1
Spee
d120596
(rad
s)
Time t (s)
Figure 4 Determination of engine target speed
in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596 119905 lt 119905
119901
120596119890(119905119904) other
(10)
where 120596119890(119905119904) and 120596
119890(0) respectively denote engine target
speed postsynchronizing and idle speed 119905119901is linearly increas-
ing time of engine speed 119905119904is time elapsed until clutch driving
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
119868119898 equivalent moment of inertia of transmission
intermediate shaft its relevant gears and final drivedriving part
119868119904 equivalent moment of inertia of final drive driven
part differential gears axle shafts wheels and com-plete vehicle which are equally converted into trans-mission output shaft
1198681198921 1198681198923 119868119892119903 moment of inertia of 1st 3rd and reverse
driven gears
1198681198922 1198681198924 1198681198925 moment of inertia of 2nd 4th and 5th
driving gears
1198941sim 1198945 119894119886 forward gear ratios and final drive ratio
119887119890 rotating viscous damping coefficient of engine
output shaft
1198871198881 rotating viscous damping coefficient of transmis-
sion NO1 input shaft
1198871198882 rotating viscous damping coefficient of transmis-
sion NO2 input shaft
119887119898 rotating viscous damping coefficient of transmis-
sion intermediate shaft
119887119904 equivalent rotating viscous damping coefficient of
axle shafts and wheels which are equally convertedinto transmission output shaft
120596119890 angular speed of engine crankshaft
1205961198881 angular speed of clutch 1 driven plate (or trans-
mission NO1 input shaft)
1205961198882 angular speed of clutch 2 driven plate (or trans-
mission NO2 input shaft)
120596119898 angular speed of transmission intermediate shaft
120596119904 angular speed of transmission output shaft
119879119890 engine output torque
1198791198881 1198791198882 transfer torque of clutch 1 and clutch 2
1198791198881198981
1198791198881198982
torque of NO1 and NO2 input shaftsacting on intermediate shaft
1198791198981198881
1198791198981198882
torque of intermediate shaft reacting onNO1 and NO2 input shafts
119879119891 driving resistance torque which is equally con-
verted into transmission output shaft
22 Dynamics Equations for Five-Speed Dry DCT DCT canuse 1st speed gear or 2nd speed gear to start Take 1st speedgear launch for example Assuming that the engine is alreadyoperating in idle state the synchronizer 1 firstly engages tothe left gear (1st gear) Because the synchronizer engagingprocess does not belong to the research focus in this paperthe detailed analysis of synchronizer is neglected After theengagement of synchronizer the clutch 1 begins to engageto transmit the torque from the engine side until the end of
launching process During the launch process clutch 1 getsthrough four phases
Free Stroke Eliminating It is to eliminate the vacant distancebetween the clutch driving and driven plates
Slipping Friction before Half-Engaging The clutch begins toengage but the transmitted torque cannot overcome thevehicle resistance to move the vehicle
Sliding Friction after Half-Engaging The clutch is furtherengaged and the torque transmitted by clutch is able to forcethe vehicle to move
Full-Engaging after Synchronizing The engaging process andthe launching process finish
The first two phases have a small effect on the launchingquality and therefore the main research attention is focusedin the last two phases especially the third phase
The four-DOF dynamics equations on the phase of slip-ping friction after half-engaging can be expressed as follows
119868119890119890= 119879119890minus 1198791198881minus 119887119890120596119890
11986811988811198881= 1198791198881minus 1198791198981198881
minus 11988711988811205961198881
(119868119898+ 1198681198921
+ 11986811989221198942
2120578 + 11986811989241198942
4120578 + 11986811989251198942
5120578) 119898
= 1198791198881119898
minus 119879119904119898
minus 119887119898120596119898
119868119904119904= 119879119898119904
minus 119879119891minus 119887119904120596119904
(1)
where 119879119890= 119891(120572 120596
119890) 1198791198881198981
= 1198791198981198881
1198941120578 119879119898119904
= 119879119904119898119894119886120578 V = 120596
119904119877119882
1198791198881=
2
3(1198773
0minus 11987731
11987720minus 11987721
)1205831119865 (1199091) 1205961198881le 120596119890
1198791198711198881
1205961198881= 120596119890
(2)
119879119891= (
119862119889119860
2115V2 + 119898119892 sin 120579 + 119898119892 cos 120579119891 + 120575119898
119889V119889119905
)119877119882 (3)
120575 = 1 +1
119898
1198681198881119894211198942119886+ 1198681198981198942119886+ 119868119904+ 119868V
119877119882
(4)
Among above formulas 120572 is engine throttle opening119891(120572 120596
119890) denotes nonlinear function of engine output torque
120578 is transmitting efficiency of transmission shafts as well asfinal drive 120583
1is kinetic friction coefficient among friction
plates of clutch 1 1198770 1198771are internal and external radius of
friction plates of clutch 1 1199091is opening of clutch 1 119865(119909
1)
denotes positive pressure function of pressure plate of clutch1 1198791198711198881
is transfer torque after full-engaging of clutch 119898 isvehicle mass 119892 is gravity acceleration 119891 is rolling resistancecoefficient V is vehicle velocity 119862
119889is wind drag coefficient119860
is windward area 120579 is road slope 120575 is conversion coefficientof rotating mass 119877
119882is radius of wheel
For the sake of easily designing the controller furtherassumptions about motional relationship among the inputintermediate and output shafts of transmission should meetthe equations 120596
1199041198941198861198941= 1205961198981198941= 1205961198881 Then the DCT dynamic
model in Figure 1 can be simplified as that in Figure 2
4 Mathematical Problems in Engineering
Clutch 1
Clutch 2
Tc1
120596c2
Tc2120596e
Te
Iebe
120596s
Tf
120596c1
Tmsbo
Io
VehicleEngine
Figure 2 DCT dynamics model after simplification
Simplify formula (1) and then some two-DOF dynamicsequations are obtained
119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881
119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891
(5)
where parameters are defined as follows
119894119890= 11989411988611989411205782
119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + 11986811988811198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119900= 119887119904+ 1198871198981198942
119886120578 + 11988711988811198942
11198942
1198861205782
(6)
When the clutch is fully engaged 1198791198881
= 1198791198711198881 He clutch
transmitted torque 1198791198881is only determined by engine output
torque and driving resistance which satisfies
1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879
119891+ 119887119900120596119904) 1198681198901198941119894119886
119868119900+ 1198681198901198941198901198941119894119886
(7)
When the clutch is fully engages the vehicle is launchedin certain gear In this sense formula (5) can still be furthersimplified as a single-DOF dynamics equation
119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)
where
119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + (119868
1198881+ 119868119890) 1198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119889= 119887119904+ 1198871198981198942
119886120578 + (119887
1198881+ 119887119890) 1198942
11198942
1198861205782
(9)
