observer-based feedback control during torque phase of clutch-to-clutch shift process

Int. J. Vehicle Design, Vol. 58, No. 1, 2012 93

Observer-based feedback control during torque

phase of clutch-to-clutch shift process

Bingzhao Gao

State Key Laboratory of Automotive Simulation and Control,Jilin University (Campus NanLing),Renmin Str. 5988, Changchun 130025, China

and

Department of Mechanical Engineering,Yokohama National University,79-5, Tokiwadai, Hodogaya-Ku,Yokohama 240-8501, JapanE-mail: [email protected]

Hong Chen*

State Key Laboratory of Automotive Simulation and Control,Jilin University (Campus NanLing),Renmin Str. 5988, Changchun 130025, China

and

Department of Control Science and Engineering,Jilin University (Campus NanLing),Renmin Str. 5988, Changchun 130025, ChinaFax: 86-431-85758650E-mail: [email protected]*Corresponding author

Jun Li

R&D Center,China FAW Group Corporation,No. 1063 Chuangye Street,Changchun 130011, ChinaE-mail: [email protected]

Lu Tian

Department of Control Science and Engineering, Jilin University(Campus NanLing),Renmin Str. 5988, Changchun 130025, ChinaE-mail: [email protected]

Copyright © 2012 Inderscience Enterprises Ltd.

94 B-Z. Gao et al.

Kazushi Sanada

Department of Mechanical Engineering,Yokohama National University,79-5, Tokiwadai, Hodogaya-Ku,Yokohama 240-8501, JapanE-mail: [email protected]

Abstract: In order to improve the shift quality of AutomaticTransmissions (ATs) adopting clutch-to-clutch shift technology, afeedback control strategy is proposed for the torque phase of shiftprocess. With the estimated clutch torque, the off-going clutch isdisengaged at the moment when transmitted torque is approaching zero,which contributes to the reduction of shift shock and prevention of clutchtie-up. The proposed control strategy is tested on a complete powertrainsimulation model. It is verified that the system is robust to the variationsof driving conditions, such as vehicle mass and road grade, etc.

Keywords: AT; automatic transmission; clutch-to-clutch shift; torqueobserver; feedback shift control.

Reference to this paper should be made as follows: Gao, B-Z., Chen, H.,Li, J., Tian, L. and Sanada, K. (2012) ‘Observer-based feedback controlduring torque phase of clutch-to-clutch shift process’, Int. J. VehicleDesign, Vol. 58, No. 1, pp.93–108.

Biographical notes: Bingzhao Gao received the BS and MS degrees fromJilin University of Technology, China, in 1998 and Jilin University,China, in 2002 respectively, and the PhD degrees in MechanicalEngineering from Yokohama National University, Japan, and ControlEngineering from Jilin University, China, in 2009. He is currently anAssociate Professor in Jilin University. His research interests includevehicle powertrain control and vehicle stability control.

Hong Chen received the BS and MS degrees in Process Control fromthe Zhejiang University, China, in 1983 and 1986, respectively, and thePhD degree from the University of Stuttgart, Germany, in 1997. In spring2001, she was a Visiting Professor (DFG Scholarship) at the Institute forSystems Theory in Engineering, University of Stuttgart. Since 1999, shehas been a Professor at the Jilin University. Her current research interestsinclude model predictive control, optimal and robust control, applicationsin process engineering and mechatronic systems.

Jun Li received the BS, MS and PhD degrees in Mechanical Engineering(Department of Internal Combustion Engine) from Jilin University ofTechnology, China in 1982, 1985 and 1989, respectively. He jointedChangchun Automotive Research Institute (CARI), FAW since 1989.He is currently the Deputy Chief Engineer of FAW Group, Directorof FAW Technical Center and President of FISITA (2012–2014). Hisresearch interest includes engine and powertrain systems and controls.

Lu Tian received the BS degree in Automation from Jilin University,China, in 2009. She is currently a Master degree candidate in the

Observer-based feedback control during torque phase 95

Department of Control Science and Engineering, Jilin University, China.Her research interest is automatic transmission control.

