study of control for the automated clutch

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2010 224: 475Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile EngineeringY-S Zhao, Z-F Liu, L-G Cai, W-T Yang, J Yang and Z Luo

control prototypingStudy of control for the automated clutch of an automated manual transmission vehicle based on rapid

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Study of control for the automated clutch ofan automated manual transmission vehiclebased on rapid control prototypingY-S Zhao1*, Z-F Liu1, L-G Cai1, W-T Yang1, J Yang2, and Z Luo3

1School of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing,

People’s Republic of China2Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas, USA3School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, New South Wales,

Australia

The manuscript was received on 20 April 2009 and was accepted after revision for publication on 10 November 2009.

DOI: 10.1243/09544070JAUTO1245

Abstract: Owing to external disturbances, parameter uncertainty, and measurement noise, ithas been a challenging task to develop an appropriate controller for the automated clutchsystem. This paper proposes a new method for electromechanical clutch position controlsystems. First, a non-linear dynamic model for the screw-nut actuator associated with a clutchis derived, and then a dynamic sliding-mode controller with fuzzy adaptive tuning is developed.The fuzzy adaptive tuning arithmetic is used to improve the robustness and stability of thecontroller. At the same time, the chattering phenomenon is alleviated by adopting theproposed controller. Based on dSPACE and MATLAB–Simulink, the rapid control prototypingof the automated clutch is used as a method to demonstrate the efficiency and robustness ofthe proposed algorithm.

Keywords: automated clutch, dynamic sliding-mode control, fuzzy adaptive control, rapidcontrol prototyping

1 INTRODUCTION

Servo actuation in conventional manual transmis-

sions has increasingly gained much attention re-

cently [1–3]. An automated manual transmission

(AMT) can be constructed on the basis of a con-

ventional manual transmission by adding a servo

actuator and control system. An AMT is actually a

manual transmission with an added-on control unit

which automates the clutch and shifts the operation

according to the vehicle’s driving condition and the

driver’s intention. The automated clutch, an im-

portant subsystem of the AMT, can be declutched

and engaged automatically. The engagement and

declutch must be controlled to satisfy different and

conflicting objectives, such as small friction losses,

minimum time needed for the engagement, and

preservation of driver comfort during the engaging

and declutching process [4]. A proper normal force

to the clutch-driven disc is the key to satisfying all

these goals.

In the literature, several control strategies have

been developed for controlling the position of the

automated clutch of an AMT vehicle. For instance,

Slicker and Loh [5] presented a scheme to design a

vehicle launch control system for an AMT. Zanasi

and Visconti [6] discussed dynamic modelling and

engagement control for an automotive dry clutch.

Sanada and Kitagawa [7] applied a proportional

reducing valve to an automotive automatic trans-

mission system to control shift operation, and a

feedback controller was designed on the basis of m

synthesis, which is also a controller design method

using conventional control theory. David and Na-

trajan [8] described a procedure to determine the

*Corresponding author: School of Mechanical Engineering and

Applied Electronics Technology, Beijing University of Technology,

Beijing 100124, People’s Republic of China.

email: [email protected]

475

JAUTO1245 Proc. IMechE Vol. 224 Part D: J. Automobile Engineering



parameters of well-established driveline modes

using signals that are readily available on a vehicle

data bus. Two control strategies based on the linear

quadratic Gaussian technique were discussed. Hahn

and Lee [9] presented a torque-estimation-based

robust controller for a passenger car torque con-

verter clutch slip system, which only used the

measurements available from inexpensive sensors

for torque estimation and feedback control. Cheng et

al. [10] proposed a sliding-mode control approach

based on the feedback linearization of an electrically

controllable clutch of AMT vehicles. Zhang et al. [11]

developed a non-linear multi-rigid-body system dyn-

amic model for an automated clutch system, and an

adaptive optimal controller was introduced for posi-

tion control of the automated clutch. The afore-

mentioned control algorithms are characterized by

high computational efficiency and easy implementa-

tion. However, these algorithms still have difficulty

in meeting the requirement of robustness for an

automated clutch system.

Some sophisticated development environments

have recently been developed to support the speci-

fication of embedded systems and to validate them

on different abstraction levels, so as to shorten the

development time for the electrical controlling sys-

tem and to verify easily the control system and its

related algorithms for new vehicles. Lee et al. [12] pro-

posed an organized development environment by

matching hardware-in-the-loop simulation (HILS)

equipment with the rapid control prototyping (RCP)

system for an automotive engine control system.

