research article dynamic modeling and control strategy ... · soil terzaghi coecients of bearing...

Research ArticleDynamic Modeling and Control Strategy Optimization fora Hybrid Electric Tracked Vehicle

Hong Wang1 Qiang Song1 Shengbo Wang2 and Pu Zeng3

1Beijing Co-Innovation Center of Electric Vehicles National Engineering Laboratory for Electric VehiclesBeijing Institute of Technology No 5 South Zhongguancun Street Haidian District Beijing 100081 China2Construction Machinery RampD Center Intelligence Research Department Shantui Construction Machinery Co LtdNo 58 Highway G327 Jining Shandong 272073 China3Shanghai Volkswagen Ningbo 315336 China

Correspondence should be addressed to Qiang Song songqiangbiteducn

Received 5 June 2015 Revised 20 September 2015 Accepted 21 September 2015

Academic Editor Xiaosong Hu

Copyright copy 2015 Hong Wang 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

A new hybrid electric tracked bulldozer composed of an engine generator two drivingmotors and an ultracapacitor is put forwardwhich can provide high efficiencies and less fuel consumption comparing with traditional ones This paper first presents theterramechanics of this hybrid electric tracked bulldozer The driving dynamics for this tracked bulldozer is then analyzed Afterthat based on analyzing the working characteristics of the engine generator and drivingmotors the power train systemmodel andcontrol strategy optimization is established by using MATLABSimulink and OPTIMUS software Simulation is performed undera representative working condition and the results demonstrate that fuel economy of the HETV can be significantly improved

1 Introduction

As a type of construction vehicle the quantity of bulldozers isincreasing significantly with tremendous social developmentusually causing energy unsustainability and poor air qual-ity Additionally the energy efficiency of the conventionalbulldozer is only 20 The electrification of the bulldozeras construction machinery is a good way to decrease airpollution and oil shortages For these reasons developing anelectric bulldozer has significant effects on energy savingsand emission reductions [1] Studies have been performed toaddress these energy issues notably regarding the utilizationof electricity as a viable replacement of oil Hybrid powersystems aremore suitable than traditional power trains for thereduction of fuel consumption and emissions In the UnitedStates Caterpillar produced the first D7E hybrid electricdrive tracked bulldozer in March 2008 Compared withtraditional models CO and NO

119909emissions were reduced

by approximately 10 and 20 respectively The D7E canimprove fuel economy by 25 [2]

Hybrid electric tracked bulldozer is a complex systemdue to its two power sources engine-generator sets andultracapacitor The working speeds of the engine and charge-discharge properties of the ultracapacitor impact the fueleconomy of the bulldozer together A reasonable energydistribution control strategy could achieve theminimum fuelconsumption How to coordinate the power flow betweenengine-generator sets ultracapacitor and drive motor effec-tively to achieve theminimum fuel consumption is a complexdesign optimization problem

In recent years scholars have proposed a variety of dif-ferent power allocation control strategies for electric vehicles[3ndash8] which can be roughly classified into two categoriesthermostat type and power follow type [9ndash12] The workingprinciple of the thermostat type control strategy is as followsengine outputs a set constant power when the SOC of batteryis lower than the set minimum value engine does not workwhen SOC is higher than the set maximum value At thistime the battery needs to meet the transient high powerdischarge requirements that could do harm to the discharge

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 251906 12 pageshttpdxdoiorg1011552015251906

2 Mathematical Problems in Engineering

efficiency and the lifetime of the battery Power follow controlstrategy requires the engine-generator sets output power toalways follow the load demand power of the vehicle causingengine speed frequently fluctuate and affecting the engineefficiency and emission properties Xiong et al [13] adoptedthe thermostat control strategy for PHEV taking battery andultracapacitor as the auxiliary power source This controlmethod improved the discharge efficiency and the lifetimeof the auxiliary power source However it is complex rarelyused in the construction machinery vehicles like bulldozerKwon et al [14] adopted power follow control strategy fora series hybrid wheel excavator taking ultracapacitor as theauxiliary power source which improved the fuel economy by24 However this control method limited the improvementof the fuel economy as engine was controlled to work at onesingle point

In this paper one power follow control strategy is putforward to combine the working features of the proposedseries hybrid electric tracked bulldozers [15 16] Bulldozersdo not require high speed and acceleration performance Butthey demand power when low-speed operation fluctuatesremarkably Considering working features of the bulldozerultracapacitor is taken as the auxiliary power source due toits high power density and short-term high power and cur-rent output capabilities By analyzing the engine-generatorworking point and the SOC state of the ultracapacitor areasonable power control strategy is proposed to improve thefuel economy of the hybrid electric tracked bulldozer Testbench experiment was performed to collect actual test benchdata to correlate and validate the proposed control strategyfor this hybrid electric tracked bulldozer

Parameter optimization for the power follow controlstrategy is also researched because of the importance of accu-rate match of control strategy parameters for fuel economyimproving [17 18] Commonly genetic algorithm is famousfor its global optimization and parallel computing capabilities[19ndash21] and has been widely used in multiple areas includingparameter estimation in system identification optimizationand neural network training [22] A genetic algorithm isestablished to solve the parameter optimization problem inthe control strategy in this study

The organization of this paper is as follows In Section 2the new configuration of the hybrid electric tracked bulldozeris described and the detailed terramechanics of the trackedbulldozer is researched to provide the theoretical basis forthemodeling of the dynamics in Section 3The power controlstrategy is described in Section 4The optimization problemprocedure and results of the control strategy are intro-duced in Section 5 Finally the conclusions are presented inSection 6

2 Terramechanics of the Tracked Bulldozer

21 Configuration of the Hybrid Electric Tracked BulldozerThe schematic of this hybrid electric tracked bulldozer(using one traditional bulldozer as the prototype) is givenin Figure 1 This hybrid electric tracked bulldozer maintainsthe vehicle body hydraulic and operation system of thetraditional bulldozer just changing the transmission form

The paths for the electric power and mechanical power aretandem in the series configurations This construction sim-plifies the propulsion and transmission system and providesgreater flexibility in the power train system

This hybrid electric tracked bulldozer uses an integratedcontroller to control two motors on both sides of the bull-dozer independently and to transfer electric energy from theDC BUS into mechanical energy to drive the bulldozer

The terramechanics of this hybrid electric tracked bull-dozer is the theoretical basis for further analysis of the drivingdynamics The working states of the tracked bulldozer canbe divided into the following six stages soil-cutting soil-transportation returning climbing turning and acceler-ating The external travel resistance operating resistancedriving force and track slide curve under the working statesare researched in the following context

22 External Travel Resistance 119865119864 The resistance caused

by the vertical deformation of the soil under the anteriortrack of the vehicle when driving is called external travelresistance It mainly results from the energy consumption ofsoil compaction and the effects of bulldozing resistance 119865

119864

can be written as the following [23]

119865119864= 119865119888+ 119865119887

119865119888=

2119887

(119899 + 1) 1198961119899

(119866

2119887119871)

(119899+1)119899

119865119887= 1205741198852

119887119896120574+ 2119887119885119888119896pc

(1)

where

119896120574= (

2119873120574

tan120595+ 1) cos2120595

119896pc = (119873119888 minus tan120595) cos2120595

(2)

where 119865119888is compaction resistance (N) 119865

119887is bulldozing

resistance (N) 119887 is track width (m) 119866 is vehicle weight (N)119871 is track length (m) 119888 is soil cohesion coefficient (KPa) 120595 issoil internal friction angle (∘) 119899 is soil deformation index 119896 issoil deformation modulus (KNm119899+2) 119885 is track amount ofsinkage (m) 120574 is unit weight (Nm3) and119873

120574and119873

119888are the

soil Terzaghi coefficients of bearing capacity [24]

23 Operating Resistance 119865119879 Consider

119865119879= 1198651+ 1198652+ 1198653+ 1198654

1198651= 106

1198611ℎ119901119896119887

1198652= 1198661199051205831cos120572 =

1198811205741205831cos 120579119896119904

1198653= 106

11986111198831205832119896119910

1198654= 1198661199051205832cos 1205752 cos 120579

119881 =

1198611(119867 minus ℎ

119901)2

119896119898

2 tan1205720

(3)