Kazushi Sanada received the BS degree and MS degree from TokyoInstitute of Technology, Tokyo, Japan, in 1981 and 1986, respectively,and the Doctoral degree in Engineering from Tokyo Institute ofTechnology in 1996. He was appointed Professor of Yokohama NationalUniversity in 2004. He is the Vice Dean of School of EngineeringScience and the councilor of Yokohama National University from 2011.His research interests include modelling and control of mechanicalsystems, robust control and fluid power systems.

1 Introduction

Automotive calls for increased ride comfort and fuel efficiency in recent years.Because of its high efficiency and control flexibility, the clutch-to-clutch shifttechnique (Cho, 1987) is used in more and more production vehicles, such as DualClutch Transmissions (DCTs) (Matthes and Guenter, 2005; Kulkarni et al., 2007)and new ATs controlling the clutches independently (Minowa et al., 1999). It iswell known that the dynamic behaviour of engine and clutch greatly effect thetorque oscillation of the driveline, and even the steering system (Yao et al., 2008;Hohn et al., 2010). Hence a smooth and fast clutch-to-clutch shift is necessary.In production transmissions, however, some one-way clutches and accumulatorsare always eliminated in order to simplify the transmission mechanical content andimprove the system flexibility, which makes the robust control of clutch-to-clutchshifts a challenge.

Clutch-to-clutch shift can be regarded as a process of one clutch to be engagedwhile another is being disengaged, which is usually divided into two phases: thetorque phase and the inertia phase (Ishihara, 1980; Haj-Fraj and Pfeiffer, 2002).During the torque phase, the engine torque is transferred from the off-going clutchto the on-coming clutch. The precise timing of releasing and applying of clutchesis crucial for the preventions of clutch tie-up and traction interruption. During theinertia phase, the on-coming clutch slips until it is synchronised. The clutch slipcontrol during the inertia phase influences shift shock and shift time greatly.

In the inertia phase, the rotational speeds of the transmission change intensively,and clutch speed control (Dolcini et al., 2008) or engine speed control (Goetz et al.,2005) can be adopted to guarantee good shift quality. In the torque phase, however,the rotational speeds of clutch shafts do not change greatly. In order to achievesmooth torque transfer between the two clutches, the off-going clutch is required tomimic the operation of one-way clutch so that it can be disengaged at the momentwhen the direction of transmitted torque switches over. In Goetz et al. (2005),a clutch slip control scheme is suggested to accomplish the function of one-wayclutch, i.e., the off-going clutch is controlled to track a small reference speed(such as 5 rad/s). This control objective can prevent clutch tie-up effectively. If the

96 B-Z. Gao et al.

pressure of the off-going clutch is not manipulated well, however, the stick-slipphenomenon (Crowther et al., 2004) is apt to be caused and results in somepowertrain vibration. Moreover, the sampling period of production transmissionsis about 10 ms, the relative long sampling time will bring difficulty to the controltask as well.

As mentioned above, a smooth torque transfer can be assured if the off-goingclutch is disengaged when the transmitted torque is reduced to zero. If theknowledge of the transmitted torque of the clutch is available, the pressure of theoff-going clutch can be controlled using the torque information. Therefore, thispaper proposes another control scheme which is based on a clutch pressure/torqueobserver. Although the information of clutch torque can help to reduce the shiftshock or traction interruption, the torque sensors are seldom used in productionvehicles because of the cost and durability. Hence, it is required to estimate theclutch torque.

There have been some studies for the estimation of transmission shaft torqueand clutch pressure, mostly using sliding mode observer design techniques (Misawaand Hedrick, 1989; Yi et al., 2000; Watechagit and Srinivasan, 2005). In Gao et al.(2010), a reduced-order clutch pressure observer is proposed in the concept ofInput-to-State Stability (ISS) (Sontag, 2005). Model uncertainties are consideredas additive disturbance inputs and an observer is designed such that the errordynamics is input-to-state stable, where the input represents modelling errors.The implementation of the designed observer benefits from its reduced order andalso from that the observer gains can be chosen to be time-invariant.