A model-based air-to-fuel ratio controller based on

a sliding-mode control scheme was implemented to

examine the feasibilities of the proposed develop-

ment environment. Noomwongs et al. [13] combined

simulation (vehicle model) and experiment (tyres) to

develop a tyre HILS for evaluating vehicle dyna-

mics. In comparison with the simulation by an off-

line linear tyre model, the results of a vehicle simu-

lated on the tyre HILS were significantly closer to

real data. Thomas and Ferit [14] developed a virtual

real-time environment for automatic transmission

control units. Test and development options offered

by HILS are illustrated in the form of examples.

Liu and Daley [15] introduced an environment com-

posed of dSPACE, MATLAB, Simulink, and Real-Time

Workshop (RTW) to implement the proposed opti-

mal-tuning non-linear proportional–integral–deriva-

tive (PID) controller for demonstrating the perfor-

mance of the controller in hydraulic position control.

Er et al. [16] presented the design, development,

and implementation of a dynamic fuzzy neural

networks (DFNNs) controller for real-time industrial

applications, and the DFNNs controller was imple-

mented via the RTW which can generate C-codes

from the Simulink block diagrams. The results of

experiment show that RCP is a valid manner to

verify the validity of the proposed controller. Thus,

it can be seen that the methods combining RCP and

HILS are becoming a standard option for speeding

up the development of complex control systems, in

particular in automotive designs.

This paper mainly discusses trajectory tracking of

the clutch position using a screw-nut actuator driven

by a permanent-magnet d.c. motor in the context

of RCP systems. In comparison with conventional

hydraulic servo systems [17], the screw-nut actuator

has a higher efficiency and saves space. However,

owing to external disturbances, it is necessary to

develop an appropriate control scheme to meet the

conflicting requirements of an automated clutch

system. In this work, to obtain optimal operating

control for the automated clutch of AMT vehicles,

the clutch system and the screw-nut actuator are

considered as a uniform unit to design a robust

controller. A dynamic sliding-mode controller with

fuzzy adaptive tuning is constructed for improving

the robustness and control precision of the auto-

mated clutch. The chattering phenomenon is alle-

viated by adopting the proposed controller. RCP of

the automated clutch is designed for the automated

clutch system based on dSPACE and MATLAB–

Simulink. The proposed control algorithms can be

easily implemented in the RCP platform via the RTW

and the customized target package.

2 THE AUTOMATED CLUTCH SYSTEM MODEL

A simplified diagram of the automated clutch system

is shown in Fig. 1. The clutch is composed of two

discs connected to the engine shaft and gearbox

shaft in the driveline. A screw-nut actuator driven by

a permanent-magnet d.c. motor is used to control

the clutch position. The torque transmitted from the

engine to the wheels is modulated and the gear

change is available during the declutching phase.

In this work, a J4001050917016 transmission used

in a JNJ7080A vehicle is adopted and a reduced

model is therefore derived for the design of the

position controller of the automated clutch. The

load–deflection curve for the membrane spring of

the clutch is plotted in Fig. 2, which can be obtained

from the experimental data. During numerical

applications, this non-linear function can be ap-

proximated by a fourth-order polynomial in terms of

476 Y-S Zhao, Z-F Liu, L-G Cai, W-T Yang, J Yang, and Z Luo

Proc. IMechE Vol. 224 Part D: J. Automobile Engineering JAUTO1245



x displacement as

Fm xð Þ~{2:69x4z60:5x3{454:9x2z1318:4xz90:5

ð1Þ

The relation between the motor angle displace-

ment hm and the membrane spring end deflection x

can be derived as

x~1

2p

ltsltl

kschm ð2Þ

where lts and ltl are the arm lengths of the lever and

ksc represents the pitch of the screw-nut actuator.

According to Kirchhoff’s laws [18], the dynamic

function of a permanent-magnet d.c. motor can be

described as

LdI

dtzIRzkdv~u ð3Þ

where I, L, and R are the current, inductance, and

resistance respectively of the permanent-magnet d.c.

motor, u represents the voltage of the d.c. supply

source, kd is the back electromotive force coefficient

of the permanent-magnet d.c. motor, and v repre-

sents the angular velocity of the permanent-magnet

d.c. motor.