Synthesizing formulas (5) and (8) the DCT launchdynamic model after eliminating the null distance of clutchcan be seen as a hybrid model namely including a two-DOF sliding frictionmodel and a single-DOF stably operatedmodel The switching condition between the two models is120596119890= 1205961198881 The controller will be designed on the basis of this
hybrid model in the following
3 Coordinating Control and Real-TimeOptimization for Dry DCT
31 Launch Control Objectives The control objectives of dryDCT in the launching process are as follows
(1) reflect the driverrsquos intention adequately to let thedriver have different driving feel according to accel-erator pedal opening and its changing rate
(2) under the condition of meeting the requirements ofshock intensity and sliding friction work to decreasethe slipping friction work as much as possible andguarantee the launch comfort (shock intensity is10ms3 in German standard [18])
(3) take the effect of launching on enginersquos working stateinto account to avoid the flameout of the engine in thelaunching process
32 Launch Controller Design Architecture A layered archi-tecture of launching control is used as shown in Figure 3Theupper layer controller is applied to determine the optimalclutch transfer torque and engine target speed (or torque)while the lower one is used to implement a servocontrol ofclutch torque and a closed-loop control of engine torque (orspeed) The upper controller can further be divided into twoparts according to the activation order the sliding controlbefore the speed synchronization and engaging control afterthe speed synchronization The sliding control is aiming atthe sliding friction after half-engaging phase and also thecore of the launching control Based on the two-DOF modelduring the sliding phase the driving intention the closed-loop control of engine speed and clutch torque and canbe realized Relatively based on the single-DOF model theengaging control is for the full-engaging after synchronizingphase and to make the clutch engage completely as quickly aspossible and prevent engaged clutch plates from falling intosliding state again due to the change of engine output torqueMeanwhile engine output torque is adjusted to match thedemand torque Even though the driving anddriven plates arealready synchronized the launch controller does not send outan accomplishment signal Only if the engine output torqueis equal to the demand torque it sends out the signal
33 Launch Sliding Friction Process Control The inputs oflaunch slipping friction process control include acceleratorpedal opening engine speed wheel speed and so forth Theoutputs contain Clutch 1 target engaging pressure and enginedemand torque They would be realized through the slidingmode variable structure tracing control algorithm
(1)Determine target control variables The target controlvariables include engine target speed and vehicle target shockintensity The engine target speed should be proportional tothe accelerator pedal opening and its changing rate in orderto partially reflect the driverrsquos intention Taking engine targetspeed and vehicle target shock intensity asmeasuring index ofdriverrsquos intention the DCT launch controller can be designedwithout considering the concrete physical characteristics ofclutch actuators thus improving the generality of launchcontroller
(2) Target tracing controller design Based on simplifiedmodels of engine and transmission sliding mode variable
Mathematical Problems in Engineering 5
Control of clutch engaging process after synchronizing
Calculation of driverdemand torque
Driver demandtorque Tde
t lt 998779tYes
Yes
No
No
Switch control ofdemand torque
Engine targetEngine model and itstorque control model
Lower control
Engine realtorque Te
Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing
pedal opening
d120573
dt
120573
Calculation ofequivalent acceleratorpedal opening
120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates
Clutch driven plate speed 120596c1
Engine real speed 120596e
Determination ofengine target speed
Engine target Sliding mode variablestructure tracingcontrol of engine speed
Engine targetEngine model and itstorque control model
Clutch model and itstorque control model
Engine realtorque Te
Clutch real Tc1transfer torque
Lower controlDeterminationof target shockintensity
Target shock Determination oftarget wheel speed
Target wheelSliding mode variablestructure tracingcontrol of wheel speed
Real wheel speed 120596s
Clutch target
Control of starting sliding friction process
120573
Accelerator
output torque Trefe
transfer torque Trefc1
output torque Trefe
speed 120596refs
speed 120596refe
intensities jp andjs
Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing
Figure 3 Design architecture of launch controller
structure controller is designed to track engine target speedand vehicle target shock intensity
331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows
(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell
(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area
(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905
119901 the engine target
speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch
driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref
119890is shown
120596refe
tp
120596e(0)
120596e(ts)
ts
120596c1
Spee
d120596
(rad
s)
Time t (s)
Figure 4 Determination of engine target speed
in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596 119905 lt 119905
119901
120596119890(119905119904) other
(10)
where 120596119890(119905119904) and 120596
119890(0) respectively denote engine target
speed postsynchronizing and idle speed 119905119901is linearly increas-
ing time of engine speed 119905119904is time elapsed until clutch driving
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
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4 Mathematical Problems in Engineering
Clutch 1
Clutch 2
Tc1
120596c2
Tc2120596e
Te
Iebe
120596s
Tf
120596c1
Tmsbo
Io
VehicleEngine
Figure 2 DCT dynamics model after simplification
Simplify formula (1) and then some two-DOF dynamicsequations are obtained
119868119890119890+ 119887119890120596119890= 119879119890minus 1198791198881
119868119900119904+ 119887119900120596119904= 1198791198881119894119890minus 119879119891
(5)
where parameters are defined as follows
119894119890= 11989411988611989411205782
119868119900= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + 11986811988811198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119900= 119887119904+ 1198871198981198942
119886120578 + 11988711988811198942
11198942
1198861205782
(6)
When the clutch is fully engaged 1198791198881
= 1198791198711198881 He clutch
transmitted torque 1198791198881is only determined by engine output
torque and driving resistance which satisfies
1198791198881=119868119900(119879119890minus 119887119890120596119890) + (119879
119891+ 119887119900120596119904) 1198681198901198941119894119886
119868119900+ 1198681198901198941198901198941119894119886
(7)
When the clutch is fully engages the vehicle is launchedin certain gear In this sense formula (5) can still be furthersimplified as a single-DOF dynamics equation
119868119889119904+ 119887119889120596119904= 119879119890119894119890minus 119879119891 (8)
where
119868119889= 119868119904+ (119868119898+ 1198681198921) 1198942
119886120578 + (119868
1198881+ 119868119890) 1198942
11198942
1198861205782
+ 11986811989221198942
21198942
1198861205782
+ 11986811989241198942
41198942
1198861205782
+ 11986811989251198942
51198942
1198861205782
119887119889= 119887119904+ 1198871198981198942
119886120578 + (119887
1198881+ 119887119890) 1198942
11198942
1198861205782
(9)
