adaptive controller design for a linear motor control systems

8/11/2019 Adaptive Controller Design for a Linear Motor Control Systems

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Adaptive Controller Design for

a Linear Motor Control System

TIAN-HUA LIU, Senior Member, IEEE

YUNG-CHING LEE

YIH-HUA CHANG

National Taiwan University of Science and Technology

Three different adaptive controllers for a permanent magnet

linear synchronous motor (PMLSM) position-control system

are proposed. The proposed controllers include: a backstepping

adaptive controller, a self-tuning adaptive controller, and a model

reference adaptive controller. The detailed systematic controllerdesign procedures are discussed. A PC-based position control

system is implemented. Several experimental results including

transient responses, load disturbance responses, and tracking

responses of square-wave, sinusoidal-wave, and triangular-wave

commands are discussed and compared. The proposed system

has a good robustness performance even though the inertia of the

system is increased to 10 times. The experimental results validate

the theoretical analysis.

Manuscript received April 21, 2003; revised December 3, 2003;

released for publication December 26, 2003.

IEEE Log No. T-AES/40/2/831380.

Refereeing of this contribution was handled by W. M. Polivka.

Authors current addresses: T. H. Liu and Y-H. Chang, Dept. ofElectrical Engineering, National Taiwan University of Science

and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan,E-mail: ([email protected]); Y-C. Lee, Mustek, Hsinchu,Taiwan.

0018-9251/04/$17.00 c 2004 IEEE

I. INTRODUCTION

Modern control systems, such as manufacturingequipment, transportation, and robots, usuallyrequire high-speed/high-accuracy linear motions.Generally speaking, these linear motions aretraditionally implemented using rotary motorswith mechanical transmission mechanisms such asreduction gears and lead screws. Such mechanical

transmissions, however, not only seriously reducelinear motion speed and dynamic response, butalso introduce backlash, large frictional and inertialloads [1]. Recently, more and more industrialproducts, such as: semiconductor manufacturingequipment, X-Y driving devices, robots, and artificialhearts require high-speed/high-accuracy motions.The linear motors, which do not use mechanicaltransmissions, show promise for widespread use inthese high-speed/high-accuracy systems [24].

Without using the conventional gears or ballscrews, the permanent magnet linear synchronousmotor (PMLSM), however, is more easily affected

by load disturbance, torque ripple, and parametervariations. As a result, the design of a controller andload disturbance compensator is very important inPMLSM drives. Many researchers have focused onthis area. For example, some researchers have useddifferent algorithms to estimate and compensatethe external disturbance load of the PMLSM drivesystem [57]. In addition, several researchers haveproposed different control algorithms for PMLSMdrive systems to improve their performance [815].For example, the linearization method has beensuccessfully used for a PMLSM [8]. This method,however, requires accurate parameters of the PMLSM

and complex control procedures. Recently, someresearchers have used fuzzy rules or neural networksto control PMLSM drives. The idea is new and good.However, it requires on-line training or designerexperience. In addition, the execution of the fuzzyrules requires a lot of selections and that of theneural networks a lot of computations [911]. Someresearchers proposed robust controllers for PMLSMdrives [1213]. The robust controller design is basedon the parameters and model of the PMLSM. In thereal world, unfortunately, the measurement of theparameters of the PMLSM is very difficult. To solvethe difficulty, adaptive controllers have been proposedfor the PMLSM [1415].

Adaptive control does not require the accurateparameters of the motor. As a result, it can be afeasible control algorithm for a PMLSM. Somepapers using adaptive control for PMLSM driveshave been published. For example, Tan et al.proposed a robust adaptive compensator to reducethe friction and force ripple of the PMLSM. Thework presented here, however, focuses on friction andforce ripple compensation but not on position-loop

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or speed-loop controller design [14]. Xu and Yaoproposed adaptive robust controller design for aPMLSM. This paper, however, only focuses onself-tuning algorithm [15]. Three different controlalgorithms, which include backstepping adaptivecontrol, model reference adaptive control, andself-tuning adaptive control algorithms are discussedand compared. The experimental results show thatthe proposed system can track a step-input command,

a square-wave command, a triangular time-varyingposition command, and a sinusoidal time-varyingposition command well. It has a good load disturbancerejection capability as well. To the authors bestknowledge, this is the first time that the three differentadaptive control algorithms are studied and comparedpractically to the PMLSM control system. In addition,the design and implementation of backsteppingadaptive control and model reference control toa PMLSM are also new ideas, and have not beenpresented in previously published papers.

