Position Control of Electric Clutch Actuator Using a Triple-Step

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 12, DECEMBER 2014 6995

Position Control of Electric Clutch ActuatorUsing a Triple-Step Nonlinear MethodBingzhao Gao, Hong Chen, Senior Member, IEEE, Qifang Liu, and Hongqing Chu

Abstract—For a novel electric clutch actuator, a nonlinearfeedforward–feedback control scheme is proposed to improvethe performance of the position tracking control. The designprocedure is formalized as a triple-step deduction, and the de-rived controller consists of three parts: steady-state-like control;feedforward control based on reference dynamics; and state-dependent feedback control. The structure of the proposed non-linear controller is concise and is also comparable to those widelyused in modern automotive control. Finally, the designed con-troller is evaluated through simulations and experimental tests,which show that the proposed controller satisfied the controlrequirement. Comparison with proportional–integral–derivativecontrol is given as well.

Index Terms—Automotive, clutch actuator, nonlinear control,position control.

I. INTRODUCTION

AN AUTOMATIC clutch system is an important part ofautomated manual transmission [1], and it is also widely

used in hybrid electric vehicles to implement the operations ofgear shifting and mode switching [2]–[4].

An automatic clutch is always actuated by electrohydraulic,electropneumatic, or electromechanical systems. The electro-hydraulic (pneumatic) actuator contains a relatively complexsystem, including pump, tank, and valves. References [5] and[6] introduce the design and simulation of this kind of actuators.An electromechanical actuator always adopts a dc motor aspower source and a worm wheel or screw nut as speed reductionmechanism [7], [8]. However, the transmission efficiency ofworm wheel and screw nut is not high (less than 50%), whichaffects the response time of the actuator and, consequently, thedynamic performance of the vehicle.

This paper is related to the position control of a novel electricclutch actuator which adopts a dc motor and a ball screw toimplement the motion control. Because the ball screw has highefficiency (larger than 90%), very fast response can be achieved.

Manuscript received April 1, 2013; revised July 3, 2013 and December 20,2014; accepted February 24, 2014. Date of publication April 14, 2014; date ofcurrent version September 12, 2014. This work was supported in part by the 973Program under Grant 2012CB821202, by the National Nature Science Foun-dation of China under Grants 61034001 and 61374046, and by the Programfor Changjiang Scholars and Innovative Research Team in University underGrant IRT1017.

B. Gao and H. Chu are with the State Key Laboratory of AutomotiveSimulation and Control, Jilin University, Changchun 130022, China.

H. Chen and Q. Liu are with the State Key Laboratory of AutomotiveSimulation and Control, Jilin University, Changchun 130022, China, and alsowith the Department of Control Science and Engineering, Jilin University(Campus NanLing), Changchun 130025, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2014.2317131

The control task is represented as a position control problembecause the torque transmitted in the clutch is determined bythe displacement of the thrust bearing of the dry clutch, whichis driven by the clutch actuator.

There have been some studies addressing the position con-trol of electric clutch actuators, including adaptive neuronproportional–integral–derivative (PID) [7], predictive controlstrategy [5], and sliding-mode control [9]. In [7], it is pointedout that a clutch actuator is a highly nonlinear system becauseof the friction force and the large hysteresis, and adaptive neuralPID control is adopted to improve tracking accuracy. In order tomake friction compensation, a lot of research studies have beencarried out, including [10]–[12].

In this paper, although a ball screw has high efficiency, itdoes not self-lock, and the preload force of the supporting bear-ings produces time-varying friction force. On the other hand,because dry clutch control is closely related with the drivabilityperformance, it requires that the clutch actuator should be fastand precise enough, which make the position control of theproposed actuator a challenging nonlinear control problem.

A variety of powerful methodologies have been developed todeal with nonlinear control problems, including the following:1) sliding-mode control [13]; 2) feedback linearization [14];3) differential flatness [15]; and 4) backstepping [16]. Eachof them has its own characteristics and successful industrialapplications. In present automotive productions, many controlsystems have map-based structure of feedforward and feedback.The feedback is in general a gain scheduling PID controller,where the PID parameters vary according to given lookup tables(maps) in order to be adaptive to different operating conditions.The feedforward, generally given as maps too, is used to pro-duce a control signal according to the reference dynamics in thenominal operating condition. In order to reduce the calibrationeffort, and inspired by the map-based feedforward–feedbackstructure widely used in automotive control engineering, atriple-step design procedure of nonlinear controller is proposedin [17] for the rail pressure control of gasoline-direct-injectionengine. This paper will extend the method to a third-ordersystem and proposes a model-based and systematic procedureto design a nonlinear position controller for an electric clutchactuator. The procedure consists of three steps in successionand delivers the final control in an additive process.