Mathematical Problems in Engineering 3

Engine

Ultracapacitor

Generator andcontroller

DC-DC controller

DCBUS

Drive motor 1

Drive motor 2

Drivemotor 1

controller

Drivemotor 2

controller

Track 1

Track 2

Mechanical connectionsElectrical connections

Figure 1 Configuration of hybrid electric tracked bulldozer

where 1198651is soil-cutting resistance (N) 119865

2is the pushing

resistance of the mound before the blade (N) 1198653is frictional

resistance between the ground and blade (N) 1198654is the

horizontal component of the frictional resistance when thesoil rises along the blade (N) 119896

119887is cutting resistance per unit

area (MPa) 1198611is blade width (m) ℎ

119901is average cutting depth

(m) 119866119905is the gravity of the mound in front of the bulldozing

plate 1205831is the friction coefficient between soil particles 120583

2is

the friction coefficient between the soil and blade 120579 is slope(∘) 119881 is the volume of the mound in front of the bulldozingplate 119896

119904is the loose degree coefficient of the soil 119896

119898is the

fullness degree coefficient of the soil119867 is blade height (m)1205720

is the natural slope angle of the soil (∘) 119896119910is cutting resistance

per unit area after the blade is pressed into the soil (MPa)119883 isthe length of the worn blade contacting the ground (m) and120575 is the cutting angle of the blade (∘) [1]

24 Driving Force 119865 The soil driving force is partly con-sumedby overcoming external travel resistance andbulldozeroperation acceleration climbing or load traction The rela-tionship between maximum driving force (adhesion force)119865max and slide ratio 119894 is given as the following [25]

119865max = 2119887119871119888 (1 +2ℎ

119887)

+ 119866 tan1205931 + 064 [ℎ119887arc cot(ℎ

119887)]

(4)

Thus driving force 119865 can be written as the following

119865 = 119865max [1 minus119870

119894119871(1 minus 119890

minus119894119871119870

)] (5)

where ℎ is the grouser height (m) and119870 is the soil horizontalshear deformation modulus (m)

119894 = 1 minusV

11990301199080

= 1 minusVV119879

=V119879minus VV119879

=

V119895

V119879

(6)

where V is the actual speed of vehicle (ms) 1199080is the angular

velocity of the sprocket wheel (rads) 1199030is the pitch radius of

the sprocket wheel (m) V119879is the theoretical speed of vehicle

V119895is the track slip velocity relative to the ground (rads)

25 Track Slide Curve Based on the parameters of thebulldozer and sandy loam shown in Table 1 the track slidecurve of this hybrid electric tracked bulldozer on sandy loamis shown in Figure 2

Table 1 Parameters of the bulldozer and soil

Name Value UnitVehicle weight (119866) 280 KNTrack width (119887) 061 mTrack length (119871) 305 mGrouser height (ℎ) 007 mSoil cohesion coefficient (119888) 1379 KPaSoil internal friction angle (120595) 28 DegreeSoil deformation index (119899) 03 NullSoil deformation modulus (119896) 146 KNm119899+2

Unit weight (120574) 17700 Nm3

Soil Terzaghi coefficients of bearing capacity(119873119888) 108 Null


Soil horizontal shear deformation modulus(119870) 002 m

From Figure 2 the driving force reaches a maximum of213 KN when the track slips completely (slide ratio 119894 = 1meaning that the track slip velocity relative to the ground isequal to the theoretical speed of vehicle) and the differencebetween the driving force and external travel resistance isused for the operation acceleration climbing and loadtraction of the bulldozer

3 Dynamic Modeling of the Hybrid ElectricTracked Bulldozer

The series hybrid power system is composed of a dieselengine permanent magnet generator motor drive systemand tracks as shown in Figure 1The hybrid electric bulldozeruses the integrated controller to control the motors on bothsides of the bulldozer independently and to transfer theelectric energy from the generator and auxiliary power supply(also from DC BUS) into mechanical energy to drive thebulldozer [26] Based on the working principle analysis andtest bench experiment of various parts of the power trainsystem a mathematical model of the hybrid power systemwas established

31 Engine-Generator Model To ensure the accuracy of themodeling test bench experimental data are used to establish


0 01 02 03 04 05 06 07 08 09 1

50

100

150

200

250

Slide ratio i

F (k

N)

Driving forceExternal travel resistance

Figure 2 Track slide curve of the tracked bulldozer on sandy loam

n (rmin)800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

25

50

75

100

125

150

Pe

(kW

)

Pe_max (kW)

201

201

201

204

204

204

204

207

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213

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216

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447

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450

450

Figure 3 Diesel engine universal characteristic curve

the diesel engine universal characteristic curve as shown inFigure 3

The engine fuel injection amount is determined bythrottle position and engine speed Engine output torque isdetermined by the following

119879119863

119890= 119879119890minus 119869119890

119889119908119890

119889119905

119879119890= 120572 lowast 119879

119890 max (119899119890)

(7)

where 119879119863119890

is dynamic engine output torque 119879119890is steady-

state engine flywheel output torque 120572 is throttle position119879119890 max(119899119890) is maximum torque at the engine speed 119899

119890 and 119869

119890

is the rotary inertia of the rotating parts in the engineThe engine fuel consumption 119887

119890(gkWh) is a function of

119879119890and 119899119890

119887119890= 119891 (119879

119890 119899119890) =

119904

sum

119895=0

119895

sum

119894=0

119860119896lowast 119879119894

119890lowast 119899119895minus1

119890

(119894 119895 = 0 1 2 119904)

(8)

085085

085

085

086086

086

087

087

087

088

088

088

089089

089

0909

09

091091

091

092092

092

093093

093

093094

094094

094095

085

085

086

086

086

087

087

087

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088

088

088

089

089

089

089

09

09

09

09091

091

091092

092

092

093

093

093

094

094

095 0950960

400

800

1200

1600

2000

2400

2800

3200

3600

4000

4400

4800

5200

5600

6000

minus800minus700minus600minus500minus400minus300minus200minus100

0100200300400500600700800

T(N

middotm)

n (rpm)

Figure 4 Motor drive system efficiency

where 119904 is model order number and 119860119896is the polynomial

coefficient 119896 = (1198952 + 119895 + 2 lowast 119894)2The generator provides current to DC BUS under gener-

ating mode the kinetic equation for the generator is given asthe following

119869119892

119889119899119892

119889119905= 119879119892minus 119879119863

119890 (9)

where 119879119892is generator shaft torque 119899

119892is generator speed and

119869119892is the rotary inertia of the generatorThe relationship between generator shaft torque speed

and output DC voltage and current of the controller side isgiven as the following

119880119892sdot 119868119892

1000 sdot 120578119892

=

119879119892sdot 119899119892

9549 (10)

where 119880119892is output DC voltage from the generator 119868

119892is

output DC current 120578119892is power generation efficiency

32 Motor Model A permanent magnet motor is adopted inthis hybrid bulldozer with a torque of 500800Nsdotm a powerof 75105 kW a rated speed of 1430 rpm and a maximumspeed of 6000 rpm In this power train system the twomotorsfollow the instructions of the control unit for torque outputThe focus of the motor model is to establish the relationshipbetween the output torque speed of the motor and the inputDC voltage and current of the motor controller Thereforethe motor model is obtained based on the test bench data ofthe motor drive system Figure 4 shows the efficiency map ofthe system

Considering the response time of themotor drive systema first-order link is added between the target torque and theactual output torque

119879119898=

119879ref120591119904 + 1

119879ref le 119879max (119899)

119879max (119899)

120591119904 + 1119879ref gt 119879max (119899)

(11)

where 119879ref is target torque 119879119898 is output torque 119899 is motorspeed 119879max(119899) is maximum torque at speed 119899 and 120591 isresponse time


w1

w2

motor 1 shaft

motor 2 shaftTo mec shaft

n1

n2power

lowastAuxiliary power

kWshaft

Auxiliary box

Acc_BraAcc

Bra

Acc bra

Velocity

Steer

Depth

Slope

Working condition

Ultracapacitor

v

Period

Motor drive 2

Motor drive 1

Power+

MeasureN

ICE speed controller

Velocity_req

Generator drive

Gain

P_Drive

P_au

G_T

E_n

Engine_Generator controller

T1

T2

Depth

Slope

n1_motor

n2_motor

u

w_axis

R

Dynamic

Diesel engine

Acc

Bra

Steer

n1

n2

Control strategy

-T-

-T-

-K--K-

-K-

InOut

Acc_Bra

Req steer

Req velocity

Req slope

Req depth

minusVdc

+VdcP_uclowast

Gspeed

au kWlowast

kWlowast

ThrolowastNlowast

Inlowast

T2lowast

T1lowast

T2lowastT1lowast

irefref

Udc

iout

d powerlowast

Drive powerlowast

Figure 5 The power train system model of the hybrid electric tracked bulldozer

The dynamic equation for the motor is as follows

119869119898

119889119899

119889119905

2120587

60= 119879119898minus 119879load (12)

where 119869119898is motor rotational inertia and 119879load is load torque

The relationship between the input DC voltage current ofthe motor controller and the shaft output torque and speedis as follows