The dynamic equation of the motor rotor can be

described as

Jrdv

dt~TM{TML

ð4Þ

where Jr is the equivalent moment of inertia of rotor,

TMLis the resistant torque of the rotor, TM5 kmI

represents the electromagnetic torque of the perma-

nent-magnet d.c. motor, and km is the torque con-

stant of the permanent-magnet d.c. motor.

Substituting equation (4) into equation (3), the

dynamic function of the permanent-magnet d.c.

motor can be obtained as

Fig. 1 The simplified diagram of an automated clutch

Fig. 2 Load–deflection curve for the membrane springclutch

Control for the automated clutch of an AMT vehicle 477




LJrkdkm

d2v

dt2z

RJrkdkm

dv

dtzv

~1

kdu{

L

kdkm

dTML

dt{

R

kdkmTML ð5Þ

For the automated clutch system, the equivalent

moment Jr of rotor inertia can be described as

Jr~JzJgzJtk2sczmbk

2scl

2ts ð6Þ

where J is the moment of inertia of the rotor, Jg is themoment of inertia of the screw rod, Jt is the momentof inertia of the lever, which is computed accordingto its supporting point, and mb represents the massof the clutch release bearing.

The load torque of the rotor TMLcan be described as

TML~kL Fm(x){cm _xx½ � ð7Þ

where kL is the coefficient of the torque of resistance,

Fm is the force of the membrane spring, and cm is the

damping coefficient of the membrane spring.

Substituting equations (2), (6), and (7) into equa-

tion (5), the dynamic function of the automated clutch

can be obtained as

LJrkdkmkh

d3x

dt3z

RJrkdkmkh

d2x

dt2z

1

kh

dx

dt

~1

kdu{

L

kdkm

dTML

dt{

R

kdkmTML

ð8Þ

where kh~ksclts=(2pltl).

The state variable vector X, control input vector U,

and external disturbance vector W can be defined

respectively as

X~½x, _xx, €xx�T~½x1, x2, x3�T

U~½u�

W~dTML

dt,TML

� �Tð9Þ

Then, the mathematical model of the automated

clutch system can be written as

_XX~AXzBUzDW ð10Þ

where

A~

0 1 0

0 0 1

0 {kdkmLJr

{R

L

2664

3775

B~

0

0kmkhLJr

2664

3775

D~

0 0

0 0

{khJr

khR

LJr

2664

3775

3 DESIGN OF THE DYNAMIC SLIDING-MODECONTROLLER WITH FUZZY ADAPTIVETUNING

For the worst working condition of the automated

clutch, many uncertain factors can occur during

vehicle running periods. For example, the clutch has

been detached and the deduction of the electronic

control unit (ECU) is obtained by judging the input

signals; this requires the clutch to engage immedi-

ately, or the initial position of the clutch is changed

owing to installation error and the longer-time wear

and tear during the running period. To achieve the

purpose of improving the automated clutch system

performance, this section presents a dynamic slid-

ing-mode controller with fuzzy adaptive tuning that

is robust to the external disturbance and measure-

ment noise. In comparison with the conventional

sliding-mode controller (CSMC), the new sliding-

mode controller can alleviate the chattering phen-

omenon of control inputs. Furthermore, fuzzy adap-

tive tuning arithmetic is adopted to improve the

robustness and stability of the automated clutch

system.

3.1 Design of the dynamic sliding-modecontroller

This study is mainly concerned with the dynamic

sliding-mode controller for an automated clutch

driven by a permanent-magnet d.c. motor. Consid-

eration of the non-linear single-input single-output

motor–mechanism coupled system gives





x1...

(t)~f (X , t)zg(X , t)u(t)zfL(X , t) ð11Þ

where u(t) is the control input. f(X, t), g(X, t), and

fL(X, t) are approximated by using the estimated

functions

ff (X , t)~{kdkmLJr

x2{R

Lx3 ð12aÞ

gg(X , t)~kmkhLJr

ð12bÞ

and

ffL X , tð Þ~{khJr

dTML

dtz

khR

LJrTML

ð12cÞ

respectively. They are bounded in terms of the

unknown functions f(X, t), g(X, t), and fL(X, t) ob-

tained by experiment. The control problem is to find

a control law so that the state X can track the desired

trajectories Xd in the presence of uncertainties. It is

required to drive the tracking error asymptotically to

zero for any arbitrary initial conditions and uncer-

tainties. Suppose that the tracking error vector has

the form

E~X{X d

~ e, _ee, €ee½ �T

~ e1, e2, e3½ �T ð13Þ

where Xd5 [xd, xd, xd]T. Then, the conventional slid-

ing surface S(t) [20] is defined as

S(t)~C1e1zC2e2ze3 ð14Þ

where C1 and C2 are constants. The sufficient

condition for the existence and reachability of S(t)

in the automated clutch system state space is to

choose a control law so that the Lyapunov function

(d/dt)[S2(t)/2]5 SS, 0 can be satisfied [21].