In this paper, therefore, the observer of Gao et al. (2010) is extended to estimatethe transmitted torque of the off-going clutch, and a closed loop control schemeis proposed for the shift torque phase. The vehicle of interest is a medium-sizepassenger car, and the rest of the paper is organised as follows. In Section 2,the motivation of the work is demonstrated through a typical up-shift process.Then the clutch torque observer and the feedback control strategy are describedrespectively in Sections 3 and 4. In Section 5, a complete powertrain simulationmodel is constructed, as well as the discrete speed sensor model, and based onthe complete simulation model, the proposed control strategy of torque phase isevaluated. Concluding remarks are given in Section 6.

2 Motivation of clutch timing control

As mentioned above, during a clutch-to-clutch shift process, if the torque transferbetween the two clutches is not well controlled, clutch tie-up or torque interruptionmay be caused.

Figure 1 gives the simulation results of a typical power-on up shift processof a 2-speed transmission (refer to Section 3.1 for detailed description). Duringthe torque phase, the pressure of the on-coming clutch is ramped up, and theoff-going clutch is controlled by three patterns in order to show the effects ofthe disengagement timing of the off-going clutch. Pattern (b) gives the best resultbecause the off-going clutch is disengaged just when its transmitted torque is


reduced to zero at 7.93 s. Pattern (a) releases the off-going clutch at a moment0.1 s earlier than the optimal release time, and pattern (c) gives a postponeddisengagement timing. It is shown that an earlier releasing will cause tractioninterruption, and the engine speed and the turbine speed will flare up. On the otherhand, a postponed timing will lead to clutch tie-up, and consequently, shift shockis enlarged and the friction loss is increased.

Figure 1 Comparison of different release timing of off-going clutch: (a) 0.1 s ahead ofoptimal timing; (b) optimal timing and (c) 0.1 s after optimal timing.(θth: throttle angle; ia: current of off-going clutch; ib: current of on-comingclutch; Ta: torque of off-going clutch; Tb: torque of on-coming clutch; ωt:turbine speed; ωa: speed difference of off-going clutch; Ts: drive shaft torque)(see online version for colours)

From the results of Figure 1, it is shown that precise timing of releasing clutchis crucial for the shift quality during the shift torque phase. Therefore, a strategyof clutch timing control is proposed in this paper, and the block diagram of theproposed system is described in Figure 2. The valve current of the on-coming clutchis controlled feed-forwardly to ramp up it is pressure, while the off-going clutch iscontrolled according to the estimated torque.

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Figure 2 Block diagram of clutch disengagement system (Ta: estimated torque of clutchA; ia: valve current of clutch A; ib: valve current of clutch B; ωe: engine speed,ωt: turbine speed, ωw: driven wheel speed)

3 Clutch torque observer

3.1 Drivetrain modelling

To investigate clutch-to-clutch shift process, without loss of generality, a front-wheel-driven passenger vehicle with a two-speed AT is considered, which isschematically shown in Figure 3.

A planetary gear set is adopted as the shift gear, two clutches are used as theactuators, and two proportional pressure valves are used to control the two clutchesrespectively. When clutch A is engaged and clutch B disengaged, the powertrainoperates in 1st gear and the speed ratio is given by

R1 = 1 +1γ

, (1)

where γ is the ratio of the sun gear’s teeth number Zs to that of the ring gear Zr,i.e., γ = Zs

Zr.

While clutch A is disengaged and clutch B engaged, the vehicle is driven in 2ndgear with the speed ratio

R2 = 1. (2)

During the shift process of this kind of ATs, the oncoming and offgoing clutchesare controlled by the proportional pressure control valves independently, thus theshift timing and cooperation of the clutches are guaranteed.

The power-on 1st to 2nd up shift is considered as an example, and the gear shiftprocess can be divided into the torque phase where the turbine torque is transferredfrom clutch A to clutch B and the inertia phase where clutch B is synchronised.In consideration of the drive-shaft compliance, and assuming that there is little slip


Figure 3 Schematic graph of Automatic Transmission

in clutch A, the motion of the drive line during the torque phase is represented bythe following equations.