119880 sdot 119868 sdot 120578119889

1000=119879119898sdot 119899

9549(119879119898gt 0)

119880 sdot 119868

1000 sdot 120578119887

=119879119898sdot 119899

9549(119879119898lt 0)

(13)

where119880 is the input DC voltage 119868 is the input DC current 120578119889

is motor efficiency when driving and 120578119887is motor efficiency

when braking

33 Driving Dynamic Model Based on the study of theterramechanics of this hybrid electric tracked bulldozer adriving dynamic model is established as follows

(1198791+ 1198792)1198940120578

119903minus 119877119871minus 119877119877= 119898V

(1198791minus 1198792)1198940120578

119903

119861

2+ (119877119871minus 119877119877)119861

2minus 119879119903= 119868

119879119903=

0 119908 = 0

120583119897119898119892

4[1 minus (

21205821

119897)

2

] 119908 = 0

(14)

where11987912

is motor output torque 1198940is the gear ratio from the

motor to the driving wheel 120578 is the efficiency from the motorshaft to the track 119903 is driving wheel radius 119877

119871and 119877

119877are left

and right side track resistance respectively119898 is vehiclemassV is the vehicle drive speed along the longitudinal direction119879

119903

is steering resistance torque 119868 is vehicle rotational inertia 119908is vehicle angular velocity 120583 is steering resistance coefficient119897 is vehicle length and 120582

1is the offset of the track contact with

the ground alone longitudinal directionThe power train system simulation model of the hybrid

electric tracked bulldozer including the driver model work-ing condition model engine-generator model motor drivesystem model vehicle dynamics model and control strategyin MATLABSimulink is shown in Figure 5 where (1)sim(3)and (14) are used in the module ldquodynamicrdquo (7)sim(8) areused in the module ldquodiesel enginerdquo (9)sim(10) are used in themodule ldquogenerator driverdquo (11)sim(13) are used in the moduleldquomotor drive 1rdquo and ldquomotor drive 2rdquo

34 Experiment Validity Analysis of the Dynamic Model of theHybrid Bulldozer To verify the accuracy of the simulationmodel of the hybrid electric tracked bulldozer the parametersand the real working conditions (as shown in Figure 6)were substituted into this simulation model to compare thesimulation results with the real vehicle experimental data

In Figure 6119881 (kmh) is the bulldozer velocity depth (m)is soil-cut depth and slope (∘) is bulldozer gradeability Theworking stages are described as follows 1sim4 s traveling stage4sim16 s soil-cutting stage 16sim31 s soil-transportation stage 31sim33 s unloading soil stage and 33sim50 s no-load stage

Figures 7 and 8 show the simulation result and realbulldozerrsquos working velocities and drive forces of single track


005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )

Figure 6 The real working condition of the bulldozer

0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)

SimulationExperiment

Figure 7 Bulldozer velocities in the simulation and experiment

under the working condition shown in Figure 6 Figure 9shows the engine output power in the simulation and exper-iment Figure 10 shows the generator and motor efficiencyunder the working condition

As we can see from Figures 7 to 8 bulldozer velocities andsingle track drive forces in the simulation and experimentaldata are identical well As can be seen fromdata the variancersquosrelative error of the single track drive forces in the simulationand experimental data is 145

In Figure 9 the engine output power in the simulationand experimental data are identical well-expected 4ndash16 s soil-cutting stage The engine output power in simulation ishigher about 15sim25 kW than that in experiment in 4ndash16 s soil-cutting stageThis is because the efficiency of the power trainsystem is different in simulation (hybrid) and experiment(traditional)The experiment transmission efficiency is setapproximately 09 which is higher than that of simulationtransmission Figure 10 shows that the simulation efficiencyis below 090 for motor in 4ndash16 s soil-cutting stage So theengine must provide higher power in simulation than that in

0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104

Figure 8 Single track drive forces in the simulation and experiment

0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)

Figure 9 Engine output power in the simulation and experiment

experiment in order to satisfy the same demand power of thebulldozer

Under the state above the simulation model (Figure 5) isvalid and can be used for the simulation research of controlstrategy for the hybrid electric tracked bulldozer

4 Control Strategy

41 Power Allocation Strategy One power follow controlstrategy is put forward to combine the working features ofthe proposed series hybrid electric tracked bulldozers whichshould be able to coordinate the power supply and needrelationship among the engine generator ultracapacitor andthe motors The engine output power should follow the loaddemand power of the bulldozer and the ultracapacitor shouldsupply the power shortage caused by the excessive loaddemand power as the auxiliary power sourceThe SOC of theultracapacitor and load power requirement determines theworking point of the engine generator The power allocationstrategy is shown in Table 2

In Table 2 119875lowast is the target demand mechanical power119875119890is engine output power 119875

119890 max is engine maximum outputpower 119875

119890 min is engine minimum output power 119875DC is DC


0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()

Motor efficiencyGenerator efficiency

Figure 10 Generator and motor efficiency

Table 2 Power allocation strategy

Judgment State of theultracapacitor Power supply

119875lowast

lt 119875119890 max

SOC lt SOCmaxCharging 119875

119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max

SOC ge SOCmaxNot working 119875

119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max

SOC gt SOCminDischarging 119875

119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max

SOC le SOCminNot working 119875

119892= 1205781lowast 119875119890 max

119875uc = 0

BUS demand electric power 119875119892is generator output power

119875uc is ultracapacitor power 1205781is power efficiency of the

generator SOCmax and SOCmin are ultracapacitor maximumand minimum state of charge respectively

119875lowast is target demand mechanical power which can be

given as

119875lowast

=119875lowast

Track120578119864-119879

=119865Track lowast 119903

120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)

where 119875lowastTrack is the demand power of the track 120578119879-119864 is the

transmission efficiency from engine to track 119865Track is theoff-road motion resistance 119865

119864is external travel resistance

calculated by (1)sim(2) 119865119879is operating resistance calculated by

(3)As can be seen from (15) and (1)sim(3) we can conclude

that the average cutting depth ℎ119901and the volume of the

mound in front of the bulldozing plate 119881 are linear to 119875lowast119875lowast is a quadratic function of the track amount of sinkage 119885

These primary parameters ℎ119901 119881 and 119885 impact the energy

management at the above levelThe flowchart for the power allocation strategy is shown

in Figure 11 The driverrsquos intention is taken as the targetrequired power 119875lowast and the vehicle management system(VMS) calculates the drive motor required power 119875lowast

119898accord-

ing to the working conditions of all components and thevehicle Simultaneously the VMS calculates the engine target

Engine-generator set

Driverrsquosintention

Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc

Figure 11 The flowchart for the power allocation strategy

Table 3 Parameters of the control strategy

Parameters InstructionsSOCmax Maximum SOCSOCmin Minimum SOC1198731

Engine working speed 11198732



speed 119899lowast and the ultracapacitor target current 119868lowastThe engine-generator set makes the output power 119875eg whereas theultracapacitormakes the output power119875uc according to a datatable lookup The output power of the engine-generator setand ultracapacitor is then sent to the drive motors throughDC BUS

In this control strategy the parameters must be properlyadjusted and optimized to reduce fuel consumption as muchas possible in order to satisfy the operational requirementsThe parameters of the control strategy are shown in Table 3

42 Engine Control Strategy An engine multipoint speedswitching control strategy is adopted here and engine work-ing speed is determined by the bulldozer load demand powerThe engine operates at low speeds when the load demandpower is low and operates at higher speeds when the loaddemand power increases Figure 12 shows the schematic ofthe engine multipoint speed switching control strategy

In Figure 12 119909-axis represents engine speed and 119910-axisrepresents load demand power Load demand power isdivided into three areas low medium and high The enginespeed in each area is fixed as 119873