The control law u(t) of the CSMC consists of the

equivalent sliding component ueq(t), which forces

the system state to slide on the sliding surface, and

the hitting control uN(t) that drives the states

towards the sliding surface. The equivalent control

law is obtained by the equation

_SS��u~ueq

~0 ð15Þ

Assuming that all uncertainty factors are zero, then

C1e2zC2e3zffzggueqzffL{ xd...

~0 ð16Þ

Solving equation (16) yields

ueq~{gg{1(C1e2zC2e3zffzffL{ xd...) ð17Þ

A Lyapunov function candidate is chosen as

V~1

2S2(X , t) ð18Þ

It is shown that, if there exists a positive constant g

such that

_VV~1

2

d

dtS2(X , t)� �

¡{g Sj j ð19Þ

then the state trajectories hit the sliding surface s. In

order to satisfy the hitting condition of equation (19)

in the presence of uncertainties, the hitting control

law is chosen as

uN~{gg{1(K sgn(S)), Kw0 ð20Þ

Equation (19) will be

_VV~S _SS~S(C1e2zC2e3zfzgUzfL{ xd...)¡{g Sj j

ð21Þ

Equation (21) can be represented as

(C1e2zC2e3zfzfL{ xd...)sgn(S)zgu sgn(S)¡{g

ð22Þ

Substituting equations (17) and (18) into equation

(22) yields

(C1e2zC2e3zfzfL{ xd...)sgn(s)

{g

gg(C1e2zC2e3zffzffL)sgn(S){

g

ggK¡{g ð23Þ

The optimal value of K will be

K¢ 1

ggg(~ffz~ff Lzg){~gg(C1e2zC2e3zffzff L)z xd

...h i

|sgn(S) ð24Þ

To improve the automated clutch performance, a

dynamic sliding-mode controller is constructed on

the basis of the conventional sliding surface S and

its derivation S, which can alleviate the chattering

phenomenon of control inputs effectively [22], and





is given by

s~ _SS tð ÞzldS tð Þ ð25Þ

where ld is a positive value. Here, the control

problem of the dynamic sliding mode is to find a

control law us so that the state X remains on the

dynamic sliding surface s5 0. A bounded stability

dynamic system can be obtained and a conventional

sliding surface S5 0 can also be satisfied during the

design of the controller. Hence, the Lyapunov sta-

bility condition

_VV s~s _ssv0 ð26Þ

must be satisfied. The equivalent control usE of the

dynamic sliding-mode controller can be derived

from s5 0 when the external disturbance is zero,

which can be described as

_ss~€SS(t)zld _SS(t)~0 ð27Þ

where

€SS(t)~C1e3zC2 ffzgguszff L{ xd...

� �

zdff

dX_XXz

dgg

dX_XXzgg _uusz

dff LdX

_XX{x(4)d

_SS(t)~C1e2zC2e3zffzgguszff L{ xd...

ð28Þ

Then, the equivalent control law usE is obtained as

_uusE~{1

ggC2z&ldð Þggz dgg

dX_XX

� �us

�

{ C2z&ldð Þ xd...

{ff{ff L

� �{x(4)d

{1

ggC1z&ldC2ð Þe3z dff

dX_XXz

dff LdX

_XXz&ldC1e2

" #

ð29Þ

Note that this control signal usE is sufficient to drive

the system once the sliding surface is reached.