ωt = c11Tt + c13µ(∆ω)RN(A pcb − Fs) + c14Ts

Rdf(3a)

ωw = c34Ts + c35Tl (3b)

Ts =Ks

RdfR1ωt − Ksωw (3c)

pcb = − 1τcv

pcb +Kcv

τcvib, (3d)

where ωt is the turbine speed, ωs is the speed of the driving wheel (front wheel),Ts is the drive-shaft torque, pcb is pressure of clutch B, Tt is the turbine torque,Tl is the resistant torque delivered from the tyres, Fs denotes the return spring forceof clutch B and µ is the friction coefficient of clutch B depending on the speeddifference ∆ω, ib is the current of valve B.

We denote the variables to be estimated as z, and rewrite the dynamics systemfor estimating the clutch pressure as follows

y = F (y, u) + G(y, u)z + Hw(y, u, z), (4a)

z = A21y + A22z + B2(u), (4b)

where y is the measured outputs, w(y, u, z) summarises model uncertainties whichis normalised by H as ‖w‖∞ ≈ 1, and in particular

y = [ωt, ωw]T , z = [Ts, pcb]T , u = ib, (5a)

100 B-Z. Gao et al.

F (y, u) =( 1

ωtft1(ωe, y1)1

ωwft2(y2)

), (5b)

G(y, u) =

(c14Ts

ωtRdf

c13µ (x2)RNApcb

ωt

c34Ts

ωw

0

), (5c)

A21 =

(Ksωt

Rdf R1Ts

−Ksωw

Ts

0 0

),A22 =

(0 00 − 1

τcv

), (5d)

B2(u) =(

0Kcv

τcv pcb

)u. (5e)

Functions ft1 and ft2 are nonlinear functions

ft1(ωe, ωt) = c11Tt − c13µ(∆ω)RNFs, (6a)

ft2(ωw) = c35Tl, (6b)

with Tt being the turbine torque, and Tl being the driving resistance

Tt = t(λ) C(λ)ω2e (7a)

Tl = Tw + CAR3wω2

w, (7b)

where C(λ) denotes the capacity factor of the torque converter, t(λ) is the torqueratio, ωe is the engine speed and λ is the speed ratio defined as λ = ωt

ωe, Tw denotes

the rolling resistant moment of tyres, Rw is the tyre radius, and CA is a constantcoefficient depending on air density, aerodynamic drag coefficient and the frontarea of the vehicle. The definition of other parameters are shown in Table 1.

Table 1 Parameters for observer design

c13 Coefficient of clutch torque in equation (5c) −11.90 1kg·m2

c14 Coefficient of clutch torque in equation (5c) −4.76 1kg·m2

c34 Coefficient of clutch torque in equation (5c) 0.0074 1kg·m2

γ Gear ratio of sun gear to ring gear 0.667R Effective radius of plates of clutch B 0.13 mN Plate number of clutch B 3A Piston area of clutch B 0.01 m2

τcv Time constant of valve B 0.04 sKcv Gain of valve B 1.0 MPa/Aµmin Minimum friction coefficient 0.10µmax Maximum friction coefficient 0.16Rdf Gear ratio of the differential box 3Ks Stiffness of drive shaft 13000 Nm/radωt Normalisation of ωt 100 rad/sωw Normalisation of ωw 10 rad/s∆ω Normalisation of ∆ω 100 rad/sTs Normalisation of Ts 1000 Nmpcb Normalisation of pcb 105 Pa


3.2 Clutch torque observer design

From Gao et al. (2010), a reduced-order observer can be designed to estimate thepressure of clutch B and the torque of drive shaft simultaneously, which is given asthe following form.

η = (A22 − LG(y, u)) (η + Ly) + A21y + B2(u) − LF (y, u), (8a)

z = η + Ly, (8b)

where L is the time-invariant observer gain.By such a design, the dynamics of the estimation error

e = z − z, (9)

satisfies

e = (A22 − LG(y, u)) e − LHw, (10)

which shows that the error system is ISS (input-to-state stable) ifA22 − LG(y, u) ≤ −κ, where κ > 0 (Gao et al., 2010).

Given the estimation results of the above observer pcb and Ts, the transmittedtorque of clutch A can be calculated according to the following relationship of theplanetary gear set.