1 1198732 and 119873

3 When the

load demand power is in low load area engine speed willbe fixed at 119873

1 as load demand power increases to medium

load area engine speed will be fixed at 1198732 as load demand

power increases to high load area engine speed will be fixedat1198733 Power hysteresis band is set between each adjacent load

power area to avoid the engine speed frequent switching

43 Real Experimental Testing of Control Strategy Test benchexperiment was performed to collect actual test benchdata to correlate and validate the proposed power followcontrol strategy for this hybrid electric tracked bulldozerThe experimental bench consists of engine generator drive


N-engine (rmin)

A

DEngine external characteristics

Generator external characteristics

CE

F

Power hysteresis bandB

Low load

High load

Medium loadP (k

W)

Figure 12 Schematic of the engine multipoint speed switchingcontrol strategy

Table 4 Basic parameters of the power train system

Name Value UnitMaximum power of the engine (119875

119890 max) 175 kWRated power of the motor (119875

119898 rated) 75 kWMaximum power of the motor (119875

119898 max) 105 kWRated power of the generator (119875

119892 rated) 175 kWMaximum power of the generator (119875

119892 max) 180 kW

motor system auxiliary power source dynamometer and thevehicle management system as shown in Figure 13(a)

This test bench adopts power follow control strategywhich was written in the vehicle management system tocoordinate the power supply among the engine generatorand the motors Dynamometer control interface shown inFigure 13(b) controls the working speed of the dynamometerand drive motor and the drive motor controller controls theload torque of the drive motor In the process of test theload torque of the drive motor was increased up from 30Nsdotmto 100Nsdotm suddenly and then down to 30Nsdotm suddenly tosimulate the load sudden changes process of the bulldozeras shown in Figure 14 Load torque is linear related to theaccelerator pedal opening degree

As we can see from the test bench result shown inFigure 15 the engine-generator output power follows the loaddemand power well under the working condition shownin Figure 14 Under the state above the proposed powerfollow control strategy is effective and can be used for thecontrol strategy optimization for the hybrid electric trackedbulldozer

5 Control Strategy Optimization

51 OptimizationModel To solve the problemof the parame-ter optimization of the power follow control strategy a math-ematical model of the entire power train system including thefuel consumption model is established based on the dynamicmodeling in Section 3 and the control strategy in Section 4

The important parameters of the power train system of thebulldozer are given in Table 4

The fuel consumption model is obtained through thefuel consumption MAP graph shown in Figure 16 where 119887

119890

(gKwh) is fuel consumption rate Minimizing fuel consump-tion is the optimization goal and the working condition hasno effect on the control strategy put forward here Thereforeone representative bulldozer working condition is adoptedhere as shown in Figure 17

In this optimization problem the object function isengine fuel consumption under the representative work-ing condition Engine minimum fuel consumption can beobtained by integration [27]

min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)

where 119861 is engine fuel consumption 119899 is engine speed attime 119905 119875

119890is engine output power at time 119905 and 119905

0and 1199051are

the start and end time of the bulldozer working conditionrespectively

In this problem the SOC of the ultracapacitor at the startand end times should remain identical Therefore the sum ofthe ultracapacitor output and input energies is zero

int

1199051

1199050

119875uc (119905) 119889119905 = 0

SOCmin le SOC le SOCmax

(17)

The other constraint conditions are the following

119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899

119890 min are the maximum and minimumspeeds of the engine respectively and 119868uc max is themaximumchargingdischarging current of the ultracapacitor

52 Control Strategy Optimization Based on the characteris-tics of the series hybrid tracked bulldozer a genetic algorithm(GA) is adopted to solve the parameter optimization problemin the control strategy The engine working speeds 119873

1 1198732

and 1198733at different power levels are set as the objective

optimized parameters The initial values of 1198731 1198732 and

1198733are determined by engineering experience Because GA

cannot address the parameters directly the parameters mustbe converted into a chromosome composed of genes witha certain structure Therefore the chromosome here is 119883

119894

(1198731 1198732 1198733) The GA operations are as follows selection

crossover and mutationA design of experiment (DOE) is used to simplify the

calculation As a design space exploration technique DOEis used for preliminary design space exploration to reflectthe relationship between the design variables and objectivefunction in fewer numbers of trials According to the givenoptimization variables 16 test sample points are constructed


DynamometerDrive motor

Generator Engine

Motor controller

(a) (b)

Figure 13 Hardware setup for experiments (a) Structure of the hybrid bulldozer test bench (b) dynamometer control interface

0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)

(a) Accelerator pedal opening degree

0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)

(b) Load torque of the drive motor

Figure 14 The test bench working condition

using an orthogonal design method The response surfaceis constructed on the basis of the DOE and can replace theoriginal model with certain accuracy On the basis of theDOE the GA is then applied to optimize the parameters inthe solution space to determine the optimal solution [28 29]The GA work flow is then established (Figure 18) by settingthe minimum fuel consumption as the target function undertypical working conditions

In this flowchart 119891(119909) and 119892119895(119909) are the objective func-

tion and constraint conditions given in (16)sim(18) The mainoptimization steps are as follows (1) initialize the first-generation chromosomes randomly 119883

119894 119894 = 1 (2) simulate

the control strategy parameters represented by each chromo-some using the vehicle simulation model for one completesimulation and determine the fitness of each individualaccording to the predetermined fitness function (3) select anew generation of chromosomes1198831015840

119894 according to the fitness

values (the selected probability is greater when the fitnessis larger) (4) crossover and mutate to generate the newchromosomes 119883

119894 119894 = 119894 + 1 (5) return to (2) and (6) halt

the process when satisfying the stopping condition

Table 5 Optimization results for the parameters

Parameters Before optimization After optimization1198731(rpm) 1000 1102

1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917

53 Optimization Results Figure 19 shows the convergenceprocess of the control strategy parameters and the objectivefunction under the combined simulation 119873

1 1198732 and 119873

3

are the engine working speeds at the engine power ranges of0ndash60 kW 60ndash120 kW and 120ndash175 kW respectively With theproceeding of the optimization process 119873

1 1198732 and 119873

3are

constantly adjusted in the engine working speed range andgradually converge to stable values

After 16 optimization calculations through the optimiza-tion in software environment of OPTIMUS one solution inthe solution space is finally found as the optimal (Table 5)


0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)

Load demand powerEngine-generator output power

Figure 15 Engine-generator output power and load demand power

n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700

Figure 16 Fuel consumption MAP graph

Figure 20 shows the right and left track velocity ofthe hybrid bulldozer under the typical working condition(Figure 17) As shown in Figure 21 the adjustment of theengine speed is great after optimization especially in lowload power and high load power areas Engine speed wasadjusted from low efficiency to high efficiency working pointto improve the fuel economy of the bulldozer as shown inFigure 22

The adjustment of the engine speed impacts the powerallocation in a certain degree As can be seen from Figure 21in the high load power area the engine maximum outputpower decreased due to the decreasing of the engine speedafter adjustment Under the same working condition theultracapacitor power supplement will be increased when thedemand power is very large Discharge current will increaseto reduce the life of the ultracapacitor to some extent

6 Conclusions

Based on the study of the terramechanics of the tracked bull-dozer and test bench experimental data a dynamic model ofthe hybrid electric tracked bulldozer power train system wasestablished combining the operation principle of each part of

minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )

Figure 17 Typical working conditions of the bulldozer

Start

No

First-generation andfitness function

Selection and generatenew chromosome Crossover

Mutation

Fitness function calculating

New generation selectionand fitness function

calculation

Meet the stop condition

Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1

gj(x) otherfitness(x) =

Figure 18 The GA flowchart of the control strategy optimization

the system To verify the accuracy of the dynamic simulationmodel the parameters and the real working conditions ofthe prototype traditional bulldozer were substituted into thesimulation model and the simulation results were comparedwith the experimental data to analyze the accuracy of the sim-ulation model A power follow strategy is proposed combin-ing the working features of the series hybrid electric trackedbulldozer Test bench experiment was performed to collectactual test bench data to correlate and validate the proposedpower follow control strategy for this hybrid electric trackedbulldozer Based on the dynamicmodel of this hybrid electrictracked bulldozer a genetic algorithm is proposed to solve thecontrol strategy parameter optimization problem Based onthe optimized control strategy parameters the simulation isperformed to compare engine fuel consumption before andafter control strategy optimization By analyzing the opti-mization results the fuel consumption of the bulldozer afteroptimization is reduced by approximately 674 compared