Furthermore, the reachability and existence of this

dynamic sliding surface are satisfied if equation (25)

is satisfied. Therefore, the hitting control law usN is

chosen as

_uusN~{1

gge sat

s

w

ð30Þ

where e is the switching gain, w. 0 is the width of the

boundary, and the saturation function sat(s/w) is

defined as

sats

w

~

{1 if sv{ws

wif {w¡s¡w

1 if sww

8>><>>: ð31Þ

The dynamic sliding-mode control output us is given

as

_uus~ _uusEz _uusN ð32Þ

In order to ensure that the Lyapunov stability

condition Vs, 0 can be satisfied, substituting equa-

tions (32), (30), and (29) into equation (26) yields

e¢ gg

g

1

sat s=fð Þ C2{ldð Þ ~ffz~ggusz~ff L

� �

zd~ff

dXz

d~gg

dXz

d~ff LdX

!_XX

#

{~gg

g

1

sat s=wð Þ C2zldð Þggz dgg

dX_XX

� �us

{ C2zldð Þ x...

d{ff{ff L

� �{x

(4)d

z C1zldC2ð Þe3z dff

dX_XXz

dff LdX

_XXzldC1e2

)ð33Þ

The control input us is easy to obtain as

us kð Þ~us k{1ð Þz _uus ð34Þ

where k is the number of iterations.

3.2 Fuzzy adaptive tuning controller

In general sliding-mode control, the switching feed-

back gain e is a constant, which can influence the

performance of the dynamic sliding-mode controller

[23]. In this section, a proportional–derivative type of

fuzzy inference mechanism [24] is used to tune the

switching gain e in equation (30) according to the

external disturbances shown in Fig. 3. The chatter-

ing phenomenon can be alleviated for the dynamic

sliding-mode controller, and the robustness and

stability are also improved. Here, the absolute value

|s| of the dynamic sliding surface and the absolute

value |s| of its derivation are used as the inputs of the

fuzzy logic adaptive controller. Replacing e with eF,

the hitting control law can be obtained as

�

#

)





_uusN~{1

ggeF sat

s

w

ð35Þ

where eF is adjusted by the fuzzy logic adaptive

tuning controller.

It is well known that the fuzzy logic controller

consists of three modules: fuzzification, inference

engine, and defuzzification. Since the input and

output have their own universe of discourse, the

scaling factors k|s|, k|s|, and keF are used to map the

fuzzy logic control inputs |s| and | s| and output eF to

the normalized universe of discourses.

The inputs |s| and |s| and output eF membership

functions for the fuzzy logic adaptive controller

block are defined in Fig. 4. The discourses are all

assigned to be [0, 1]. Table 1 presents the fuzzy logic

rule base, which is based on the experiment of the

system and extensive simulations performed in this

study.

The linguistic control rules are defined as follows:

PB, positive big; PM, positive medium; PS, positive

small; ZE, zero. An example of the fuzzy linguistic

rules is shown in Table 1. If |s| is PS and |s| is PB,

then eF is PM. The hitting control law is tuned by

multiplying the defuzzified signal eF. Consequently

Fig. 3 A block diagram of the fuzzy adaptive tuning controller

Fig. 4 Membership functions for |s|, | s|, and eF

Table 1 Linguistic rule base for the fuzzy adaptivetuning controller

|s|

eF for the following |s|

ZE PS PM PB

ZE ZE ZE PS PMPS ZE PS PS PMPM PS PS PM PBPB PM PM PB PB





a more robust control output us can be obtained.

In this paper, a centre average defuzzification, a

Mamdani implication in the rule base, and a product

inference engine are used in the designed defuzzi-

fication segment. The output of the fuzzy logic

adaptive tuning controller can be written as

eF~

Pri~1 ai P

pj~1 mij Ij

� �Pr

i~1 Ppj~1 mij Ij

� � ð36Þ

where r is the number of rules, ai5 [a1, a2,…, ar]T is

the vector of the centres of the membership func-

tions of eF, Ij5 [|s|, |s|]T is the input vector, and p is

the number of inputs.

4 RESULTS

The automated clutch system of this study is shown

in Fig. 5. A dSPACE DS1005 card is adopted as the

ECU to handle all the input–output data for the

whole system and to calculate the control para-

meters. A Z11-PWM current amplifier was selected

for the automated clutch system to drive the

permanent-magnet d.c. motor and screw-nut actua-

tor, and a DJZ14-type eddy current dynamometer

was adopted as the load of the automated clutch.

The Bosch Hall displacement sensor and Hall shift

sensor return the clutch small end displacement and

shift signal respectively of the automated clutch into

the dSPACE. Since the voltage signal is liable to be

disturbed by the environmental noise, and is

amplified during the numerical difference operation,

a digital filter and an RC filter circuit were intro-

duced to solve this problem.