Tt − Tb =γ

1 + γT0 = γ(Ta + Tb), (11)

where Ta and Tb are transmitted torque of clutch A and clutch B respectively, T0is transmission output torque. The transformation of the above equation yields

Ta = T0 − Tt, (12)

or

Ta =1γ

Tt − γ + 1γ

Tb. (13)

Then the estimated torque of clutch A can be given as

Ta =1

RdfTs − Tt, (14)

or

Ta =1γ

Tt − γ + 1γ

µR N (A pcb − Fs), (15)

where Ts and pcb are the results of observer equation (8), and Tt is the estimatedturbine torque

Tt = t(λ) C(λ)ω2e . (16)

In the results of this papers, equation (14) is used to estimate the torque of clutchA because of its simpler form compared to equation (15).

102 B-Z. Gao et al.

4 Clutch control strategy

During the torque phase, the valve current of on-coming clutch (clutch B) iscontrolled feed-forwardly to ramp up its pressure, while the off-going clutch (clutchA) is controlled according to the estimated torque Ta. With the increase of pressureof clutch B, the transmitted torque in clutch A decreases. It is desired that theengagement force of clutch A is controlled to zero when the transmitted torque ofit decreases to zero.

When the clutch is sticking (locked up), the maximally transmittable torque islimited by pca, i.e.,

Tamax = (Aa pca − Fsa) µsRa Na, (17)

where pca is pressure of clutch A, Fsa is return spring force, µs is the staticfriction coefficient, Aa, Ra, Na are friction area, effective radius and plate numberrespectively.

Together with the dynamics of valve A

pca = − 1τcva

pca +Kcva

τcvaia, (18)

and using the static relationship of the current ia and the pressure pca, we candetermine the desired current ia as

ia = κca1

Kcva

1Aa

(Ta

µsRa Na+ Fsa

), (19)

where κca is a coefficient larger than 1. If the value is small, clutch slip may becaused before the transmitted torque reaches zero. On the other hand, if κc is toolarge, the disengagement timing may be delayed. In this paper, the tuned value isκc = 1.3. It is clear that by such a clutch disengagement strategy, the off-goingclutch will be disengaged when the transmitted torque Ta approaches zero, andbefore that, the clutch is locked up.

5 Simulation results

5.1 Powertrain simulation model

In this section, the proposed clutch control strategy (8), (14) and (19) is evaluatedon a powertrain simulation model. The model is established by commercialsimulation software AMESim, which supports the Simulink environment byS-Function. The constructed model can capture the important transient dynamicsduring vehicle shift process, such as the drive shaft oscillation and tyreslip. Moreover, time-delay and time-varying parameters of the proportionalvalves (Sanada and Kitagawa, 1998) are also considered in the simulation model,which are neglected in the controller design. The detailed description can be foundin Gao et al. (2010).


Because the precision of speed measurement greatly influences the observeraccuracy (Masmoudi and Hedrick, 1992; Yi et al., 1999; Moskwa and Pan,1995), the discrete characteristic of the speed sensors is also considered in thispaper. In production vehicles, magnetic pickup sensors are available for themeasurement of transmission speeds and wheel speeds. It is necessary to investigatethe measurement noise brought about by this kind of sensor. With measuring thetime interval corresponding to a certain number of teeth, the shaft speed can becalculated from

ω =2π nin

∆t n, (20)

where n is the total tooth number, nin is the tooth number corresponding for timemeasuring, ∆t is the counted time interval.

Measurement delay results from the time required for the new tooth to passthe pickup. Moreover, the irregularities of the teeth position and the randomnessof the trigger, which convert the analogue signal into the square-wave signal, mayintroduce random sensor noise. The speed sensors of this work are assumed to have48 teeth, and the time interval corresponding to three teeth is recorded to calculatethe rotational speed. A relative tolerance of teeth location of 0.169% (Masmoudiand Hedrick, 1992) and a trigger randomness of 1.5% are considered.

5.2 Simulation results

In order to get an in-vehicle assessment of the proposed clutch control system, thedesigned observer is discretised by a sampling rate of 100 Hz (Hahn and Lee, 2002)with zero-order holder discretisation.