900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)

2 4 6 8 10 12 14 16Number of cycles




N1

(rpm

)N

3(r

pm)

N2

(rpm

)

Figure 19 The convergence process of the objective function

0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)

Right track velocityLeft track velocity

Figure 20 The right and left track velocities of the bulldozer

0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)

Before optimizationAfter optimization

Nen

gine

(rpm

)

Figure 21 Comparison of engine speed

0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)

After optimizationBefore optimization

b e(g

kW

h)

Figure 22 Comparison of engine fuel consumption

with the former condition This result verifies the validityof the method proposed in this paper which can reduce thedifficulty of the design and optimize the control strategy

Conflict of Interests

The authors declare no conflict of interests regarding thepublication of this paper

Acknowledgment

The authors gratefully acknowledge the support from theNational Key Technologies RampD Program of China (Grantno 2011BAG04B02)

References

[1] H Wang and F C Sun ldquoDynamic modeling and simulation ona hybrid power system for dualmotormdashdrive electric trackedbulldozerrdquo Applied Mechanics and Materials vol 494-495 pp229ndash233 2014

[2] Q Song and H Wang ldquoParameters matching for dual-motor-drive electric bulldozerrdquo Journal of Beijing Institute of Technol-ogy vol 20 pp 169ndash170 2011

[3] J Wang Q N Wang P Y Wang J N Wang and N W ZouldquoHybrid electric vehicle modeling accuracy verification andglobal optimal control algorithm researchrdquo International Jour-nal of Automotive Technology vol 16 no 3 pp 513ndash524 2015

[4] C Sun X Hu S J Moura and F Sun ldquoVelocity predictors forpredictive energymanagement in hybrid electric vehiclesrdquo IEEETransactions on Control Systems Technology vol 23 no 3 pp1197ndash1204 2015

[5] R Ghorbani E Bibeau P Zanetel and A Karlis ldquoModelingand simulation of a series parallel hybrid electric vehicle usingREVSrdquo in Proceedings of the American Control Conference (ACCrsquo07) pp 4413ndash4418 IEEE New York NY USA July 2007

[6] P Caratozzolo and M Canseco ldquoDesign and control of thepropulsion systemof a series hybrid electric vehiclerdquo inProceed-ings of the Electronics Robotics and Automotive Mechanics Con-ference (CERMA rsquo06) pp 270ndash273 Mexico Russia September2006

[7] Z Y Song H Hofmann J Q Li J Hou X B Han and MG Ouyang ldquoEnergy management strategies comparison for


electric vehicles with hybrid energy storage systemrdquo AppliedEnergy vol 134 pp 321ndash331 2014

[8] X Hu L Johannesson N Murgovski and B Egardt ldquoLonge-vity-conscious dimensioning and power management of thehybrid energy storage system in a fuel cell hybrid electric busrdquoApplied Energy vol 137 pp 913ndash924 2015

[9] X Y Li XM Yu J Li and Z XWu ldquoControl strategy for serieshybrid-power vehiclerdquo Journal of Jilin University (Engineeringand Technology Edition) vol 2 pp 122ndash126 2005

[10] E Mehrdad Y Gao and A Emadi Modem Electric HybridElectric and Fuel Cell Vehicles Fundamentals Theory andDesign CRC Press New York NY USA 2010

[11] X Hu N Murgovski L Johannesson and B Egardt ldquoEnergyefficiency analysis of a series plug-in hybrid electric bus withdifferent energy management strategies and battery sizesrdquoApplied Energy vol 111 pp 1001ndash1009 2013

[12] C Sun S J Moura X Hu J K Hedrick and F Sun ldquoDynamictraffic feedback data enabled energy management in plug-inhybrid electric vehiclesrdquo IEEE Transactions on Control SystemsTechnology vol 23 no 3 pp 1075ndash1086 2015

[13] R Xiong H He Y Wang and X Zhang ldquoStudy on ultra-capacitor-battery hybrid power system for PHEV applicationsrdquoHigh Technology Letters vol 16 no 1 pp 496ndash500 2010

[14] T-S Kwon S-W Lee S-K Sul et al ldquoPower control algorithmfor hybrid excavator with supercapacitorrdquo IEEE Transactions onIndustry Applications vol 46 no 4 pp 1447ndash1455 2010

[15] G GWang I Horowitz S HWang and CW Chen ldquoControldesign for a tracked vehicle with implicit nonlinearities usingquantitative feedback theoryrdquo in Proceedings of the 27th IEEEConference on Decision and Control pp 2416ndash2418 IEEEAustin Tex USA December 1988

[16] Y H Li X M Lu and N C Kar ldquoRule-based control strategywith novel parameters optimization using NSGA-II for power-split PHEV operation cost minimizationrdquo IEEE Transactions onVehicular Technology vol 63 no 7 pp 3051ndash3061 2014

[17] S Zhang C N Zhang R Xiong and W Zhou ldquoStudy onthe optimal charging strategy for lithium-ion batteries used inelectric vehiclesrdquo Energies vol 7 no 10 pp 6783ndash6797 2014

[18] J K Peng HW He andN L Feng ldquoSimulation research on anelectric vehicle chassis system based on a collaborative controlsystemrdquo Energies vol 6 no 1 pp 312ndash328 2014

[19] C M Qi and P Li ldquoAn exponential entropy-based hybridant colony algorithm for vehicle routing optimizationrdquo AppliedMathematics amp Information Sciences vol 8 no 6 pp 3167ndash31732014

[20] K B Wipke M R Cuddy and S D Burch ldquoADVISOR 21a user-friendly advanced powertrain simulation using a com-bined backwardforward approachrdquo IEEE Transactions on Vehi-cular Technology vol 48 no 6 pp 1751ndash1761 1999

[21] L Guzzella and A Amstutz ldquoCAE tools for quasi-static model-ing and optimization of hybrid powertrainsrdquo IEEE Transactionson Vehicular Technology vol 48 no 6 pp 1762ndash1769 1999

[22] J H Pu C L Yin and J W Zhang ldquoApplication of geneticalgorithm in optimization of control strategy for hybrid electricvehiclesrdquo China Mechanical Engineering vol 16 Article ID649650 2005

[23] MG BekkerOff-RoadLocomotionTheUniversity ofMichiganPress Ann Arbor Mich USA 1960

[24] C G Zhang K H Zeng and J H Zhao ldquoAnalytical solutions ofcritical load andTerzaghirsquos ultimate bearing capacity for unsatu-rated soilrdquo Journal of Tongji University (Natural Science) vol 38no 12 pp 1736ndash1739 2010

[25] G Bekker M Theory of Land Locomotion The University ofMichigan Press Ann Arbor Mich USA 1956

[26] Q Song P Zeng and H Wang ldquoStudy on the power flowingcontrol strategy of a series hybrid tracked bulldozer at thetypical working conditionrdquo Journal of Mechanical Engineeringvol 50 no 2014 pp 136ndash143 2014

[27] R C Wang R He J B Yu and C H Hu ldquoParameter optimi-zation of a PSHEV based on genetic algorithmrdquo ChinaMechan-ical Engineering vol 24 no 18 pp 2544ndash2549 2013

[28] A Piccolo L Ippolito V Zo Galdi and A Vaccaro ldquoOptimi-sation of energy flow management in hybrid electric vehiclesvia genetic algorithmsrdquo in Proceedings of the IEEEASMEInternational Conference on Advanced Intelligent Mechatronicspp 434ndash439 Como Italy July 2001

[29] B Wang Z P Yang F Lin and W Zhao ldquoAn improved geneticalgorithm for optimal stationary energy storage system locatingand sizingrdquo Energies vol 7 no 10 pp 6434ndash6458 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


efficiency and the lifetime of the battery Power follow controlstrategy requires the engine-generator sets output power toalways follow the load demand power of the vehicle causingengine speed frequently fluctuate and affecting the engineefficiency and emission properties Xiong et al [13] adoptedthe thermostat control strategy for PHEV taking battery andultracapacitor as the auxiliary power source This controlmethod improved the discharge efficiency and the lifetimeof the auxiliary power source However it is complex rarelyused in the construction machinery vehicles like bulldozerKwon et al [14] adopted power follow control strategy fora series hybrid wheel excavator taking ultracapacitor as theauxiliary power source which improved the fuel economy by24 However this control method limited the improvementof the fuel economy as engine was controlled to work at onesingle point