The digital filter can be represented as

yy kð Þ~ayy k{1ð Þz 1{að Þy kð Þyy 0ð Þ~y 0ð Þ, k~1, 2, . . . ,n

ð37Þ

where a [ (0, 1) is the adjustable variable. A larger

value of a provides a better filter but poorer curve-

fitting ability. In this study, the parameter a is

selected as 0.3 on the basis of operation experience.

The RCP framework of the automated clutch is

built as shown in Fig. 6. The clutch-driven plate ro-

tational speed, engine rotational speed, shift signal,

throttle position, and brake signal are introduced

as the input signals, in which the throttle position

and brake signal are virtual signals generated from a

signal generator. The logic implementation of the

engaging and declutching process for the automated

clutch system is implemented using a Stateflow

block. The dynamic sliding-mode controller with

fuzzy adaptive tuning is implemented through the

RTW, as shown in Fig. 7. In this RTW model, a set of

input–output devices is created in the Simulink

library to provide an interface between the down-

loaded Simulink model and the automated clutch

system. The dSPACE ControlDesk is used to observe

real-time results and to change the input parameters

online, which makes the development of controllers

much more effective. Real-time changes can be

made to the input values of the automated clutch

system by adjusting the knobs of the ControlDesk

Fig. 5 Automated clutch system: (a) plant test of the automated clutch; (b) dSPACE and powersupply





Fig. 6 RCP framework of the automated clutch system (PC, personal computer; PWM, pulsewidth modulation)

Fig. 7 Simulink block diagram for the proposed controller, CSMC, and PID controller





graphical user interface. Moreover, the proposed

controller can also be enabled or disabled online to

see its effect on the automated clutch performance.

In order to compare the performance of the

proposed controller with those of the CSMC and

PID controller [25], the system parameters and the

coefficient of the hyperplane are chosen to be the

same. The declutching process is implemented in

0.22 s, which meets the performance requirement of

the automated clutch system. Therefore, the engage-

ment control is the key to satisfying different and

sometimes conflicting objectives of the automated

clutch. According to reference [11], the whole pro-

cess of launching or shifting a vehicle consists of

four stages from separation to engagement of the

clutch, as shown in Fig. 8. In the first stage, a0a1 is

the clearance space between the driving and driven

plates at full separation of the clutch. Since no

torque is transmitted, the driven plate should move

as rapidly as possible. In the a1a2 stage, the trans-

mitted friction torque Tc increases from zero to the

static friction resistance torque Tr. In the a2a3 stage,

the friction torque Tc continues to rise until a syn-

chronization of the angular velocities ve and vc is

achieved between the engine output and the clutch-

driven shafts. This stage must be controlled to satisfy

different and conflicting objectives, such as small

friction losses, the minimum time needed for the

engagement, and preservation of driver comfort. In

the fourth stage, a3a4 represents the displacement

after synchronization, which continues to meet the

requirements for the clearance between the release

thrust bearing and operating fork until the pressure

is up to the maximum. In this paper, the vehicle

launch of the automated clutch is chosen as the

typical operating condition to validate the proposed

controller, which is driven according to the desired

trajectory, which is obtained from the previous

theoretical analysis and experimental data and is

given by

xd

~

0, t¡0:3

1:8|10{3z5:2|10{3 t{0:3ð Þ2, 0:3vtv1:3

8, t¢1:3

8>><>>:

ð38Þ

According to the Hurwitz polynomial, suppose

that the eigenroot of the sliding mode is [2300,280];

then C15 2.46104 and C25 380. In addition, the

gains of the CSMC law are obtained by using w5 0.01

and K5 26103. The parameters of the dynamic

sliding-mode controller with fuzzy adaptive tuning

are e5 36103, ld5 4.15, k|s|5 661022, k|s|5 1.2561022, and ksF~2|102; the parameters of the PID

controller are a proportional value of 340, an integral

value of 0.5, and a derivative value of 60; the

parameters of the automated clutch are set accord-

ing to the measurement results as R5 0.2V, L5 861024, Jr56.12561024Nms2, kd50.0764, km50.7296,

kh5 0.0055, cm5 0.01N/ms, and kL5 0.1.

The sampling time step size for the RCP is 2ms.