Figure 4 shows the simulation results of a power-on 1st to 2nd up shift. Duringthe torque phase, the pressure of clutch B is ramped up, and clutch A is controlledby the proposed feedback control strategy. The driving condition is the same withthe nominal driving condition of Table 1, i.e., the condition for the controllerdesign. The observer gain used in Figure 4 are

L =(

−2.0 15.0−6.0 −20.0

), (21)

which are kept constant in all the simulations of this paper.Because there are inevitably errors associated with the estimated clutch torque,

in order to avoid clutch tie-up, after Ta reaches a small value (such as 50 Nm),clutch A is controlled by the following on-off logic

if ωa ≤ −5 rad/s, ia = 0.3A (22a)

if ωa > −5 rad/s, ia = 0, (22b)

where ωa is the speed difference of clutch A, i.e., the speed of the ring gear. ωa

becomes minus when clutch A is released earlier than it should be (see Figure 1(a)for reference). Note that because the transmitted torque is already reduced to a lowlevel, the switching control of pressure valve will not bring about large drive-lineoscillation. However, if the switching logic is triggered from the first beginning of

104 B-Z. Gao et al.

Figure 4 Simulation results: nominal driving condition (torque characteristics of engineand torque converter: standard; m: 1500 kg; θg: 0 deg; It=0.06 kg m2)(see online version for colours)

the torque phase, it is demonstrated through simulations that the torque oscillationwill become unacceptable.

It is shown that clutch A is fully disengaged at 7.90 s when the estimated torqueof clutch A Ta approaches zero. We can see that the turbine speed does not flareup, and there is no clutch tie-up and torque interruption shown in the result of thedrive shaft torque.

In order to examine the robustness of the proposed control strategy, the drivingconditions and parameters are changed, and the results are shown in Figures 5and 6. The following items are changed:

• torque characteristics of the engine and the torque converter

• vehicle mass

• road slope angle

• inertia moment of the torque converter turbine,


Figure 5 Simulation results: different driving condition (torque characteristics of engineand torque converter: standard × 115%; m: 2000 kg; θg: 5 deg; It=0.1 kg m2)(see online version for colours)

because they are highly correlative with the performance of the torque observer, butdifficult to obtain the true values. We can see that although the enlarged modellingerrors bring about larger estimation error of Ta, the timing of release of clutch A isnot affected seriously (it is 7.95 s in Figure 5 and 7.92 s in Figure 6) and there is nointensive fluctuation of the drive shaft torque, which shows that the shift quality isstill good enough.

6 Conclusions

A new observer-based clutch control strategy is proposed for the torque phaseof clutch-to-clutch shift process. Along with the increase of the pressure ofoncoming clutch, the off-going clutch is fully disengaged when its transmittedtorque approaches zero.

106 B-Z. Gao et al.

Figure 6 Simulation results: different driving condition (torque characteristics of engineand torque converter: standard × 85%; m: 1275 kg; θg: 5 deg; It=0.04 kg m2)(see online version for colours)

An AMESim powertrain simulation model, together with a discrete speed sensormodel, is constructed to test the proposed clutch control strategy. Simulation resultsshow that by using the estimated clutch torque, the strategy can provide smoothtorque transfer in the torque phase without clutch tie-up or traction interruption.

It is also demonstrated that the control strategy is robust to the variations ofdriving conditions and parameters, such as the change of engine characteristics,vehicle mass, and the road grade, etc.

Acknowledgements

This work is supported by the National Science Fund of China for DistinguishedYoung Scholars (60725311) and the National Nature Science Foundation of China(61034001, 51005093).


References

Cho, D. (1987) Nonlinear Control Methods for Automotive Powertrain Systems, PhD Thesis,MIT.

Crowther, A., Zhang, N., Liu, D.K. and Jeyakumaran, J.K. (2004) ‘Analysis andsimulation of clutch engagement judder and stick-slip in automotive powertrainsystems’, Proceedings of the Institution of Mechanical Engineers, Part D: Journal ofAutomobile Engineering, Vol. 218, No. 12, pp.1427–1446.

Dolcini, P., Wit, C.C. and Béchart, H. (2008) ‘Lurch avoidance strategy and itsimplementation in amt vehicles’, Mechatronics, Vol. 18, Nos. 5–6, pp.289–300.