In this paper one power follow control strategy is putforward to combine the working features of the proposedseries hybrid electric tracked bulldozers [15 16] Bulldozersdo not require high speed and acceleration performance Butthey demand power when low-speed operation fluctuatesremarkably Considering working features of the bulldozerultracapacitor is taken as the auxiliary power source due toits high power density and short-term high power and cur-rent output capabilities By analyzing the engine-generatorworking point and the SOC state of the ultracapacitor areasonable power control strategy is proposed to improve thefuel economy of the hybrid electric tracked bulldozer Testbench experiment was performed to collect actual test benchdata to correlate and validate the proposed control strategyfor this hybrid electric tracked bulldozer

Parameter optimization for the power follow controlstrategy is also researched because of the importance of accu-rate match of control strategy parameters for fuel economyimproving [17 18] Commonly genetic algorithm is famousfor its global optimization and parallel computing capabilities[19ndash21] and has been widely used in multiple areas includingparameter estimation in system identification optimizationand neural network training [22] A genetic algorithm isestablished to solve the parameter optimization problem inthe control strategy in this study

The organization of this paper is as follows In Section 2the new configuration of the hybrid electric tracked bulldozeris described and the detailed terramechanics of the trackedbulldozer is researched to provide the theoretical basis forthemodeling of the dynamics in Section 3The power controlstrategy is described in Section 4The optimization problemprocedure and results of the control strategy are intro-duced in Section 5 Finally the conclusions are presented inSection 6

2 Terramechanics of the Tracked Bulldozer

21 Configuration of the Hybrid Electric Tracked BulldozerThe schematic of this hybrid electric tracked bulldozer(using one traditional bulldozer as the prototype) is givenin Figure 1 This hybrid electric tracked bulldozer maintainsthe vehicle body hydraulic and operation system of thetraditional bulldozer just changing the transmission form

The paths for the electric power and mechanical power aretandem in the series configurations This construction sim-plifies the propulsion and transmission system and providesgreater flexibility in the power train system

This hybrid electric tracked bulldozer uses an integratedcontroller to control two motors on both sides of the bull-dozer independently and to transfer electric energy from theDC BUS into mechanical energy to drive the bulldozer

The terramechanics of this hybrid electric tracked bull-dozer is the theoretical basis for further analysis of the drivingdynamics The working states of the tracked bulldozer canbe divided into the following six stages soil-cutting soil-transportation returning climbing turning and acceler-ating The external travel resistance operating resistancedriving force and track slide curve under the working statesare researched in the following context

22 External Travel Resistance 119865119864 The resistance caused

by the vertical deformation of the soil under the anteriortrack of the vehicle when driving is called external travelresistance It mainly results from the energy consumption ofsoil compaction and the effects of bulldozing resistance 119865

119864

can be written as the following [23]

119865119864= 119865119888+ 119865119887

119865119888=

2119887

(119899 + 1) 1198961119899

(119866

2119887119871)

(119899+1)119899

119865119887= 1205741198852

119887119896120574+ 2119887119885119888119896pc

(1)

where

119896120574= (

2119873120574

tan120595+ 1) cos2120595

119896pc = (119873119888 minus tan120595) cos2120595

(2)

where 119865119888is compaction resistance (N) 119865

119887is bulldozing

resistance (N) 119887 is track width (m) 119866 is vehicle weight (N)119871 is track length (m) 119888 is soil cohesion coefficient (KPa) 120595 issoil internal friction angle (∘) 119899 is soil deformation index 119896 issoil deformation modulus (KNm119899+2) 119885 is track amount ofsinkage (m) 120574 is unit weight (Nm3) and119873

120574and119873

119888are the

soil Terzaghi coefficients of bearing capacity [24]

23 Operating Resistance 119865119879 Consider

119865119879= 1198651+ 1198652+ 1198653+ 1198654

1198651= 106

1198611ℎ119901119896119887

1198652= 1198661199051205831cos120572 =

1198811205741205831cos 120579119896119904

1198653= 106

11986111198831205832119896119910

1198654= 1198661199051205832cos 1205752 cos 120579

119881 =

1198611(119867 minus ℎ

119901)2

119896119898

2 tan1205720

(3)


Engine

Ultracapacitor


DC-DC controller

DCBUS

Drive motor 1

Drive motor 2

Drivemotor 1

controller

Drivemotor 2

controller

Track 1

Track 2




2is the pushing









2is



119898is the





119865max = 2119887119871119888 (1 +2ℎ

119887)

+ 119866 tan1205931 + 064 [ℎ119887arc cot(ℎ

119887)]

(4)


119865 = 119865max [1 minus119870

119894119871(1 minus 119890

minus119894119871119870

)] (5)


119894 = 1 minusV

11990301199080

= 1 minusVV119879

=V119879minus VV119879

=

V119895

V119879

(6)

















0 01 02 03 04 05 06 07 08 09 1

50

100

150

200

250

Slide ratio i

F (k

N)



n (rmin)800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

25

50

75

100

125

150

Pe

(kW

)

Pe_max (kW)

201

201

201

204

204

204

204

207

207

207

207

210

210

210

210

213

213

213

213

216

216

216

216

219

219

219

219

222

222

222

222

225

225

225

225

228

228

228

228

231

231

231

231

234

234

234

237

237

237

240

240

240

243

243

243

246

246

246

249

249

249

252

252

252

255

255

255

258

258

258

261

261

261

264

264

264

267

267

267

270

270

270

273

273

273

276

276

276

279

279

279

282

282

282

285

285

285

288

288

288

291

291

291

294

294

294

297

297

297

300

300

300

303

303

303

306

306

306

309

309

309

312

312

312

315

315

315

318

318

318

321

321

321

324

324

324

327

327

327

330

330

330

333

333

333

336

336

336

339

339

339

342

342

342

345

345

345

348

348

348

351

351

351

354

354

354

357

357

357

360

360

360

363

363

363

366

366

366

369

369

369

372

372

372

375

375

375

378

378

378

381

381

381

384

384

384

387

387

387

390

390

390

393

393

393

396

396

396

399

399

399

402

402

402

405

405

405

408

408

408

411

411

411

414

414

414

417

417

417

420

420

420

423

423

423

426

426

426

429

429

429

432

432

432

435

435

435

438

438

438

441

441

441

444

444

444

447

447

447

450

450

450




119879119863

119890= 119879119890minus 119869119890

119889119908119890

119889119905

119879119890= 120572 lowast 119879

119890 max (119899119890)

(7)

where 119879119863119890



119890 and 119869

119890



119879119890and 119899119890

119887119890= 119891 (119879

119890 119899119890) =

119904

sum

119895=0

119895

sum

119894=0

119860119896lowast 119879119894

119890lowast 119899119895minus1

119890

(119894 119895 = 0 1 2 119904)

(8)

085085

085

085

086086

086

087

087

087

088

088

088

089089

089

0909

09

091091

091

092092

092

093093

093

093094

094094

094095

085

085

086

086

086

087

087

087

088

088

088

088

089

089

089

089

09

09

09

09091

091

091092

092

092

093

093

093

094

094

095 0950960

400

800

1200

1600

2000

2400

2800

3200

3600

4000

4400

4800

5200

5600

6000


0100200300400500600700800

T(N

middotm)

n (rpm)





119869119892

119889119899119892

119889119905= 119879119892minus 119879119863

119890 (9)





119880119892sdot 119868119892

1000 sdot 120578119892

=

119879119892sdot 119899119892

9549 (10)


119892is




119879119898=

119879ref120591119904 + 1

119879ref le 119879max (119899)

119879max (119899)

120591119904 + 1119879ref gt 119879max (119899)