The main merits of the design controller cover the followingpoints: 1) using lookup tables as a steady-state control, whichis commonly used in automotive control; 2) based on the ref-erence dynamics and tracking error dynamics, the closed-loopsystem design is completed to enhance control performance;and 3) most importantly, the resulting control strategy has a

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6996 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 12, DECEMBER 2014

Fig. 1. Schematic graph of electric clutch actuator.

structure comparable to the standard structure of the existingautomotive control, which seems reasonable to be applied inimplementation.

The rest of this paper is organized as follows. In Section II,a dynamic model of the considered electric actuator is derived,and the control problem is described. The nonlinear controlleris designed in Section III, and in Section IV, the robustnessanalysis of the implemented controller is given. Section V issimulation and experimental results, and finally, some conclu-sions are given in Section VI.

II. SYSTEM MODELING AND PROBLEM STATEMENT

The electric clutch actuator, as shown in Fig. 1, adopts adc motor as the power source and a ball screw as the speedreduction mechanism; there is no other gear set. The rotationalmotion of the motor is transformed into linear motion bythe ball screw, and then, the clutch lever is pushed (clutchdisengaged) or released (clutch engaged). A potentiometer isinstalled on the nut to measure the position of the clutch lever.

A. System Modeling

The dc motor is driven by an H-bridge circuit, which con-sists of four MOSFETs, and pulsewidth-modulation (PWM)control is used to modulate the motor current. Because thePWM frequency can be set as a high value, such as 10 kHz,the current could be controlled without noticeable dither. Thevoltage balance equation of the armature circuit is

Laia = vbatu− va − kv θm (1)

and the torque balance equation is given as

Tm = ktia − Tmf − Jmθm (2)

where vbat is the battery voltage, va is the voltage reductioncaused by the resistance of the armature circuit, La is thearmature inductance, ia is the armature current, u is the PWMduty ratio, kv is the back electromotive force coefficient, θm isthe motor rotational angle, Tm and Tmf are the output torqueand friction torque of the motor, respectively, kt is the torquecoefficient, and Jm is the inertia.

The motor shaft is connected to the screw shaft, and the screwnut is connected to the load side, i.e., the clutch lever. When themotor rotates, the screw nut moves forward or backward to dis-engage or engage the clutch. The dynamic equation is given as

my =2π

hTm − Fs − Ff (3)

where y is the displacement of the screw nut, m is the mass ofmoving parts, h is the lead of the screw, Fs is the load force,i.e., the return force of the diaphragm spring, and Ff is thefriction force.

The relationship of the rotational and the linear movementssatisfies that

θm =2π

hy (4a)

Fm =2π

hTm (4b)

where Fm is the linear force produced by the motor torque.From (1)–(4) and defining the clutch displacement y as x1,

clutch speed y as x2, armature current ia as x3, we have thestate-space form of the actuator system

x1 =x2 (5a)

x2 =1

m

2π

hKtx3 −

1

mFs(x1)−

1

mFf (x1, x2) (5b)

x3 = − 1

La

2π

hKvx2 −

1

Lava(x3) +

1

Lavbatu (5c)

where

m =m+

(2π

h

)2

Jm (6a)

Ff =Ff +2π

hTmf . (6b)

B. Control Problem Statement

From experimental tests, it is found that the functions of loadforce Fs, friction force Ff , and the resistance voltage of va areall nonlinear functions. Hence, the considered control problemhere is summarized as a tracking problem in consideration ofthe system nonlinearities, wherein x1, the clutch position, iscontrolled to track the reference values. The operation of clutchis important for the drivability of the vehicle. The responsespeed and tracking precision are crucial for longitudinal dy-namic performance of the vehicle. From the requirement of thedriving performance, the following are requested.

1) The full disengagement (or engagement) time should beless than 0.15 s.