Synthesizing formulas (5) and (8) the DCT launchdynamic model after eliminating the null distance of clutchcan be seen as a hybrid model namely including a two-DOF sliding frictionmodel and a single-DOF stably operatedmodel The switching condition between the two models is120596119890= 1205961198881 The controller will be designed on the basis of this
hybrid model in the following
3 Coordinating Control and Real-TimeOptimization for Dry DCT
31 Launch Control Objectives The control objectives of dryDCT in the launching process are as follows
(1) reflect the driverrsquos intention adequately to let thedriver have different driving feel according to accel-erator pedal opening and its changing rate
(2) under the condition of meeting the requirements ofshock intensity and sliding friction work to decreasethe slipping friction work as much as possible andguarantee the launch comfort (shock intensity is10ms3 in German standard [18])
(3) take the effect of launching on enginersquos working stateinto account to avoid the flameout of the engine in thelaunching process
32 Launch Controller Design Architecture A layered archi-tecture of launching control is used as shown in Figure 3Theupper layer controller is applied to determine the optimalclutch transfer torque and engine target speed (or torque)while the lower one is used to implement a servocontrol ofclutch torque and a closed-loop control of engine torque (orspeed) The upper controller can further be divided into twoparts according to the activation order the sliding controlbefore the speed synchronization and engaging control afterthe speed synchronization The sliding control is aiming atthe sliding friction after half-engaging phase and also thecore of the launching control Based on the two-DOF modelduring the sliding phase the driving intention the closed-loop control of engine speed and clutch torque and canbe realized Relatively based on the single-DOF model theengaging control is for the full-engaging after synchronizingphase and to make the clutch engage completely as quickly aspossible and prevent engaged clutch plates from falling intosliding state again due to the change of engine output torqueMeanwhile engine output torque is adjusted to match thedemand torque Even though the driving anddriven plates arealready synchronized the launch controller does not send outan accomplishment signal Only if the engine output torqueis equal to the demand torque it sends out the signal
33 Launch Sliding Friction Process Control The inputs oflaunch slipping friction process control include acceleratorpedal opening engine speed wheel speed and so forth Theoutputs contain Clutch 1 target engaging pressure and enginedemand torque They would be realized through the slidingmode variable structure tracing control algorithm
(1)Determine target control variables The target controlvariables include engine target speed and vehicle target shockintensity The engine target speed should be proportional tothe accelerator pedal opening and its changing rate in orderto partially reflect the driverrsquos intention Taking engine targetspeed and vehicle target shock intensity asmeasuring index ofdriverrsquos intention the DCT launch controller can be designedwithout considering the concrete physical characteristics ofclutch actuators thus improving the generality of launchcontroller
(2) Target tracing controller design Based on simplifiedmodels of engine and transmission sliding mode variable
Mathematical Problems in Engineering 5
Control of clutch engaging process after synchronizing
Calculation of driverdemand torque
Driver demandtorque Tde
t lt 998779tYes
Yes
No
No
Switch control ofdemand torque
Engine targetEngine model and itstorque control model
Lower control
Engine realtorque Te
Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing
pedal opening
d120573
dt
120573
Calculation ofequivalent acceleratorpedal opening
120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates
Clutch driven plate speed 120596c1
Engine real speed 120596e
Determination ofengine target speed
Engine target Sliding mode variablestructure tracingcontrol of engine speed
Engine targetEngine model and itstorque control model
Clutch model and itstorque control model
Engine realtorque Te
Clutch real Tc1transfer torque
Lower controlDeterminationof target shockintensity
Target shock Determination oftarget wheel speed
Target wheelSliding mode variablestructure tracingcontrol of wheel speed
Real wheel speed 120596s
Clutch target
Control of starting sliding friction process
120573
Accelerator
output torque Trefe
transfer torque Trefc1
output torque Trefe
speed 120596refs
speed 120596refe
intensities jp andjs
Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing
Figure 3 Design architecture of launch controller
structure controller is designed to track engine target speedand vehicle target shock intensity
331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows
(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell
(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area
(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905
119901 the engine target
speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch
driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref
119890is shown
120596refe
tp
120596e(0)
120596e(ts)
ts
120596c1
Spee
d120596
(rad
s)
Time t (s)
Figure 4 Determination of engine target speed
in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596 119905 lt 119905
119901
120596119890(119905119904) other
(10)
where 120596119890(119905119904) and 120596
119890(0) respectively denote engine target
speed postsynchronizing and idle speed 119905119901is linearly increas-
ing time of engine speed 119905119904is time elapsed until clutch driving
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
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Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
Control of clutch engaging process after synchronizing
Calculation of driverdemand torque
Driver demandtorque Tde
t lt 998779tYes
Yes
No
No
Switch control ofdemand torque
Engine targetEngine model and itstorque control model
Lower control
Engine realtorque Te
Single-DOF in 1st gear stably operatingdynamics model of dry dual clutchtransmission after synchronizing
pedal opening
d120573
dt
120573
Calculation ofequivalent acceleratorpedal opening
120573 Has the clutch been synchronized or notCalculations of speed differenceand slip rate between clutchdriving and driven plates
Clutch driven plate speed 120596c1
Engine real speed 120596e
Determination ofengine target speed
Engine target Sliding mode variablestructure tracingcontrol of engine speed
Engine targetEngine model and itstorque control model
Clutch model and itstorque control model
Engine realtorque Te
Clutch real Tc1transfer torque
Lower controlDeterminationof target shockintensity
Target shock Determination oftarget wheel speed
Target wheelSliding mode variablestructure tracingcontrol of wheel speed
Real wheel speed 120596s
Clutch target
Control of starting sliding friction process
120573
Accelerator
output torque Trefe
transfer torque Trefc1
output torque Trefe
speed 120596refs
speed 120596refe
intensities jp andjs
Two-DOF starting dynamicsmodel of dry dual clutchtransmission after synchronizing
Figure 3 Design architecture of launch controller
structure controller is designed to track engine target speedand vehicle target shock intensity
331 Determining Method of Engine Target Speed The prin-ciples of determining engine target speed are as follows
(1) In order to avoid the stalling of engine and attrition ofclutch due to overhigh speed the target speed is notless than the engine idle speed (set as 800 rmin) andis limited to a maximum value (set as 2000 rmin) aswell