II. MATHEMATICAL MODEL

The mathematical model of a permanent magnetsynchronous motor can be described, in the two-axisd-qsynchronously rotating frame, by the followingdifferential equations [8]:

pid= 1

Ld

vd Rsid+

veLqiq

(1)

piq=

1

LqvqRsiq

veLdid

3

2

maxve

(2)

wherep is the differential operator d=dt,id

andiq

arethed-axis andq-axis currents, Ld andLq are the d-andq-axis inductances,vd andvq are the d-axis andq-axis stator voltages, Rs is the stator resistance, is the pole pitch, ve is the velocity, and max is themaximum flux linkage due to permanent magnet ineach phase. The electro-mechanical equation of thePMLSM is

Fe=

(Ld Lq)idiq+

3

2maxiq

: (3)

In this paper, the PMLSM is a surface-mountedPMLSM. As a result,Ld is equal to Lq. Then, (3) can

be simplified as

Fe=

3

2

maxiq (4)

=Ktiq (5)

whereKt is the torque constant of the motor. Thedynamic mechanical speed-movement equation is

pvm= 1

M(FeBvmFL) (6)

and

vm= 2

Pove (7)

where vm is the mechanical speed, Mis the mass,B is the friction coefficient, FL is the external force,andPo is the pole number of the motor. The dynamicmechanical position-movement equation is

pym= vm (8)

where ym is the mechanical position of the motor.

III. CONTROLLER DESIGN

The proportional-integral (PI) controller hasbeen widely used in industry for a long time dueto its simplicity and reliability. Unfortunately, usinga fixed PI controller, it is difficult to obtain both agood transient response and a good load disturbancerejection capability. To solve the difficulty, an adaptivecontroller has been proposed. Several different types

of adaptive controllers have been discussed [1415].Here, three different types of adaptive controllerare used to control the linear motor. The details arediscussed as follows.

A. Backstepping Adaptive Controller Design

By substituting (5) into (6), we can obtain

d

dtvm=_vm

= 1

M(Fe FLBvm)

= 1

M(Ktiq FLBvm)

=A1iq+A2FL+A3vm (9)

where A1=Kt=M,A2= 1=M andA3= B=M arethe parameters of the system. In the real world, themotor parameters cannot be precisely measured. Inaddition, these parameters are varied while the motoris saturated or its temperature is increased. As a result,the real parameters of the system include the nominalparameters and their variations [14]. Then, (9) can berewritten as

_vm=A1iq+A2FL+A3vm+ A1iq+ A2FL+ A3vm

=A1iq+ (A2FL+ A1iq+ A2FL+ A3vm) +A3vm

=A1iq+ d1+A3vm (10)

where d1 is the amount of the parameter variationsand external load, and it can be expressed as

d1=A2FL+ A1iq+ A2FL+ A3vm: (11)

602 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 2 APRIL 2004


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The position error, the difference between theposition command and the real position, is expressedas

e1=ymym: (12)

From (12), we can take the derivation of the positionerror and express the result as

_e1=_ym _ym: (13)

We define the velocity command of the PMLSM as

vm=_ym+ De1+F

e1dt

=_ym+ De1+Fx1 (14)

wheree1 is the position error. D is the proportionalcontroller gain,Fis the integral gain, and x1 is theintegral result ofe1. By taking the differential of (14),we can obtain

_vm=ym+ D _e1+Fe1: (15)

After that, we can define the speed error of the motoras

e2= vm vm: (16)

By taking the differential of (16) and substituting (15)and (10) into it, we can easily obtain