2) The steady-state tracking error should be less than 0.1 mm.

Because of the large load force and friction force, this is achallenging control requirement. The triple-step design pro-cedure of nonlinear controller proposed by Chen et al. [17]is concise and has standard structure; this method will beextended to third-order system to solve the aforementionedcontrol problem.

GAO et al.: POSITION CONTROL OF ELECTRIC CLUTCH ACTUATOR USING A TRIPLE-STEP NONLINEAR METHOD 6997

III. NONLINEAR CONTROLLER DESIGN

We rewrite the aforementioned clutch actuator system as

x1 =x2 (7a)x2 = a2(x1, x2) + b2x3 (7b)

x3 = a3x2 −1

Lava(x3) + b3u (7c)

where

a2 = − 1

mFs(x1)−

1

mFf (x1, x2) (8a)

b2 =1

m

2π

hKt (8b)

a3 = − 1

La

2π

hKv (8c)

b3 =1

Lavbat. (8d)

The clutch position y = x1 is the controlled output, andwe want to design a controller to drive the nonlinear systemtracking a given reference trajectory y∗, which is derived fromthe upper controller of vehicle drive-train control system. Thecalculation of y∗ is out of the scope of this paper, and it isomitted here.

In the following, we design a nonlinear position controller forthe electric clutch actuator using a model-based and systematicprocedure, which consists of three steps in succession: The firststep is to design a steady-state-like control, the second stephandles the derivative requirements of tracking, and the thirdstep handles the final tracking offset. The final control is derivedby the triple-step method in an additive process.

A. Step 1: Steady-State-Like Control

The first step is to design a steady-state-like control, denotedas fs(x), by setting the system in steady state.

We differentiate y until the control input u appears

y =x2 (9a)y = a2(x1, x2) + b2x3 (9b)...y =

∂a2∂x1

y +∂a2∂x2

y + b2

(a3x2 −

1

Lava(x3) + b3u

). (9c)

In order to obtain the form of (9c), x1 = y and x2 = y are used.By letting y = 0, y = 0, and

...y = 0, we obtain a steady-state-

like control as follows:

fs(x) = u = −a3x2

b3+

va(x3)

Lab3. (10)

It is called “steady-state-like” because this part of the controlis obtained by setting the system in steady state and imple-mented according to the current measured or estimated statex but not the true steady state xs. A justification for the formof (10) is the widely used map-based control in automotive en-gineering, where the control map (or lookup table) is calibratedfrom a large amount of experimental data in the steady state andthe control is implemented according to the current measured orestimated state. The merit of using such form can be found inthe following derivation.

B. Step 2: Reference-Dynamics-Based Feedforward Control

We know that a steady-state control is not enough for achiev-ing satisfying performance. Hence, we introduce an additionalu1 and define

u = fs(x) + u1

where u1 is to be determined. Substituting into (9c) leads to...y = A1(x)y +A2(x)y +Bu1 (11)

with

A1(x) =∂a2∂x1

= −1

m

∂

∂x1Fs(x1)−

1

m

∂

∂x1Ff (x1, x2) (12a)

A2(x) =∂a2∂x2

= − 1

m

∂

∂x2Ff (x1, x2) (12b)

B = b2b3 =1

m

2π

hKt

1

Lavbat. (12c)

We stress that the clear form of (11) benefits from the state-dependent form of (10).

Then, by enforcing y = y∗, y = y∗, and...y =

...y∗

for (11), i.e.,...y∗= A1(x)y

∗ +A2(x)y∗ +Bu1 (13)

we obtain a feedforward control related to the reference dynam-ics as follows:

u1=1

B

...y∗−A1(x)

By∗−A2(x)

By∗=:ff (x, y

∗, y∗,...y∗). (14)

The obtained u1 has clearly an affine form in y∗, y∗ and...y∗;

hence, we call it as reference dynamics feedforward and denoteit as ff (x, y∗, y∗,

...y∗).