Gao, B-Z., Chen, H., Zhao, H-Y. and Sanada, K. (2010) ‘A reduced-order nonlinear clutchpressure observer for automatic transmission’, IEEE Transactions on Control SystemsTechnology, Vol. 18, No. 2, pp.446–453.

Goetz, M., Levesley, M.C. and Crolla, D.A. (2005) ‘Dynamics and control of gearshiftson twin-clutch transmissions’, Proceedings of the Institution of Mechanical Engineers,Part D: Journal of Automobile Engineering, Vol. 219, No. 8, pp.951–963.

Hahn, J.O. and Lee, K.I. (2002) ‘Nonlinear robust control of torque converter clutch slipsystem for passenger vehicles using advanced torque estimation algorithms’, VehicleSystem Dynamics, Vol. 37, No. 3, pp.175–192.

Haj-Fraj, A. and Pfeiffer, F. (2002) ‘A model based approach for the optimisation ofgearshifting in automatic transmissions’, International Journal of Vehicle Design,Vol. 28, Nos. 1–3, pp.171–188.

Hohn, B.R., Pflaum, H., Lechner, C. and Draxl, T. (2010) ‘Efficient CVT hybrid drivelinewith improved drivability’, International Journal of Vehicle Design, Vol. 53, Nos. 1–2,pp.70–88.

Ishihara, T. (1980) Automotive Engineering Handbook 9, Drivetrain, Sankaido Publishing,Tokyo, in Japanese.

Kulkarni, M., Shim, T. and Zhang, Y. (2007) ‘Shift dynamics and control of dual-clutchtransmissions’, Mechanism and Machine Theory, Vol. 42, No. 2, pp.168–182.

Masmoudi, R.A. and Hedrick, K. (1992) ‘Estimation of vehicle shaft torque usingnonlinear observers’, ASME J. Dynamic Systems, Measurement, and Control, Vol. 114,pp.394–400.

Matthes, B. and Guenter, F. (2005) Dual Clutch Transmissions – Lessons Learned andFuture Potential, SAE Technical Paper 2005-01-1021.

Minowa, T., Ochi, T., Kuroiwa, H. and Liu, K. (1999) Smooth Gear Shift ControlTechnology for Clutch-to-Clutch Shifting, SAE Technical Paper 1999-01-1054.

Misawa, E. and Hedrick, J. (1989) ‘Nonlinear observers – a state-of-the-art survey’,ASME J. Dynamic Systems, Measurement, and Control, Vol. 111, pp.344–352.

Moskwa, J.J. and Pan, C. (1995) ‘Engine load torque estimation using nonlinear observers’,Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, LA,pp.3397–3402.

Sanada, K. and Kitagawa, A. (1998) ‘A study of two-degree-of-freedom control of rotatingspeed in an automatic transmission, considering modeling errors of a hydraulic system’,Control Engineering Practice, Vol. 6, pp.1125–1132.

Sontag, E.D. (2005) Input to State Stability: Basic Concepts and Results, Lecture Notes inMathematics, Springer-Verlag, Berlin.

Watechagit, S. and Srinivasan, K. (2005) ‘Implementation of on-line clutch pressureestimation for stepped automatic transmissions’, Proc. American Control Conference,Portland, OR, USA, Vol. 3, pp.1607–1612.

108 B-Z. Gao et al.

Yao, Z., Mousseau, C., Kao, B.G. and Nikolaidis, E. (2008) ‘An efficient powertrainsimulation model for vehicle performance’, International Journal of Vehicle Designs,Vol. 47, Nos. 1–4, pp.189–214.

Yi, K., Hedrick, K. and Lee, S.C. (1999) ‘Estimation of tire-road friction using observerbased identifiers’, Vehicle System Dynamics, Vol. 31, No. 4, pp.233–261.

Yi, K., Shin, B.K. and Lee, K.L. (2000) ‘Estimation of turbine torque of automatictransmissions using nonlinear observers’, ASME J. Dynamic Systems, Measurement,and Control, Vol. 122, pp.276–283.

observer-based feedback control during torque phase of clutch-to-clutch shift process

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