The objective is to control the clutch to move from

the initial position to the end. Hence, the vehicle

launch can be analysed in this investigation by

adopting the PID controller, the CSMC, and the

dynamic sliding-mode controller with fuzzy adaptive

tuning respectively. The dynamic responses ob-

tained by employing the PID controller, the CSMC,

and the proposed controller are shown in Fig. 9. A

preferable tracking response can be observed by

employing the proposed dynamic sliding-mode

controller with fuzzy adaptive tuning. The actual

trajectory response of the proposed controller

approaches the desired trajectory xd(t) rapidly, as

shown in Fig. 9(c1). After the actual trajectory

reaches the desired trajectory, the actual trajectory

response x1(t) is almost identical with the desired

command xd(t). In comparison with the proposed

controller, it is difficult to follow the desired

trajectory by adopting the PID controller. Although

the CSMC can work normally in this case, its anti-

interference performance is worse than that of the

proposed controller. The steady state tracking errors

are 0.79mm, 0.21mm, and 0.18mm for the PID con-

troller, CSMC, and the proposed controller respec-

tively. In order to validate the robustness of the

proposed controller, the digital filter is removed. The

CSMC and the PID controller will not work in thisFig. 8 Relationship between the torque, angular velo-

city, and distance of travel





Fig. 9 Response trajectories of the launch control for (a1) the PID controller, (b1) the CSMC, (c1)the proposed controller, and (d1) the proposed controller without a digital filter, togetherwith (a2), (b2), (c2), (d2) (their corresponding errors)





case. However, the proposed controller can be op-

erated normally (Fig. 9(d1)), which shows that the

proposed controller is robust to the measurement

noise.

For the automated clutch system, the transmitted

torque and rotational speed of the vehicle are gen-

erally recommended. The output rotational speed

and torque of the automated clutch on adopting

the PID controller, the CSMC, and the proposed

controller are shown in Fig. 10. The rotational speed

of the automated clutch can be increased more

smoothly by using the proposed controller than by

using the PID controller or the CSMC, as shown in

Fig. 10(a); this can improve the passenger comfort

and reduce the friction loss. Correspondingly, the

output torque of the automated clutch system

transmitted from the engine to the clutch is more

progressive than for the CSMC and PID controller

during the launch process. Therefore, the AMT

vehicle can be rapidly launched so as to reflect the

intention of the driver and depress the impact by

adopting the proposed dynamic sliding-mode con-

troller with fuzzy adaptive tuning. The results of RCP

show that the proposed controller can effectively

improve the robustness and track accuracy of the

automated clutch system.

5 CONCLUSION

This paper proposed a dynamic sliding-mode con-

troller with fuzzy adaptive tuning for the automa-

ted clutch system. The sufficient condition for the

existence and reachability of the dynamic sliding

mode controller was approved by using the Lyapu-

nov theorem. The robustness and stability of the

controller were improved by means of the fuzzy

adaptive tuning arithmetic. Based on dSPACE and

MATLAB–Simulink, the RCP of the automated clutch

is established. A preferable tracking response can be

observed by employing the proposed controller. The

AMT vehicle will be rapidly launched so as to reflect

the intention of the driver and to depress the impact

by adopting the proposed dynamic sliding-mode

controller with fuzzy adaptive tuning.

ACKNOWLEDGEMENTS

This paper is supported by the Doctor ScientificResearch Foundation of Beijing University of Tech-nology (Grant X0001211200801) and the NationalEleventh Five-Year Plan scientific and technologicalsupport project (Grant 2006BAF0109-04).

F Authors 2010

REFERENCES

1 Shen, S. W. and Wu, C. Q. An expert fuzzy controlof automatic mechanical transmission clutch. SAEpaper 1999-01-2814, 1999.

2 Hibino, R., Osawa, M., and Yamada, M. H‘ controldesign for torque-converter-clutch slip system. InProceedings of the 35th Conference on Decisionand control, Kobe, Japan, 1996, pp. 1797–1802(IEEE, New York).

3 Glielmo, L., Iannelli, L., Vacca, V., and Vasca, F.Gearshift control for automated manual transmis-sions. IEEE/ASME Trans. Mechatronics, 2006, 11(1),17–26.

4 Horn, J., Bamberger, J., and Michau, P. Flatness-based clutch control for automated manual trans-missions. Control Engng Practice, 2003, 11, 1353–1359.