C. Step 3: Error Feedback Control

After the aforementioned two steps, what is not consideredis just the requirement of tracking offset. To deal with the finaltracking offset error, we add a new control action u2, whichis to be determined, into the steady-state-like control and thereference dynamics feedforward. Substitute

u = fs(x) + ff (x, y∗, y∗,

...y∗) + u2

into (9c) to infer...y =A1(x)y+A2(x)y+

...y∗−A1(x)y

∗−A2(x)y∗+Bu2. (15)

By defining the tracking error as

e1 = y∗ − y (16)

(15) becomes

...e 1 = A1(x)e1 +A2(x)e1 −Bu2. (17)

Defining e2 = e1 and e3 = e1, (17) can be rewritten as

e1 = e2 (18a)e2 = e3 (18b)e3 =A1(x)e2 +A2(x)e3 −Bu2. (18c)


With the help of the predeterminedfs(x) andff (x, y∗, y∗,...y∗),

we obtain an explicit expression of the tracking error dynamics.Moreover, it is affine in the tacking error and in the u2 to be de-termined. This simplifies significantly the determination of u2

such that the tracking error dynamics is asymptotically stable,as shown in the following. Take e3 as a virtual control for thelinear subsystem, and choose a PID as the virtual control law

e∗3 = k0χ+ k1e1 + k2e2 (19)

where χ =∫e1dt. Then, we have

...χ = k0χ+ k1χ+ k2χ− η (20)

with η = e∗3 − e3. According to Routh’s stability criterion, wecan choose k0,1,2 satisfying

k0 < 0 k2 < 0 k0 + k1k2 > 0 (21)

to render the linear subsystem asymptotically stable. Moreover,because a stable linear system is input-to-state stable (ISS)[18, p. 174], (20) is ISS with respect to the input η. Thatis, there exist α > 0, γ > 0 and an ISS-Lyapunov functionV1(χ, e1, e2) satisfying [19]

V1 ≤ −α ‖(χ, e1, e2)‖2 + γη2. (22)

Finally, u2 is determined to enforce x3 tracking x∗3 using

Lyapunov’s direct method. By defining

V2 =1

2η2 (23)

and using (18c) and (19), we infer

V2 = ηη = η (e∗3 − e3) (24)= η ((k2 −A2)e3 + (k1 −A1)e2 + k0e1 +Bu2) . (25)

Now, we choose the control law as

u2 =−k0e1 − (k1 −A1)e2 − (k2 −A2)e3 − k3η

B(26)

to achieve

V2 = −k3η2 ≤ 0 (27)

where k3 > 0.For the whole error system given in (18), we define a

Lyapunov function as follows:

V = V1 + V2. (28)

Differentiating it and substituting (22) and (27), we have

V ≤ −α ‖(χ, e1, e2)‖2 + γη2 − k3η2. (29)

If we choose k3 > γ, the control law (26) makes the whole errordynamics (18) asymptotically stable.

By substituting e3 = e∗3 − η and (19) into (26), we canrearrange u2 as

u2 =−k0k3B

χ+−(k0 + k1k3)

Be1 +

−(k1 −A1 + k2k3)

Be1

+−(k2 −A2 − k3)

Be1 (30)

Fig. 2. Diagram of control scheme.

which admits the form of a proportional–integral–double-derivative (PIDD) controller.

D. Formalized Control Law

By combining (10), (14), and (30), the control law as a wholeis given as follows:

u = − a3x2

b3+

va(x3)

Lab3+

1

B

...y∗ − A1(x)

By∗ − A2(x)

By∗

+−k0k3B

χ+−(k0 + k1k3)

Be1 +

−(k1 −A1 + k2k3)

Be1

+−(k2 −A2 − k3)

Be1. (31)

We rewrite the derived control law as

u = fs(x) + ff (x) + fP (x)e1 + fI(x)

∫e1dt+ fD(x)e1

+fDD(x)e1 (32)

where

fs(x) = − a3x2

b3+

va(x3)

Lab3(33a)

ff (x) =1

B

...y∗ − A1(x)

By∗ − A2(x)

By∗ (33b)

fP (x) =−(k0 + k1k3)

B(33c)

fI(x) =−k0k3B

(33d)

fD(x) =−(k1 −A1(x) + k2k3)

B(33e)

fDD(x) =−(k2 −A2(x)− k3)

B. (33f)

Apparently, the structure of the proposed nonlinear controlleris in a concise order, as shown in Fig. 2. The fs(x) expressesa steady-state control with the similar function of the widelyused lookup tables. Concerning the dynamics of the trackingreference, ff (x) works as a feedforward control. The feedbackcontrol is derived based on Lyapunov’s direct method with errorstate which can be finally rearranged into the form of PIDDcontroller with state-dependent parameters.