(11)



w1

w2

motor 1 shaft


n1

n2power


kWshaft

Auxiliary box

Acc_BraAcc

Bra

Acc bra

Velocity

Steer

Depth

Slope

Working condition

Ultracapacitor

v

Period

Motor drive 2

Motor drive 1

Power+

MeasureN


Velocity_req

Generator drive

Gain

P_Drive

P_au

G_T

E_n


T1

T2

Depth

Slope

n1_motor

n2_motor

u

w_axis

R

Dynamic

Diesel engine

Acc

Bra

Steer

n1

n2

Control strategy

-T-

-T-

-K--K-

-K-

InOut

Acc_Bra

Req steer

Req velocity

Req slope

Req depth

minusVdc

+VdcP_uclowast

Gspeed

au kWlowast

kWlowast

ThrolowastNlowast

Inlowast

T2lowast

T1lowast

T2lowastT1lowast

irefref

Udc

iout

d powerlowast

Drive powerlowast



119869119898

119889119899

119889119905

2120587

60= 119879119898minus 119879load (12)



119880 sdot 119868 sdot 120578119889

1000=119879119898sdot 119899

9549(119879119898gt 0)

119880 sdot 119868

1000 sdot 120578119887

=119879119898sdot 119899

9549(119879119898lt 0)

(13)



when braking


(1198791+ 1198792)1198940120578

119903minus 119877119871minus 119877119877= 119898V

(1198791minus 1198792)1198940120578

119903

119861

2+ (119877119871minus 119877119877)119861

2minus 119879119903= 119868

119879119903=

0 119908 = 0

120583119897119898119892

4[1 minus (

21205821

119897)

2

] 119908 = 0

(14)

where11987912



119871and 119877

119877are left


119903









005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )


0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)






0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104


0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)




4 Control Strategy






0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Engine

Ultracapacitor


DC-DC controller

DCBUS

Drive motor 1

Drive motor 2

Drivemotor 1

controller

Drivemotor 2

controller

Track 1

Track 2




2is the pushing









2is



119898is the





119865max = 2119887119871119888 (1 +2ℎ

119887)

+ 119866 tan1205931 + 064 [ℎ119887arc cot(ℎ

119887)]

(4)


119865 = 119865max [1 minus119870

119894119871(1 minus 119890

minus119894119871119870

)] (5)


119894 = 1 minusV

11990301199080

= 1 minusVV119879

=V119879minus VV119879

=

V119895

V119879

(6)

















0 01 02 03 04 05 06 07 08 09 1

50

100

150

200

250

Slide ratio i

F (k

N)



n (rmin)800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

25

50

75

100

125

150

Pe

(kW

)

Pe_max (kW)

201

201

201

204

204

204

204

207

207

207

207

210

210

210

210

213

213

213

213

216

216

216

216

219

219

219

219

222

222

222

222

225

225

225

225

228

228

228

228

231

231

231

231

234

234

234

237

237

237

240

240

240

243

243

243

246

246

246

249

249

249

252

252

252

255

255

255

258

258

258

261

261

261

264

264

264

267

267

267

270

270

270

273

273

273

276

276

276

279

279

279

282

282

282

285

285

285

288

288

288

291

291

291

294

294

294

297

297

297

300

300

300

303

303

303

306

306

306

309

309

309

312

312

312

315

315

315

318

318

318

321

321

321

324

324

324

327

327

327

330

330

330

333

333

333

336

336

336

339

339

339

342

342

342

345

345

345

348

348

348

351

351

351

354

354

354

357

357

357

360

360

360

363

363

363

366

366

366

369

369

369

372

372

372

375

375

375

378

378

378

381

381

381

384

384

384

387

387

387

390

390

390

393

393

393

396

396

396

399

399

399

402

402

402

405

405

405

408

408

408

411

411

411

414

414

414

417

417

417

420

420

420

423

423

423

426

426

426

429

429

429

432

432

432

435

435

435

438

438

438

441

441

441

444

444

444

447

447

447

450

450

450




119879119863

119890= 119879119890minus 119869119890

119889119908119890

119889119905

119879119890= 120572 lowast 119879

119890 max (119899119890)

(7)

where 119879119863119890



119890 and 119869

119890



119879119890and 119899119890

119887119890= 119891 (119879

119890 119899119890) =

119904

sum

119895=0

119895

sum

119894=0

119860119896lowast 119879119894

119890lowast 119899119895minus1

119890

(119894 119895 = 0 1 2 119904)

(8)

085085

085

085

086086

086

087

087

087

088

088

088

089089

089

0909

09

091091

091

092092

092

093093

093

093094

094094

094095

085

085

086

086

086

087

087

087

088

088

088

088

089

089

089

089

09

09

09

09091

091

091092

092

092

093

093

093

094

094

095 0950960

400

800

1200

1600

2000

2400

2800

3200

3600

4000

4400

4800

5200

5600

6000


0100200300400500600700800

T(N

middotm)

n (rpm)





119869119892

119889119899119892

119889119905= 119879119892minus 119879119863

119890 (9)





119880119892sdot 119868119892

1000 sdot 120578119892

=

119879119892sdot 119899119892

9549 (10)


119892is




119879119898=

119879ref120591119904 + 1

119879ref le 119879max (119899)

119879max (119899)

120591119904 + 1119879ref gt 119879max (119899)

(11)



w1

w2

motor 1 shaft


n1

n2power


kWshaft

Auxiliary box

Acc_BraAcc

Bra

Acc bra

Velocity

Steer

Depth

Slope

Working condition

Ultracapacitor

v

Period

Motor drive 2

Motor drive 1

Power+

MeasureN


Velocity_req

Generator drive

Gain

P_Drive

P_au

G_T

E_n


T1

T2

Depth

Slope

n1_motor

n2_motor

u

w_axis

R

Dynamic

Diesel engine

Acc

Bra

Steer

n1

n2

Control strategy

-T-

-T-

-K--K-

-K-

InOut

Acc_Bra

Req steer

Req velocity

Req slope

Req depth

minusVdc

+VdcP_uclowast

Gspeed

au kWlowast

kWlowast

ThrolowastNlowast

Inlowast

T2lowast

T1lowast

T2lowastT1lowast

irefref

Udc

iout

d powerlowast

Drive powerlowast



119869119898

119889119899

119889119905

2120587

60= 119879119898minus 119879load (12)



119880 sdot 119868 sdot 120578119889

1000=119879119898sdot 119899

9549(119879119898gt 0)

119880 sdot 119868

1000 sdot 120578119887

=119879119898sdot 119899

9549(119879119898lt 0)

(13)



when braking


(1198791+ 1198792)1198940120578

119903minus 119877119871minus 119877119877= 119898V

(1198791minus 1198792)1198940120578

119903

119861

2+ (119877119871minus 119877119877)119861

2minus 119879119903= 119868

119879119903=

0 119908 = 0

120583119897119898119892

4[1 minus (

21205821

119897)

2

] 119908 = 0

(14)

where11987912



119871and 119877

119877are left


119903









005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )


0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)






0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104


0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)




4 Control Strategy






0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 01 02 03 04 05 06 07 08 09 1

50

100

150

200

250

Slide ratio i

F (k

N)



n (rmin)800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

25

50

75

100

125

150

Pe

(kW

)

Pe_max (kW)

201

201

201

204

204

204

204

207

207

207

207

210

210

210

210

213

213

213

213

216

216

216

216

219

219

219

219

222

222

222

222

225

225

225

225

228

228

228

228

231

231

231

231

234

234

234

237

237

237

240

240

240

243

243

243

246

246

246

249

249

249

252

252

252

255

255

255

258

258

258

261

261

261

264

264

264

267

267

267

270

270

270

273

273

273

276

276

276

279

279

279

282

282

282

285

285

285

288

288

288

291

291

291

294

294

294

297

297

297

300

300

300

303

303

303

306

306

306

309

309

309

312

312

312

315

315

315

318

318

318

321

321

321

324

324

324

327

327

327

330

330

330

333

333

333

336

336

336

339

339

339

342

342

342

345

345

345

348

348

348

351

351

351

354

354

354

357

357

357

360

360

360

363

363

363

366

366

366

369

369

369

372

372

372

375

375

375

378

378

378

381

381

381

384

384

384

387

387

387

390

390

390

393

393

393

396

396

396

399

399

399

402

402

402

405

405

405

408

408

408

411

411

411

414

414

414

417

417

417

420

420

420

423

423

423

426

426

426

429

429

429

432

432

432

435

435

435

438

438

438

441

441

441

444

444

444

447

447

447

450

450

450




119879119863

119890= 119879119890minus 119869119890

119889119908119890

119889119905

119879119890= 120572 lowast 119879

119890 max (119899119890)