_e2=ym+ D _e1+Fe1 A1iq d1A3vm: (17)

Combining (8), (13), and (16), we can derive

_e1=_ym _ym

=_ym vm

=_ym v

m+ e2: (18)

By substituting (14) into (18), we can easily obtain

_e1= De1Fx1+ e2: (19)

Then, we can define a Lyapunov function as

V=1

2e21+

1

2e22+

1

2

1

d21+

1

2Fx21 (20)

whereV is the Lyapunov function, e1 is the positionerror, e2 is the speed error, is the positive weightingfactor, and d1 is the error between the real uncertainty

and the estimated uncertainty. The estimated error

d1is defined as

d1= d1 d1 (21)

where d1 is the estimating value of the totaluncertaintyd1.

From (20), we can obtain the derivation of theLyapunov function as

_V= e1 _e1+ e2 _e2+1

d1

_d1+Fx1e1: (22)

By combining (17), (19), (21), and (22), we canobtain

_V= De21+ e2[(1+F)e1+ D _e1+ym A1iq d1 d1 A3vm]

1

d1

_d1: (23)

In this work, to simply the control algorithm, weassume the real current can track the current command

well. Then, we set the current command as the controlinput, and it is expressed as

u = iq= iq

= 1

A1[(1+F)e1+ D _e1+y

m d1A3vm+ Ge2]

(24)

where iq is the current command amplitude, and G isa positive gain.

Substituting (24) into (23), it is not difficult toobtain

_V= De

2

1Ge2

2

1

d1

_

d1 d1e2: (25)

By designing an adaptive law _d1= e2, we can

remove the last two terms. Equation (25), therefore,can be reduced as

_V=De21 Ge22 0: (26)

In order to discuss the convergence of the drivesystem, the Barbalats lemma is applied here. First,the functionZ(t) is defined as follows

Z(t) = De21Ge22: (27)

By integrating both sides of (27), we can obtain 0

Z()d= V(e1(0), e2(0),d1(0))

V(e1(), e2(), d1()): (28)

The values ofe1(0), e2(0), andd1(0) are bounded.

In addition, the _V 0, therefore, the values ofe1(),

e2(), andd1() are also bounded. Then, from (28),

we can observe that the integration ofZ(t) is bounded.From (27), it is easy to understand that the integration

of the position error square e21(t) and the integrationof the speed error square e22(t) are bounded as well.After deriving that the e1(t)

2 ande2(t)2 are uniformly

continuous, one can use Barbalats lemma and obtainthat

limt

Z(t) = 0: (29)

Equation (29) means while the time approachesinfinite, the position error and the speed errorconverge to zero. As a result, the proposed PMLSM

LIU ET AL.: ADAPTIVE CONTROLLER DESIGN FOR A LINEAR MOTOR CONTROL SYSTEM 603


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Fig. 1. Block diagram of backstepping adaptive control system.

drive system is stable. The block diagram of theproposed closed-loop drive system is shown in Fig. 1.

B. Self-Tuning Adaptive Controller Design

Equation (9) can be easily rewritten as

M_vm= Bvm+ iq FL: (30)

The parameters of (30) can be defined as follows

M=M

Kt(30a)

B= B

Kt(30b)

FL=FLKt

: (30c)

Then, by substituting (8) into (30), we can obtain

Mym= B _ym+ iq FL: (31)

In this work, we select the variable W as

W= 1e1+ e2= 1e1+_e1: (32)

By taking the differential of (32), we can obtain

_W= 1 _e1+_e2: (33)

Then, by combining (13), (16), (31), and (33), we canobtain

M _W= M[1( _ym _ym) + ( _v

m _vm)]

=iq+ M(1e2+_v

m) +

Bvm+FL: (34)

In the real world, however, the M, B, and FL cannotbe precisely measured. The estimated parameters toreplace the real parameters of the motor are used here.We select the estimating parameter vector as

T = [

M

B FL]: (35)

Then, we define the state vector Y as

Y= [1e2+_vm vm 1]

T: (36)