(2) Within optional limits of target speed on one handthe target speed changes along with the variation ofaccelerator pedal opening and its changing rate andit can ensure that engine has enough output power tomeet the launch demands under different conditionsOn the other hand the selected target speed canmakethe engine work in an economic area
(3) When the difference between engine real speed andclutch driven plate speed is more than the settingthreshold value Δ120596 and the clutch sliding frictiontime is less than the time variable 119905
119901 the engine target
speedwill coordinatewith the accelerator pedal open-ing and its changing rate If the condition is reversethe target speed will be fixed as synchronous speed120596119890(119905119904) namely the speed when engine and clutch
driven plate are at the moment of synchronizingThe calculation of engine target speed 120596ref
119890is shown
120596refe
tp
120596e(0)
120596e(ts)
ts
120596c1
Spee
d120596
(rad
s)
Time t (s)
Figure 4 Determination of engine target speed
in Figure 4 and Formula (10) The engine outputcharacteristic can be seen in Figure 15 Consider
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596 119905 lt 119905
119901
120596119890(119905119904) other
(10)
where 120596119890(119905119904) and 120596
119890(0) respectively denote engine target
speed postsynchronizing and idle speed 119905119901is linearly increas-
ing time of engine speed 119905119904is time elapsed until clutch driving
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
Table 1 Engine synchronous target speed
Equivalent accelerator pedalopening 120573V
Engine synchronous targetspeed 120596
119890(119905119904)(rmin)
0sim10 100010sim20 100020sim30 110030sim40 120040sim50 130050sim60 140060sim70 150070sim80 160080sim90 170090sim100 2000
and driven plates are synchronized Δ120596 is set threshold valueof the difference between clutch driving and driven plates
In order to reflect the driverrsquos intention easily anddetermine 120596
119890(119905119904) equivalent accelerator pedal opening 120573V is
introduced to synthesize the information of accelerator pedalopening and its changing rate The relationship between 120573Vand 120596
119890(119905119904) is shown in Table 1
Consider
120573V (119905) = 120573 (119905) + 119896 120573 (119905) (11)
where 120573(119905) is real value of accelerator pedal opening 120573(119905)
is changing rate of accelerator pedal opening 119896 is weightindex and must be determined according to the practice toguarantee the 120573
119905(119905) falling into the scope of [0ndash100]
332 Determining Method of Target Shock Intensity in theLaunching Process The launch target shock intensity not onlyreflects the driverrsquos intention but also guarantees that theintensity is in a reasonable extent The friction process isdivided into three parts in [19] which qualitatively elaboratedcontrol key points when a vehicle was launched and itsclutch driving and driven plates were synchronizing In [20]the shock intensity while the clutch driving and drivenplates were synchronizing is derived which showed that itis proportional to the difference between engine accelerationand acceleration of clutch driven plate at the instant ofpresynchronization That is
119888(+) minus
119888(minus) =
119868119890
119868119890+ 119868119888119886
[119890(minus) minus
119888(minus)] (12)
where 119888(minus)
119888(+) denote accelerations of clutch driven plate
at the instant of presynchronization and post- synchroniza-tion
119890(minus) is engine acceleration at the instant of presynchro-
nization 119868ca is moment of inertia of complete vehicle and itstransmission system which are equally converted to clutchdriven plate
Suppose that the transmission system is rigid namelyV =
119904119877119882
= 1198881198941119894119886119877119882 The shock intensity of vehicle can
Table 2 Driverrsquos intention
Launch mode Slow Moderate AbruptEquivalent acceleratorpedal opening 120573V
0sim20 20sim50 50sim100
Target shock intensity119895119901(ms3) 05 15 25
be equally converted into the shock intensity of clutch drivenplate Consider Formula (12) If the difference between engineacceleration and acceleration of clutch driven plate is zero theshock intensity will be zero at the moment of synchronizingThe condition is called no-impact synchronizing conditionAs the engine target speed is determined in precedingpassage namely the rotary speed difference is less than thethreshold value Δ120596 or the elapsed time of sliding frictionprocess is more than the time variable 119905
119901 the engine speed
remains constant as the same as synchronous target speedSo the engine acceleration is zero For the sake of no-impactat the moment of synchronizing the speed of clutch drivenplate should be equal to the target speed and its accelerationshould be zero
The authors divide the launch sliding friction process intothree phases determine the target shock intensity in differentphases and obtain related target vehicle acceleration andtarget vehicle velocity via integral It is shown in Figure 5
Phase One During the time slot 0 sim 119905119901 the target shock
intensity 119895119901is positive It changes along with the equivalent
acceleration which reflects the driverrsquos intention As theparticularity of creeping launchthat is the clutch drivingand driven plates should maintain slipping state during thewhole launching process without considering their speedsynchronization In view of this creeping launch is out ofconsideration in this paper Therefore on the basis of equiv-alent accelerator pedal opening and engine output torquecapacity driverrsquos intention is divided into three categories[3 6] which is shown in Table 2
Phase Two During the time slot 119905119901
sim 119905119904 the target shock
intensity 119895119901is negative The main goal is to lower the vehicle
acceleration so that the speed and acceleration of clutchdriven plate stay the same as the enginersquos at the moment ofsynchronizing in order to realize no-impact synchronizingThe values are synchronous target speed and zero respec-tively Theoretically different values are selected accordingto different target shock intensity in Phase One Howeverconsidering that clutch driving plate and its driven plate areapproaching to synchronize the target shock intensity 119895
119904is set
as a constant value in order to accelerate the engaging speedand decrease the total sliding friction work in the launchingprocess Equations can be established as follows
119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
051198951199011199052
119901+ 119895119901119905119901(119905119904minus 119905119901) + 05119895
119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(13)
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
js
ts
Time t (s)
Shoc
k in
tens
ityj
(ms3)
tp
jp
(a) Target shock intensity
ts
Time t (s)
Acce
lera
tiona
(ms2)
tp
(b) Target vehicle acceleration
ts
Time t (s)
Velo
city
(ms
)
tp
(c) Target vehicle velocity
Figure 5 Target curves in the launching process
where 119895119901is target shock intensity in phase one of sliding
friction process 119895119904is target shock intensity in Phase Two of
sliding friction process 120596(119905119904) is speed of clutch driven plate
at time 119905119904 namely the synchronous target speed
By solving formula (13) the following can be obtained
119905119901= radic
120596 (119905119904) 119877119882
(05119895119901minus 051198952
119901119895119904)
119905119904= 119905119901(1 minus
119895119901
119895119904
)
(14)
According to equivalent accelerator pedal opening at theinitial moment of sliding friction process the synchronoustarget speed and target shock intensity in Phase One can beobtained by looking up Tables 1 and 2 respectively Basedon above values 119905