The proposed procedure can avoid explosion of terms causedby multiple differentiations, which are always necessary inexisting nonlinear methods. Moreover, the designed controlleris comparable to a standard two-degree-of-freedom structureof the automotive control in practice, most of which containsPID, feedforward maps, and sometimes correction maps. Whilemap calibration is time and cost consuming, the suggested


Fig. 3. Second-order filter for input shaping.

method has potential in improvement of dynamic performanceand reduction of calibration work.

1) First, the steady-state control reflects some dominantcharacteristics of the system, and when the system ap-proaches steady state, this part becomes dominant andprovides the control action.

2) Second, the feedforward part provides correction actionaccording to the reference dynamics, which depends onstate and helps to improve the transient performance.

3) Third, with the help of the steady-state and feedforwardcontrol, the resulted error feedback becomes an affinelinear system, and the designed state-dependent PID pos-sesses gain scheduling performance, which canceled thelaborious effort of gain calibration.

E. Implementation Issues

1) Signal Processing and Calculation of High-OrderDerivatives: We use an input shaping technique [20] for signalprocessing and, at the same time, obtain the first- and second-order differentiations of y∗ and y, which are necessary for thederived control law (32). Here, we assume that the referencetrajectory does not vibrate frequently (which is true in practice),and the third differentiation of it,

...y∗

in (33b), is ignored.Let the original reference trajectory y∗ and the measurement

value of the output ym pass through a second-order filter, andthe output of the filter is the reference value y∗ or the filteredoutput y, which are actually used in the control system.

y∗

y∗=

ω2n

s2 + 2ξωns+ ω2n

(34)

the block diagram of which is shown in Fig. 3, and the filter forym, the measured output, is the same as above. Then, e1 ande1 can be achieved from e1 = y∗ − y, and e1 = y∗ − y. Notethat, although the derivatives of system output are calculated bythe filter instead of designing a state observer, the calculationprecision is accurate enough if ωn and ξ are chosen reasonably.

It is also worth noting that fDD(x)e1, the term of the second-order differentiation in the control law, is ignored if we assumethat the amplitude of fDD(x)e1 is much less than the otherterms. In fact, except for the very short moment when the signalis changed intensively, this is the truth because the coefficientfDD(x) is indeed much smaller than fD(x), which can be seenfrom the values of k0,1,2 given in Section V.

2) Calculation of A1(x), A2(x), and va(x): The controllaw also requires to know the values of A1(x) and A2(x), andconsequently, from (12) and (8a), it is necessary to calculate(∂/∂x1)Fs(x1), (∂/∂x1)Ff (x1, x2), and (∂/∂x2)Ff (x1, x2).

Fig. 4. Load force of spring.

Fig. 5. Identified friction force.

The functions of load force Fs and friction force Ff areidentified from experiment measurement data, which are shownin Figs. 4 and 5.

In Fig. 4, x0 denotes the position where the diaphragmspring begins to be deflected, and xf denotes the kiss pointof the clutch (the position where the clutch plates begin to betouched). The characteristics of Fs, the resistance force of thediaphragm spring, is fitted as a third-order polynomial func-tion Fs(x1) = −0.86x3

1+17.97x21−33.08x1+2.38, and then,

(∂/∂x1)Fs(x1) can be calculated as a second-order polynomialfunction of x1

∂

∂x1Fs(x1) = −2.58x2

1 + 35.94x1 − 33.08. (35)

The friction force Ff , as shown in Fig. 5, is a functionof moving direction and speed, and it also increases with thedisplacement of x1 because of the increasing load force

Ff = (Ff0(x2) + Ffs(x1)) sign(x2) (36)

where Ff0(x2) is the absolute value of the friction force whenthe load force is zero and Ffs(x1) is the additional frictioncaused by spring load force. Then, according to the identifiedfriction force shown in Fig. 4, we have that, when x2 > 0

∂

∂x1Ff (x1, x2) =

∂

∂x1Ff (x1, x2) = 7.5× 103 N/m (37a)

∂

∂x2Ff (x1, x2) =

∂

∂x2Ff0(x2) = 190 N/(m/s) (37b)


TABLE IPARAMETERS USED IN THE CONTROLLER

Fig. 6. Voltage reduction caused by resistance.

and, when x2 < 0

∂

∂x1Ff (x1, x2) = −7.5× 103 N/m (38a)

∂

∂x2Ff (x1, x2) = −190 N/(m/s). (38b)

The other parameters used in the controller are given inTable I, and the map of resistive voltage va, which is containedin the steady-state control fs(x), is shown in Fig. 6.