Fig. 10 Outputs of (a) the rotational speed and (b) the torque





5 Slicker, J. M. and Loh, R. N. K. Design of robustvehicle launch control system. IEEE Trans. ControlSystems Technol., 1996, 4(4), 326–335.

6 Zanasi, R. and Visconti, A. Dynamic modelingand control of a car transmission system. In Pro-ceedings of the 2001 IEEE/ASME InternationalConference on Advanced intelligent mechatronics,Como, Italy, 2001, pp. 416–421 (IEEE/ASME, NewYork).

7 Sanada, K. and Kitagawa, A. A study of two-degree-of-freedom control of rotating speed in anautomatic transmission, considering modeling er-rors of a hydraulic system. Control Engng Practice,1998, 6, 1125–1132.

8 David, J. and Natarajan, N. Design of an optimalclutch controller for commercial trucks. In Pro-ceedings of the 2005 American Control Conference,Portland, Oregon, USA, 2005, pp. 1599–1606 (IEEE,New York).

9 Hahn, J. O. and Lee, K. I. Nonlinear robust controlof torque converter clutch slip system for pass-enger vehicles using advanced torque estimationalgorithms. Veh. System Dynamics, 2002, 37(3), 175–192.

10 Cheng, D. S., Zhang, J. W., Ye, X. F., and Huang,X.-F. Sliding mode control approach for electricallycontrollable clutch of AMT based on the feedbacklinearization. J. Dong Hua Univ., Engl. Edn, 2003,20(3), 88–93.

11 Zhang, J., Chen, L., and Xi, G. System dynamicmodeling and adaptive optimal control for auto-matic clutch engagement of vehicles. Proc. IMechE,Part D: J. Automobile Engineering, 2002, 216(12),983–991. DOI: 10.1243/095440702762508236.

12 Lee, W., Park, S., and Sunwoo, M. Towards aseamless development process for automotive en-gine-control system. Control Engng Practice, 2004,12, 977–986.

13 Noomwongs, N., Yoshida, H., Nagai, M., Kobaya-shi, K., and Yokoi, T. Study on handling andstability using tire hardware-in-the-loop simulator.JSAE Rev., 2003, 24, 457–464.

14 Thomas, B. and Ferit, K. Virtual real-time environ-ment for automatic-transmission control units inthe form of hardware-in-the-loop. Int. J. Veh.Autonomous Systems, 2003, 1(2), 177–195.

15 Liu, G. P. and Daley, S. Optimal-tuning nonlinearPID control of hydraulic systems. Control EngngPractice, 2000, 8, 1045–1053.

16 Er, M. J., Low, C. B., Nah, K. H., Lim, M. H., andNg, S. Y. Real-time implementation of a dynamicfuzzy neural networks controller for a SCARA.Microprocessor Microsystems, 2002, 26, 449–461.

17 Montanari, M. and Ronchi, F. Control and perfor-mance evaluation of a clutch servo system withhydraulic actuation. Control Engng Practice, 2004,12, 1369–1379.

18 Lyshevski, S. A. and Nazarov, A. Control andanalysis of synchronous reluctance motors. InProceedings of the American Control Conference,San Diego, California, USA, 1999, pp. 1682–1686(IEEE, New York).

19 Yu, F. M., Chung, H. Y., and Chen, S. Y. Fuzzysliding mode controller design for uncertain time-delayed systems with nonlinear input. Fuzzy SetsSystems, 2003, 140, 359–374.

20 Lee, J.-H. and Youn, M.-J. A new improvedcontinuous variable structure controller for accu-rately prescribed tracking control of BLDD servomotors. Automatica, 2004, 40, 2069–2074.

21 Pieper, J. First order dynamic sliding mode control.In Proceedings of the 37th IEEE Conference onDecision and control, Tampa, Florida, USA, 1998,pp. 2415–2420 (IEEE, New York).

22 Abdelhameed, M. M. Enhancement of slidingmode controller by fuzzy logic with application torobotic manipulators. Mechatronics, 2005, 15, 439–458.

23 Fung, R. F. and Shaw, C. C. Region-wise linearfuzzy sliding mode control of the motor-mechan-ism systems. J. Sound Vibr., 2000, 234(3), 471–489.

24 Kiam, H. A., Gergory, C., and Yun, L. PID controlsystem analysis, design and technology. IEEE Trans.Control Systems Technol., 2005, 13(4), 559–576.





study of control for the automated clutch

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