119901and 119905119904 the target speed of clutch 1 in the
sliding friction process will be listed in the following throughthe integral of 119895
119901and 119895119904twice
120596ref119904
= int119905119904
0
int119905119904
0
119895
119877119882
119889119905
120596ref1198881
= 120596ref1199041198941119894119886
(15)
Note that both 119905119901and 119905119904are measured in a coordinate
system whose origin is the initial moment of sliding frictionprocess
PhaseThree During the time slot over 119905119904 clutch driving plate
and its driven part are already synchronized andDCTmodelis switched from sliding frictionmodel to 1st speed gear stablyoperated model So the control of sliding friction makes nosense any more In order to meet the requirement of no-impact synchronizing the target acceleration is set as zeroand the target speed is constant
333 Rolling Determination of Target Value and GeneticOptimization of Shock Intensity The determining method ofengine target speed and launch target shock intensity statedabove can ensure no stalling of engine and ride comfortof vehicle in the launching process and partially reflect thedriverrsquos intention but some shortages also exist as follows
(1) Engine synchronizing target speed and target shockintensity in Phase One are only based on equiva-lent accelerator pedal opening at the initial momentof sliding friction process without considering thewhole sliding friction process The transformation ofequivalent accelerator pedal opening obviously doesnot accord with the fact
(2) Neglect the sliding friction work in the launchingprocess when determining the target speed
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Discrete Dynamics in Nature and Society
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Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
0
1
2
3
t0
middotmiddotmiddot
middot middot middot
Time t (s)
Velocity(m
s)
t0 + Δt t0 + 2Δt t0 + 3Δt
Figure 6 Schematic diagram of the rolling calculation of launchtarget vehicle velocity
In order to overcome the above shortages predictive con-trol thoughts are used to optimize the target curves online Itmeans that during a time slot (namely at an optimizing step)these variables such as 120596
119890(119905119904) 119905119901 119905119904 and 119895
119901can be obtained
by minimizing the sliding friction work on the basis of theequivalent accelerator pedal opening and vehicle velocityAnd then the target curves can also be obtained
Determination of Rolling Algorithm of Target Vehicle VelocityThe target vehicle velocity curve is recalculated in a timeinterval Δ119905 Both vehicle velocity and acceleration are notequal to 0 at every calculation moment Figure 6 shows thatV0 V1 V2 and V
3represent the target vehicle velocities at these
moments of 1199050 1199050+ Δ119905 119905
0+ 2Δ119905 and 119905
0+ 3Δ119905 respectively
Figure 7 shows the calculation method of target vehiclevelocity in a certain time According to the condition of no-impact synchronizing formula (13) can be rewritten as
119886 (1199050) + 119895119901119905119901+ 119895119904(119905119904minus 119905119901) = 0
V (1199050) + 119886 (119905
0) 119905119901+1
21198951199011199052
119901+ (120572 (119905
0) + 119895119901119905119901) (119905119904minus 119905119901)
+1
2119895119904(119905119904minus 119905119901)2
= 120596 (119905119904) 119877119882
(16)
where 1199050is optimizingmoment 120572(119905
0) denotes vehicle acceler-
ation at the optimizingmoment V(1199050)denotes vehicle velocity
at the optimizing moment and 120596119890(119905119904) denotes synchronous
target revolving speed which updates its value at everyoptimizing step according to virtual accelerator pedal signalby looking up Table 1
In a word firstly at every optimizing step synchronoustarget rotary speed 120596
119890(119905119904) and target shock intensity are
obtained by looking upTables 1 and 2 according to the currentequivalent accelerator pedal opening Secondly solve (16) andget the latest values of 119905
119901 119905119904 Finally according to formula (15)
we get the target vehicle velocity in the launching process
The rolling determining method of engine target speedresembles the above description According to (10) followingformula can be obtained
120596ref119890
=
120596119890(119905119904) minus 120596119890(0)
119905119901
119905 + 120596119890(0) (120596
119890minus 1205961198881) ge Δ120596
1199050lt 119905 lt (119905
0+ 119905119901)
120596119890(119905119904) other
(17)
Determination of Optimal Algorithm of Target Shock IntensityThe target shock intensity stated above is obtained by lookingup Tables But it does not ensure that the target curve isoptimal It is discussed below how to determine 119895
119901and 119895
119904
through genetic algorithm and real-time optimization In thetime slot 119905
0sim 1199050+ 119905119904 the predictive sliding friction work is
119882 = int1199050+119905119904
1199050
1198881(120596
ref119890
minus 1205961198881) 119889119905
1198881=119868119900ref119904
+ 119887119900120596ref119904
+ 119898119892119877119882120583
11989411988611989411205782
(18)
where 1198881is estimated clutch transfer torque If |119879
1198881minus1198881| lt 120576
estimated value 1198881replaces real value 119879
1198881 and target shock
intensities 119895119901and 119895119904can be obtained byminimizing the sliding
friction work The selected fitness function based on geneticalgorithm is the reciprocal of predictive sliding friction work
119865 =1
119882 (19)
The optimizing process of parameters 119895119901and 119895
119904can be
seen in Figure 8
334 Design of Sliding Mode Variable Structure TracingController Based on the design of previous details the targetvehicle velocity and target engine speed are already obtainedin the launch sliding friction process However whether itcan track accurately or not depends on the performanceof launch controller completely Considering immeasurabledriving resistance a kind of sliding mode variable structurecontrol algorithm with interference rejection has been putforward in the paper which aims at tracking engine speed andwheel speed accurately
Regardless of the influence of temperature and slip speeddifference on clutch friction coefficient 120583
1 the relationship
between pressure 1198651of the clutch pressure plate and its
transfer torque is determined uniquely when the internal andexternal radius of friction plates are given For the sake ofeasy description clutch transfer torque is used to describe theclutch engaging law in the following
Tracing Control of Wheel Speed On the basis of launchdynamics equations of DCT transmission system (referringto Formula (5)) supposing 119909
1= 120579119904 1199092= 120596119904 there is
1= 1199092
2=
119894119890
119868119900
1198791198881minus1198870
1198680
1199092minus119879119891
1198680
(20)
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
t0 t0 + ts
a(t0)
Time t (s)
Acce
lera
tiona
(ms2)
t0 + tp
(a) Target acceleration
(t0)
t0 t0 + ts
Time t (s)
Velo
city
(ms
)
t0 + tp
(b) Target vehicle velocity
Figure 7 Calculation schematic diagram of target vehicle velocity at time 1199050
Equivalentacceleratorpedal opening
Rollingdetermination
of engine speedand vehicle
velocity
Engine target speed
Clutchtransfertorque
estimation
Clutch driven plate target speed
Targ
et im
pact
stren
gth
optim
izat
ion
Geneticalgorithm
Calculationsof estimated
slidingfriction
energy andfitness
function
jp and js after optimizing
Figure 8 Optimizing process of target shock intensity