3) Final Control Law: Therefore, the control law to beimplemented becomes

uim=fs(x)+ffim(x)+fP (x)e1+fI(x)

∫e1dt+fD(x)e1 (39)

where

ffim(x) = −A1(x)

By∗ − A2(x)

By∗. (40)

IV. ROBUSTNESS ANALYSIS

In the aforementioned deduction of the implemented controllaw (39), several high-order derivatives have been ignoredand removed, including

...y∗

in ff (x) and fDD(x)e1, whichbrings errors/disturbances into the system input. Moreover, thenonlinear functions A1(x), A2(x), and va(x) are obtained fromidentified curves, which also introduce errors inevitably. Bylumping these errors/uncertainties as an additive disturbance d,we have

u = uim + d. (41)

Indeed, other uncertainties might be included in d, too. Ifwe apply the control given in (39) into the system, the error

dynamics then becomes

e1 = e2 (42a)e2 = e3 (42b)e3 =A1(x)e2 +A2(x)e3 +Bu2 +Bd. (42c)

Thus, the derivative of V2 given in (23) turns to be

V2 = ηη = −k3η2 −Bηd. (43)

For V = V1 + V2 given as (28), the Lyapunov function of thewhole system, we have

V ≤ − α ‖(χ, e1, e2)‖2 + γη2 − k3η2 −Bηd

≤ − α ‖(χ, e1, e2)‖2 + γη2 − k3η2 +

1

2η2 +

B2

2d2. (44)

If k3 > γ + (1/2), then the whole system is ISS with respectto d, and equivalently, it is robust against the considered uncer-tainties [19].

V. TEST RESULTS

A. Simulation and Parameter Tuning

Before the designed control, given in (39) with (33), and(40) is implemented on the real bench, simulations are carriedout. Parameters are chosen according to the aforementionedtheoretical analysis. The summary is as follows.

1) k0, k1 and k2 are the PID parameters of the virtual controllaw (19) and are tuned based on the PID rules in thesatisfaction of the stability condition (21).

2) k3 should be large enough, at least much larger than 0.5,to ensure the robustness of the closed-loop system.

3) ωn and ξ in (34) are tuned to trade off the filter perfor-mance and the resulting delay.

Finally, by consulting with simulation, the parameters of theproposed nonlinear controller are chosen as follows:

k0 = − 106, k1 = −3× 104 (45a)k2 = − 300, k3 = 100 (45b)ωn =280 rad/s, ξ = 0.9. (45c)

The results of step response (from 0 to 10 mm and from 10to 11 mm) are shown in Fig. 7(a). The PWM in the first subplotmeans the duty ratio of PWM of the motor, which is also thecontrol input u of the system. It can be seen that the settlingtime is less than 0.15 s, and the tracking error is less than0.1 mm, which satisfies the control requirements. Note that, inthis study, the stroke to disengage the clutch is 13 mm, and thefull stroke is 17 mm.

As comparison, results of PID control are also shown inFig. 7. The well-tuned PID parameters are Kp = 70000, Ki =28000, and Kd = 2000, wherein the requests of small steady-state error, small overshot, and small settling time were consid-ered. Although a low-pass filter (with time constant of 0.01 s)is used, the large Kd still increases the sensor noise and resultsin dither of the control signal and, consequently, the armaturecurrent. Moreover, the tracking error of PID control is largerthan that of the nonlinear control.


Fig. 7. Simulation results: Step response, 0 → 10 → 11 → 0 mm.(a) Proposed nonlinear controller. (b) PID controller.

B. Experimental Results

The test system consists of an actuator unit installed with apotentiometer, a load spring, a motor driver, and an NI6024Econtrol board installed in a host PC, which is shown in Fig. 8.The analog input channels of NI6024E are with 12-b resolution.The motor is a dc motor with nominal power of 110 W (atspeed of 2000 r/min). The PWM frequency of the motor driver(H-bridge circuit) is set as 10 kHz, and the system samplingtime is set as 1 ms.