(7)

where 119879119863119890



119890 and 119869

119890



119879119890and 119899119890

119887119890= 119891 (119879

119890 119899119890) =

119904

sum

119895=0

119895

sum

119894=0

119860119896lowast 119879119894

119890lowast 119899119895minus1

119890

(119894 119895 = 0 1 2 119904)

(8)

085085

085

085

086086

086

087

087

087

088

088

088

089089

089

0909

09

091091

091

092092

092

093093

093

093094

094094

094095

085

085

086

086

086

087

087

087

088

088

088

088

089

089

089

089

09

09

09

09091

091

091092

092

092

093

093

093

094

094

095 0950960

400

800

1200

1600

2000

2400

2800

3200

3600

4000

4400

4800

5200

5600

6000


0100200300400500600700800

T(N

middotm)

n (rpm)





119869119892

119889119899119892

119889119905= 119879119892minus 119879119863

119890 (9)





119880119892sdot 119868119892

1000 sdot 120578119892

=

119879119892sdot 119899119892

9549 (10)


119892is




119879119898=

119879ref120591119904 + 1

119879ref le 119879max (119899)

119879max (119899)

120591119904 + 1119879ref gt 119879max (119899)

(11)



w1

w2

motor 1 shaft


n1

n2power


kWshaft

Auxiliary box

Acc_BraAcc

Bra

Acc bra

Velocity

Steer

Depth

Slope

Working condition

Ultracapacitor

v

Period

Motor drive 2

Motor drive 1

Power+

MeasureN


Velocity_req

Generator drive

Gain

P_Drive

P_au

G_T

E_n


T1

T2

Depth

Slope

n1_motor

n2_motor

u

w_axis

R

Dynamic

Diesel engine

Acc

Bra

Steer

n1

n2

Control strategy

-T-

-T-

-K--K-

-K-

InOut

Acc_Bra

Req steer

Req velocity

Req slope

Req depth

minusVdc

+VdcP_uclowast

Gspeed

au kWlowast

kWlowast

ThrolowastNlowast

Inlowast

T2lowast

T1lowast

T2lowastT1lowast

irefref

Udc

iout

d powerlowast

Drive powerlowast



119869119898

119889119899

119889119905

2120587

60= 119879119898minus 119879load (12)



119880 sdot 119868 sdot 120578119889

1000=119879119898sdot 119899

9549(119879119898gt 0)

119880 sdot 119868

1000 sdot 120578119887

=119879119898sdot 119899

9549(119879119898lt 0)

(13)



when braking


(1198791+ 1198792)1198940120578

119903minus 119877119871minus 119877119877= 119898V

(1198791minus 1198792)1198940120578

119903

119861

2+ (119877119871minus 119877119877)119861

2minus 119879119903= 119868

119879119903=

0 119908 = 0

120583119897119898119892

4[1 minus (

21205821

119897)

2

] 119908 = 0

(14)

where11987912



119871and 119877

119877are left


119903









005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )


0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)






0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104


0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)




4 Control Strategy






0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










w1

w2

motor 1 shaft


n1

n2power


kWshaft

Auxiliary box

Acc_BraAcc

Bra

Acc bra

Velocity

Steer

Depth

Slope

Working condition

Ultracapacitor

v

Period

Motor drive 2

Motor drive 1

Power+

MeasureN


Velocity_req

Generator drive

Gain

P_Drive

P_au

G_T

E_n


T1

T2

Depth

Slope

n1_motor

n2_motor

u

w_axis

R

Dynamic

Diesel engine

Acc

Bra

Steer

n1

n2

Control strategy

-T-

-T-

-K--K-

-K-

InOut

Acc_Bra

Req steer

Req velocity

Req slope

Req depth

minusVdc

+VdcP_uclowast

Gspeed

au kWlowast

kWlowast

ThrolowastNlowast

Inlowast

T2lowast

T1lowast

T2lowastT1lowast

irefref

Udc

iout

d powerlowast

Drive powerlowast



119869119898

119889119899

119889119905

2120587

60= 119879119898minus 119879load (12)



119880 sdot 119868 sdot 120578119889

1000=119879119898sdot 119899

9549(119879119898gt 0)

119880 sdot 119868

1000 sdot 120578119887

=119879119898sdot 119899

9549(119879119898lt 0)

(13)



when braking


(1198791+ 1198792)1198940120578

119903minus 119877119871minus 119877119877= 119898V

(1198791minus 1198792)1198940120578

119903

119861

2+ (119877119871minus 119877119877)119861

2minus 119879119903= 119868

119879119903=

0 119908 = 0

120583119897119898119892

4[1 minus (

21205821

119897)

2

] 119908 = 0

(14)

where11987912



119871and 119877

119877are left


119903









005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )


0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)






0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104


0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)




4 Control Strategy






0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










005

115

225

335

V (k

mh

)

minus0050

00501

01502

Dep

th (m

)

5 10 15 20 25 30 35 40 45 50minus1

01

t (s)

5 10 15 20 25 30 35 40 45 50t (s)

5 10 15 20 25 30 35 40 45 50t (s)

Slop

e (∘ )


0 5 10 15 20 25 30 35 40 45 500

051

152

253

354

t (s)

V (k

mh

)






0 5 10 15 20 25 30 35 40 45 50minus5

0

5

10

15

t (s)

Sing

le tr

ack

driv

e for

ce (N

)


times104


0 5 10 15 20 25 30 35 40 45 500

153045607590

105120135150

t (s)


Pen

gine

(kW

)




4 Control Strategy






0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 5 10 15 20 25 30 35 40 45 50075

08

085

09

095

1

t (s)

Effici

ency

()





119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 119875DC minus 119875119892

119875lowast

lt 119875119890 max


119892= 1205781lowast 119875119890

119875uc = 0

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 119875DC minus 119875119892

119875lowast

gt 119875119890 max


119892= 1205781lowast 119875119890 max

119875uc = 0





given as

119875lowast

=119875lowast

Track120578119864-119879


120578119864-119879

=(119865119864+ 119865119879) lowast 119903

120578119864-119879

(15)











119898accord-




Drive motor system

VMS Vehicle

Ultracapacitor

nlowast

Plowast

Ilowast

Pmlowast

Peg

Pm

Puc











1 1198732 and 119873

3 When the








N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










N-engine (rmin)

A



CE

F


Low load

High load

Medium loadP (k

W)








119892 max) 180 kW








119890



min119861 = int1199051

1199050

119861 (119899 119875119890 119905) 119889119905 (16)



0and 1199051are



int

1199051

1199050

119875uc (119905) 119889119905 = 0


(17)


119875119890 min le 119875119890 le 119875119890 max

119899119890 min le 119899119890 le 119899119890 max

119868uc le 119868uc max

(18)

where 119899119890 max and 119899



1 1198732





119894






Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Generator Engine

Motor controller

(a) (b)


0 2 4 6 8 10 12 144

6

8

10

12

14

Acc (

)

t (s)


0 2 4 6 8 10 12 14

20

40

60

80

100

120

t (s)

M_m

otor

(Nmiddotm

)






119894 119894 = 1 (2) simulate








1198732(rpm) 1400 1395

1198733(rpm) 1650 1621

119861 (g) 4200 3917


1 1198732 and 119873

3


1 1198732 and 119873

3are




0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40P

(kW

)

t (s)



n-P-be

b e(g

(kW

h))

P (kW) n (rmin)800 10001200

1400 16001800

050

100150

200100200300400500600700




6 Conclusions


minus100

10

Velo

city

(km

h)

02040

Stee

r (

00102

Dep

th(m

)

0 50 100 150 200 250 300 350 4000

20

Slop

e (

t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

0 50 100 150 200 250 300 350 400t (s)

∘ )∘ )


Start

No



Mutation



calculation


Over

Yesf(x)gj(x) ge 0

Δ

j = 1 2 m

fworst +m

sumj=1





900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










900100011001200

135014001450

160016501700

350040004500

Fuel

cons

umpt

ion

(g)





N1

(rpm

)N

3(r

pm)

N2

(rpm

)


0 50 100 150 200 250 300 350 400minus15

minus10

minus5

0

5

10

15

t (s)

V (k

mh

)



0 50 100 150 200 250 300 350 400800

1000

1200

1400

1600

1800

t (s)


Nen

gine

(rpm

)


0 50 100 150 200 250 300 350 400200

250

300

350

400

450

500

550

t (s)


b e(g

kW

h)





Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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