Supposing that 1198901= 119909119903minus1199091 1198902= 119903minus1199092 1199061= 1198791198881 where
119909119903is the expectation of 119909
1 there is
[1198901
1198902
] = [
[
0 1
0 minus1198870
1198680
]
]
[1198901
1198902
] + [
[
0
minus119894119890
1198680
]
]
1199061+ [
0
1198912
] + [0
1198913
] (21)
where 1198912= 119903+ (11986801198870)119903 which is measurable interference
and 1198913= 1198791198911198680 which is immeasurable interference related
to the driving resistanceIn order to reduce the gain of sliding mode variable
structure it should contract the upper and lower boundariesof interference as much as possible According to the compu-tational formula of driving resistance the rolling resistanceis regarded as a part of measurable interference namelymeasurable interference 119891
2can be rewritten as
1198911015840
2= 119903+1198680
1198870
119903+119898119892119891
1198870
(22)
And the immeasurable interference1198913can be rewritten as
1198911015840
3=119879119891
1198680
minus119898119892119891
1198870
(23)
The switching function is designed as119904 = 11988811198901+ 11988821198902 (24)
where 1198881gt 0 1198882gt 0 Take the approaching rate
119904 = minus119896 sdot 119904 minus 119889 sdot 119892 (119904) + 11988821198911015840
3 (25)
where 119889 gt |11988821198911015840
3|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901
sin (119901 sdot 119904) |119904| lt120587
2119901
119901 gt 0 (26)
While it is 119901 rarr infin 119892(119904) rarr sgn(119904) The control input 1199061
is calculated via the formula below
1199061=
1198680
1198882119894119890
[119896 sdot 119904 + 119889 sdot 119892 (119904) + 1198902(1198881minus 1198882
1198870
1198680
) + 11988821198911015840
2] (27)
Tracing Control of Engine Speed Because engine model isa double-input (119879
119890and 119879
1198881)-single-output (120596
119890) model and
clutch transfer torque 1198791198881is available in use of wheel speed
tracing controller stated previously 1198791198881
is a measurableinterference of enginemodel Based on the rotation dynamicsof crankshaft (refer to Formula (5)) we can suppose that
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
100
90
80
70
60
50
40
30
20
10
0050 15 2 25 3 35 41
Time t (s)
Acce
lera
tion
peda
l ope
ning120573
()
NO1 conditionNO2 condition
(a) Acceleration pedal opening value
0500
15 2 25 3 35 41
250
200
150
100
50
Time t (s)
Targ
et sp
eed120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(b) Target rotational speed
050 15 2 25 3 35 410
250
200
150
100
50
Time t (s)
Real
spee
d120596
(rad
s)
Clutch on the NO1 conditionEngine on the NO1 conditionClutch on the NO2 conditionEngine on the NO2 condition
(c) Actual rotational speed
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Targ
et sh
ock
inte
nsityj
(ms3)
NO1 conditionNO2 condition
(d) Target impact strength
050 15 2 25 3 35 41
6
4
2
0
minus2
minus4
minus6
Time t (s)
Real
shoc
k in
tens
ityj
(ms3)
NO1 conditionNO2 condition
(e) Actual impact strength
140
120
100
80
60
40
20
0050 15 2 25 3 35 41
Time t (s)
Engi
ne o
utpu
t tor
queT
e(N
m)
NO1 conditionNO2 condition
(f) Engine output torque
Figure 9 Continued
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
050 15 2 25 3 35 41
140
120
100
80
60
40
20
0
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
NO1 conditionNO2 condition
(g) Clutch transfer torque
050 15 2 25 3 35 41
20
18
16
14
12
10
8
6
4
2
0
Time t (s)
Vehi
cle v
eloc
ity
(km
h)
NO1 conditionNO2 condition
(h) Vehicle velocity
Figure 9 Simulation results of launch performance
1199091119890
= 120579119890 1119890
= 120579119890= 120596119890 1198901119890
= 119909119903119890minus 1199091119890 1198902119890
= 119903119890minus 1199092119890
where 119909119903119890is the expectation of 120579
119890 namely
[1198901119890
1198902119890
] = [
[
0 1
0 minus119887119890
119868119890
]
]
[1198901119890
1198902119890
] + [
[
0
minus1
119868119890
]
]
1199062+ [
0
1198912119890
] (28)
where 1199062= 119879119890 1198912119890
= (1198791198881119868119890) + 119903119890+ (119887119890119868119890)119903119890 which are
measurable interferencesThe switching function is designed as
119904119890= 11988811198901198901119890+ 11988821198901198902119890 (29)
where 1198881119890gt 0 1198882119890gt 0 Take the approaching rate
119904119890= minus119896119890sdot 119904119890minus 119889119890sdot 119892 (119904119890) (30)
where 119889119890gt |11988821198901198912119890|
119892 (119904) =
sgn (119904) |119904| ge120587
2119901119890
sin (119901119890sdot 119904) |119904| lt
120587
2119901119890
119901 gt 0 (31)
The control output 1199062is calculated via the following
formula
1199062=119868119890
1198882
[119896119890sdot 119904119890+ 119889119890sdot 119892 (119904119890) + 1198902119890(1198881119890minus 1198882119890
119887119890
119868119890
) + 11988821198901198912119890]
(32)
34 Switching Control of Engine Demand Torque in theEngaging Process after Synchronizing When engine speedand clutch driven plate speed approach to synchronizing and
reach set threshold values according to switching conditionsDCT launch models switch over namely the two-DOF slid-ing friction model transforms into the single-DOF 1st speedgear stable operated model At the moment the controllerof sliding friction process does not work any longer Andswitching controller of demand torque begins to work whichis in charge of converting engine torque into driver demandtorque It satisfies
119879119889
119890= 119879119871
119890+ 119870119890119905 (33)
119870119890= (
119879119889119890minus 119879119871119890
Δ119905) (34)
wherein 119879119871119890is real engine torque at the switching moment
of DCT launch models 119879119889119890is driver demand torque 119870
119890is
changing slope of engine torque and Δ119905 is switching timeelapsed of demand torque
In order to meet the requirement of vehicle shockintensity in the switching process Δ119905 has a minimum valueAccording to the 1st speed gear stably operated model(formula (8)) shock intensity is proportional to the changingrate of engine torque regardless of driving resistance andfriction damping That is
119895 =119894119890119877119882
119868119889
119890 (35)
According to the requirement of shock intensity in thelaunching process namely 119895 le 10ms3 the upper limitedvalue of changing rate of engine torque can be calculatedTheminimum time elapsed in the switching process of torque alsocan be obtained on the basis of formula (33)
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
050 15 2 25 3 35 41
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
etp
(s)
Time t (s)
NO1 conditionNO2 condition
(a) Optimizing process of 119905119901
050 15 2 25 3 35 41
3
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
ets
(s)
Time t (s)
NO1 conditionNO2 condition
(b) Optimizing process of 119905119904
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(c) Clutch transfer torque under NO1 condition
050 15 2 25 3 35 41
100
90
80
70
60
50
40
30
20
10
0
Real valueEstimated value
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Time t (s)
(d) Clutch transfer torque under NO2 condition
Figure 10 Comparisons of results of rolling optimization under NO1 and NO2 condition
Similarly according to the two-DOF launch model (For-mula (5)) in the launch sliding friction process we knowthat vehicle shock intensity in the sliding friction process isproportional to the changing rate of clutch transfer torqueregardless of driving resistance and friction damping Sothere is
119895 =119894119890119877119882
1198680
1198881 (36)
4 Simulation Results and Analysis
Based on the previously established dynamic model of dryDCT and its launch controller the launch simulation model