Fig. 8. Test bench of electric clutch actuator.

Fig. 9. Experimental results: Step response between 1 and 11 mm.(a) Proposed nonlinear controller. (b) PID controller.

The position of the actuator is measured through a poten-tiometer with a linear precision of 0.2%, and for simplicity, x1

and x2, the position and the speed of the actuator, respectively,are obtainable from the filter designed in Section III-E. We canalso design an observer to estimate x2 if necessary. State x3,


Fig. 10. Experimental results: Step response between 11 and 12 mm.(a) Proposed nonlinear controller. (b) PID controller.

the current of the motor, is measurable by means of a lowresistance. Step response and sinusoidal response are carriedout to check the control performance.

The step responses are shown in Figs. 9 and 10, and thesinusoidal responses are shown in Fig. 11. The zoomed-in viewof the tracking error is also given to distinguish the trackingspeed and the steady-state error. For comparison, the results ofthe PID controller designed in the last section are given as well.

It can be seen that the tracking error of nonlinear control issignificantly less than that of PID control. The steady-state errorof nonlinear control is less than 0.1 mm, while the steady-stateerror of PID control reaches 0.25 mm.

From Figs. 10 and 11, it is shown that the settling time ofnonlinear control is restrained within 0.15 s, while that of PIDcontrol is longer than 0.3 s. It is also shown in Fig. 11 that thepeak error of PID control reaches 0.6 mm, which is two timesthat of the nonlinear control.

Fig. 11. Experimental results: Sinusoidal response of 4 rad/s. (a) Proposednonlinear controller. (b) PID controller.

Finally, it should be noted that the dither of control signal u ofthe nonlinear control is greatly less than that of the PID control,which helps improve the durability of the mechanical system.

VI. CONCLUSION

A nonlinear control scheme has been proposed for the po-sition tracking control of an electric clutch actuator. The for-malized control scheme consists of three parts: steady-state-likecontrol, feedforward control based on reference dynamics, andstate-dependent feedback control. The benefit of the proposedmethod is that it offers a concise derivation procedure forengineering implementation. Finally, the designed controller isevaluated through simulations and experimental tests. Compar-ison results show that the proposed controller has better controlperformance than that of the PID. The designed controller alsosatisfies the stringent clutch operation requirements.


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Bingzhao Gao received the B.S. degree in au-tomotive engineering from the Jilin University ofTechnology, Changchun, China, in 1998, the M.S.degree in vehicle engineering from Jilin University,Changchun, in 2002, the Ph.D. degree in mechani-cal engineering from Yokohama National University,Yokohama, Japan, in 2009, and the Ph.D. degree incontrol engineering from Jilin University in 2009.

He is currently a Professor with Jilin University.His research interests include vehicle power-traincontrol and vehicle stability control.

Hong Chen (M’02–SM’12) received the B.S. andM.S. degrees in process control from Zhejiang Uni-versity, Zhejiang, China, in 1983 and 1986, respec-tively, and the Ph.D. degree in system dynamics andcontrol engineering from the University of Stuttgart,Stuttgart, Germany, in 1997.

In 1986, she joined Jilin University of Technology,Changchun, China. From 1993 to 1997, she was aWissenschaftlicher Mitarbeiter with the Institut fuerSystemdynamik und Regelungstechnik, Universityof Stuttgart. Since 1999, she has been a Professor

with Jilin University, Changchun, where she is currently a Tang AoqingProfessor. Her research interests include model predictive control, optimal androbust control, nonlinear control, and applications in process engineering andmechatronic systems.

Qifang Liu received the B.S. degree in automationfrom Jilin University, Changchun, China, in 2009,where she is currently working toward the Ph.D.degree in control theory and control engineering.

Her research interests include vehicle power-traincontrol and nonlinear control.

Hongqing Chu received the B.S. degree in vehicleengineering from the Shandong University of Tech-nology, Zibo, China, in 2012. He is currently work-ing toward the Ph.D. degree in control theory andcontrol engineering at Jilin University, Changchun,China.

His research interests include vehicle power-traincontrol and system identification.

Documents

Position Control of Electric Clutch Actuator Using a Triple-Step