of vehicle equipped with dry DCT is built on the Mat-labsimulink software platform Immediately the perfor-mance of vehicle is simulated under typical launch conditionThe detailed parameters of adopted DCT can be seen in theappendix
Figure 9 and Table 3 demonstrate simulation results oflaunch condition which are defined as that the changing rateof accelerator pedal angle is constant and that the final valuesare different It means that changing rate of accelerator is04 sminus1 and that the final values are 20 and 40 respectivelyRelatively they are called NO1 and NO2 conditions respec-tively which are shown in Figure 9(a) Compared with NO4condition (it reaches the final value at 1 s) NO3 conditionrequires a slower launch process
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 13
(a) Photo of dry DCT test bench
Key signal
Accelerator pedal signal
Brake pedal signal
Shifting knob signal
Clutch 1 position signal
Clutch 2 position signal
1st 3rd gears position signal
2nd 4th gears position signal
5th gear position signal
Reverse gear position signal
control system
Monitor PC andcontroldesk interface
Clutch 1 actuator
Clutch 2 actuator
Shifting motor of 1stand 3rd gears
Shifting motor of 2ndand 4th gears
Shifting motor of 5thand reverse gears
MicroAutoBox
(b) Interfaces of DCT prototyping controller
Figure 11 DCT test bench and prototyping controller
Table 3 Comparisons of simulated results of NO1 and NO2 con-ditions
Working condition NO1 NO2Time elapsed when clutch driving anddriven plates are synchronized 119905
119904s 2355 2535
Vehicle velocity when clutch driving anddriven plates are synchronized V(kmh) 81052 96367
Time elapsed when the demand torqueswitch over (119905
119904+ Δ119905)s 314 333
Vehicle velocity when the demand torqueswitch over 119907(kmh) 83558 10371
Total slipping friction work119882J 37399 47673Time elapsed for launch 119905s 314 333
In Figures 9(b) 9(c) and 9(g) and Table 3 both thesynchronizing moment of clutch driving and driven platesand the switching finishing moment under NO1 conditionare earlier than that of NO2 working condition At anymoment vehicle velocity is quite little under NO1 conditionSo it can be concluded that the designed launch controllercan reflect the driving intention In Figures 9(d) and 9(e)launch impact strengths are less than 10ms3 whichmeet thedemands In Figures 9(f) and 9(g) engine output and clutchtransfer torque can also be divided into five parts
Figures 10(a) and 10(b) demonstrate optimal time vari-ables 119905
119901and 119905
119904calculated at every rolling optimization
The total optimizing frequency is 22 under NO1 conditionwhile the time elapsed is 153 s at the last optimizationRelatively the total optimizing frequency is 24 times underNO2 condition while the time elapsed is 164 s at the lastoptimization Figures 10(c) and 10(d) show that estimatedvalue of119879
1198881is quite approaching to its real value in the launch
sliding friction process It ensures that sliding friction is leastin the launching process to some degree
5 Rapid Prototyping Experiments for DryDCT in the Launching Process
51 Five-Speed Dry DCT Transmission Actuator In order toshorten the development cycle of dry DCT control systemand test the real-time property and effectiveness of slid-ing mode variable structure control algorithm as well theresearch group has established a dry DCT test bench (shownin Figure 11(a)) and used MicroAutoBox1401 of dSPACECorporation as prototype controller Somemodels are set upsuch as five-speed dry DCT vehicle models (including enginemean value model DCT model and vehicle longitudinaldynamics model) and DCT control strategymodelThe rapidprototyping experiments are conducted at the same time
The interfaces of dryDCT prototype controller are shownin Figure 11(b) Before testing calibrate the signals of sensorsfirstly and test the working performance of actuator motordriving units and actuator mechanisms in an open loop inorder to ensure the reliability of hardware system Secondlytest and verify the coordinating control strategy of clutchtorque in a closed-loop Thirdly conduct the rapid proto-typing experiments of sliding mode variable structure uppercoordinating control strategy after proving its effectivenessand calibrating relative control parameters
52 Results and Analysis of Rapid Prototyping Tests Bymeansof making use of RTI1401 toolbox offered by dSPACE Cor-poration defining input signal pins such as accelerator pedalsignal brake pedal signal and contacting with the previouslydesigned DCT launch upper control module the uppercontroller can be established
The launch trigger signal is defined as follows when thecurrent speed gear is 1st speed gear the brake pedal signal iszero (in loose state) The accelerator pedal opening is morethan or equal to 3 A trigger signal for preselecting 2ndspeed gear is delayed 05 s after the launch is finished
The trigger signal of shifting 1st speed gear to the 2nd onecan be defined as follows when the vehicle velocity is bigger
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
14 Mathematical Problems in Engineering
Time t (s)
100
80
60
40
20
08 10 12 14 16
Acce
lera
tor p
edal
ope
ning120573
()
(a) Acceleration pedal opening
250
200
150
100
50
0
EngineClutch oneClutch two
8 10 12 14 16
Time t (s)
Targ
et ro
tatio
nal s
peed120596
(rad
s)
(b) Target rotational speed
EngineClutch oneClutch two
8 10 12 14 16
250
200
150
100
50
0
Time t (s)
Real
spee
d120596
(rad
s)
(c) Real rotational speed
10
5
0
minus5
minus108 10 12 14 16
Shoc
k in
tens
ityj
(ms3)
Time t (s)
(d) Shock intensity
7
6
5
4
3
2
1
08 9 10 11 12 13 14 15 16 17
Time t (s)
Slid
ing
fric
tion
wor
kW
(kJ)
(e) Sliding friction work
Time t (s)8 10 12 14 16
120
100
80
60
40
20
0
Torq
ueT
(Nm
)
EngineClutch oneClutch two
(f) Torque
Figure 12 Continued
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 15
25
20
15
10
5
0
Time t (s)8 10 12 14 16
Vehi
cle v
eloc
ity
(km
h)
(g) Vehicle velocity
120
100
80
60
40
20
08 9 10 11 12 13
Time t (s)
Clut
ch tr
ansfe
r tor
queT
c1(N
m)
Estimated valueReal value
(h) Clutch transfer torque
25
2
15
1
05
0
Opt
imiz
atio
n va
riabl
et(s
)
8 9 10 11 12 13
Time t (s)
tPts
(i) Optimization process of launch variables
15
10
5
0
Clut
ch se
para
ting
strok
ex(m
m)
Time t (s)8 10 12 14 16
Clutch one target valueClutch one actual value
Clutch two target valueClutch two actual value
(j) Tracing response of clutch separating stroke
Figure 12 Rapid prototyping experiment results of launch and shifting from the 1st gear to the 2nd one
Figure 13 Photo of real car chassis dynamometer test
than the 1st to 2nd gear shifting speed 12 kmh and the targetgear is 2nd gear
The rapid prototyping experiment results of upper con-troller are demonstrated in Figure 12 and Table 4 It can
Table 4 Rapid prototyping experiment results of dry DCT in thelaunching process
Launch moment 1199050s 9425
Synchronizing moment of launch clutch 1 driving anddriven plates (119905
0+ 119905119904)s 1196
Vehicle velocity at the synchronizing moment of clutch1 V(kmh) 9029
Switching finishing moment of launch demand toque(1199050+ 119905119904+ Δ119905)s 1274
Vehicle velocity at the switching finishing moment ofdemand toque V(kmh) 9498
Total sliding friction work119882J 4416Rolling optimization frequency of time variable 24Time elapsed for launch 119905s 3315
be seen that the performance indexes of shock intensityand sliding friction work meet the standard demands in
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
16 Mathematical Problems in Engineering
100
80
60
40
20
08194 8198 8202 8206 821 8214
Time t (s)
Acce
lera
tor o
peni
ng120573
()
(a) Accelerator pedal opening
8194 8198 8202 8206 821 8214
350
300
250
200
150
100
50
0
EngineTransmission input shaft
Time t (s)
Rota
tiona
l spe
ed120596
(rad
s)
(b) Rotational speed
8194 8198 8202 8206 821 8214
10
5
0
minus5
Time t (s)
Shoc
k in
tens
ityj
(ms3)
(c) Shock intensity
Figure 14 Results of dry DCT prototype car chassis dynamometer test
the launching process and that results of rapid prototypingexperiments coincide with simulated results It is also provedthat the stated slidingmode variable structure dryDCTuppercontroller can meet the requirement of real-time controlbased on real-time optimization
6 Chassis Dynamometer Test of Real CarEquipped with Dry DCT
After rapid prototyping experiments the independentlydevelopmental five-speed dry DCT control unit is used toreplace theMicroAutoBox1401 rapid prototype controller Onthe basis of simulation and bench test results the corre-sponding MAP of prototype car equipped with dry DCT isrecalibrated After DCT software is developed the real carchassis dynamometer test is conducted The test photo isshown in Figure 13
The results of launch test can be seen in Figure 14 Theexperiment results demonstrate that on the basis of sliding
mode variable structure upper coordinating control strategythe developed dry DCT control software not only reflectsthe launch riding comfort of vehicle but also reflects thevariation of driverrsquos intention
As can been seen from Figure 14 under the proposedlaunching strategies the vehicle is launched within 2 s andthe shock intensity is below 10ms3 Besides when theaccelerator pedal opening is increasing the correspondingshock intensity is relatively larger which is consistent with thecontrol strategies Comparedwith the rapid prototyping teststhe results obtained in the chassis dynamometer test are alsoconsistent thus validating the effectiveness of the proposedcontrol strategies
7 Conclusion
Thefour-DOF launch dynamicsmodel of five-speed dryDCTis established After simplifying the model two-DOF slidingfriction model and single-DOF in-gear operation model areobtained which provide a basis for the design and control
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 17Th
e eng
ine o
utpu
t tor
que (
Nm
)
The throttle openingThe engine rotating speed (rmin)
The engine output torque characteristic
250
200
150
100
50
0100
8060
4020
0 10002000
30004000
50006000
Figure 15
Table 5 The parameters of adopted DCT
Parameters Value119868119890 0273 kgsdotm2
1198681198881 0014 kgsdotm2
1198681198882 0014 kgsdotm2
119868119898 001 kgsdotm2
119868119904 1470392 kgsdotm2
I1198921
simI1198925 0005 kgsdotm2
119868119892119903 0005 kgsdotm2
i1 simi53615 2042 1257
0909 0714119894119886 3895119887119890 0011198871198881 0011198871198882 001119887119898 001119887119904 001119898 1550 kg119891 00137119892 98ms2
119860 2095m119862119889 0293
119877119908 0308m
120578 0921198770 0228m
1198771 015m
of launch controller Driverrsquos intention is reflected by usingengine speed and vehicle shock intensity Taking advantageof the idea of predictive control and genetic algorithm thetracing curves of engine speed and vehicle target velocity aredetermined by rolling optimization online The sliding modevariable structure controller (SMVS) is designed Launchsimulatingmodel is built on theMATLABSimulink softwareplatform for the dry DCT the launch rapid prototyping
experiment is conducted Simulation and experiment resultsshow that the designed SMVS coordinating controller caneffectively reflect the driverrsquos intention and improve the vehi-clersquos launch performance Furthermore chassis dynamometertest result of DCT prototype car also shows that the proposedSMVS launch coordinating control strategy is effective andfeasible
Appendices
A The Engine Output Characteristics (Map)
See Figure 15
B The Parameters of Adopted DCT in ThisPaper
See Table 5
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] D Qin Y Liu J Hu and R Chen ldquoControl and simulation oflaunch with two clutches for dual clutch transmissionsrdquoChineseJournal of Mechanical Engineering vol 46 no 18 pp 121ndash1272010
[2] D Qin and Q Chen ldquoUniversal clutch starting control ofAMTDCT automatic transmission based on optimal controlrdquoChinese Journal of Mechanical Engineering vol 47 no 12 pp85ndash91 2011
[3] C Sun and J Zhang ldquoOptimal control applied in automaticclutch engagements of vehiclesrdquo Chinese Journal of MechanicalEngineering vol 17 no 2 pp 280ndash283 2004
[4] Q-H Chen D-T Qin and X Ye ldquoOptimal control about AMTheavy-duty truck starting clutchrdquoChina Journal of Highway andTransport vol 23 no 1 pp 116ndash121 2010
[5] F Garofalo L Glielmo L Iannelli et al ldquoOptimal tracking forautomotive dry clutch engagementrdquo in Proceedings of the Inter-national Federation of Automatic Control (IFAC rsquo02) pp 367ndash372 2002
[6] I A Amir D T Qin and J J Liu ldquoA control strategy on launchup a vehicle with AMTrdquo Information Technology Journal vol 4no 2 pp 140ndash145 2005
[7] G Lucente M Montanari and C Rossi ldquoModelling of anautomated manual transmission systemrdquo Mechatronics vol 17no 2-3 pp 73ndash91 2007
[8] A Serrarens M Dassen and M Steinbuch ldquoSimulation andcontrol of an automotive dry clutchrdquo in Proceedings of the 2004American Control Conference (AAC rsquo04) pp 4078ndash4083 July2004
[9] C H Yu H Y Chen and H R Ding ldquoA study on fuzzy controlof AMT clutch in launch phaserdquo Automotive Engineering vol27 no 4 pp 423ndash426 2004
[10] Z Qi Q Chen and A Ge ldquoFuzzy control of the AMT vehiclersquosstarting process based on genetic algorithmrdquo Chinese Journal ofMechanical Engineering vol 37 no 4 pp 8ndash24 2001
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
18 Mathematical Problems in Engineering
[11] M Yong D Y Sun D T Qin et al ldquoResearch on partial fuzzycontrol of car clutch in launch phaserdquo Automotive Technologyvol 12 pp 12ndash15 2008
[12] H Kong F Ren and Y M Ren ldquoApplication of the geneticalgorithm to optimizing fuzzy control strategy in the vehiclersquoslaunch processrdquo Journal of Hefei University of Technology vol32 no 1 pp 21ndash23 2009
[13] M X Wu J W Zhang T L Lu et al ldquoResearch on optimalcontrol for dry dual-clutch engagement during launchrdquo Journalof Automobile Engineering vol 224 no 6 pp 749ndash763 2010
[14] G Q Wu and D M Zhan ldquoA research on the way of clutchactuation during DCT upshift based on optimality theoryrdquoAutomotive Engineering vol 31 no 3 2009
[15] Y Li Z Zhao and T Zhang ldquoResearch on optimal control oftwin clutch engagement pressure for dual clutch transmissionrdquoChina Mechanical Engineering vol 21 no 12 pp 1496ndash15012010
[16] W Yang Q Chen GWu and D Qin ldquoStarting control strategyfor dual clutch transmission based on intelligent control andthe performance simulationrdquo Chinese Journal of MechanicalEngineering vol 44 no 11 pp 178ndash185 2008
[17] Y Liu D Qin H Jiang and Y Zhang ldquoA systematic model fordynamics and control of dual clutch transmissionsrdquo Journal ofMechanical Design Transactions of the ASME vol 131 no 6 pp0610121ndash0610127 2009
[18] Y S Zhao Integrated control of dual clutch transmission system[MS thesis] Chongqing University
[19] H-O Liu H-Y Chen H-R Ding and Z-B He ldquoAdaptiveclutch engaging process control for automatic mechanicaltransmissionrdquo Journal of Beijing Institute of Technology vol 14no 2 pp 170ndash174 2005
[20] F Garofalo L Glielmo L Iannelli et al ldquoSmooth engagementfor automotive dry clutchrdquo in Proceedings of the IEEE ControlSystems Society Conference vol 1 pp 529ndash534 2001
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of