By substituting (35) and (36) into (34), we can obtain

M _W= iq+ TY: (37)

We select the control inputiq as

iq=TY + 2W (38)

substituting (38) into (37), it is not difficult to obtain

M _W=TY2W (39)and

T = T T

= [M M B

B FL

FL]: (40)

We select the Lyapunov function V as [16]

V= 12 1MW 2 + 12

T: (41)

By taking the differential of equation (41), we canobtain

_V= 1WM _W + T_: (42)

Substituting (39) into (42), we can obtain

_V= T(1WY + _) 12W

2: (43)

We select the adaptive law as

_ =1WY: (44)


_V=12W2: (45)

From (39), we can derive

0

W2d= 112

0

_Vd

= 1

12[V(0)V()]: (46)

TheW is bounded because V(0) and V() arebounded. In addition, the W is uniformly continuous.According to Barbalats lemma, we can obtain

limt

W(t) = 0: (47)



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Fig. 2. Block diagram of self-tuning control system.

Fig. 3. Block diagram of model reference control system.

Then, from (32), we can obtain

limt

e1(t) = 0: (48)

Equation (48) shows that using a self-tuning controllerand in steady-state condition, the position error of thePMLSM is equal to zero. The block diagram of theself-tuning control system is shown in Fig. 2.

C. Model Reference Adaptive Controller Design

The proposed model reference adaptive PMLSMposition control system is shown in Fig. 3. By on-lineadjusting the feedback gains, the PMLSM positioncontrol system can match the reference model well.

The details are discussed as follows.In order to obtain a model reference adaptive

controller, an adaption law is used here to adjust thefeedback gain vector to an ideal vector Q. First,define the control input u as

u = Qw= [K Q1 Q2 Q

3]

r

w1

w2

yp

(49)

where Q is the ideal feedback gain vector .

According to Fig. 3, the dynamic system can bedescribed as

_Yc=

Ap 0 0

0 h 0

CTp 0 h

xp

w1

w2

+

Bp

1

0

u

=Ac1Yc+ Bcu: (50)

In (50), it is easy to observe that

Ac1=

Ap 0 0

0 h 0

CTp 0 h

(51)

and

Bc=

Bp

1

0

, Yc=

xp

w1

w2

: (52)

Equation (50) includes two parts: the uncontrolledsystem states xp and the feedback controller statesw1 andw2. The uncontrolled system dynamics can



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be described as

_xp=

_yr_vr

=

0 1

0 B

M

yr

vr

+

0KtM

u

=Apxp+ Bpu (52a)

and

yp= CT

pxp

= [1 0]

yr

vr

: (52b)

Next, we derive the closed-loop system dynamicequation. First, by substituting control u shown in (49)into (50), and suitably arrange it, we can obtain

_Yc=Ac1Yc+ Bcu

=Ac1Yc+ BcQTw + Bc(uQ

Tw)

=AcYc+ BcKTr + Bc(uQ

Tw) (53a)

and

yp= CTPxp

= [CTp 00]Yc

= CTcYc: (53b)

In (53a), the matrixAc is expressed as

Ac=

Ap+ BpQ3C

Tp BpQ

1 BpQ

2

Q3CT

p h + Q1 Q

2

CTp 0 h

: (54)

In this paper, the reference model is expressed as

_Ym=AcYm+ BcKr (55)

andym= C

TcYm (56)

whereYm is the output vector, and ym is the position ofthe motor.

From (53a) and (55), we can obtain

_e = _Yc _Ym

=Ace + Bc(uQTw) (57)

ande1= C

Tce (58)

wheree is the error vector between the real outputvector Yc and the reference output vector Ym, ande1 is the error between the real position yp and thereference positionym. According to (55)(56), we canobtain

ym= CTc(sIAc)

1BcKr

= Wm(s)r: (59)

In (59), we can observe that the transfer function ofthe model reference is

Wm(s) = CTc(sIAc)

1BcK: (60)

Substituting (60) into (57) and (58), we can derive

e1= 1

KWm(s)(uQ

Tw): (61)

In order to make the adaptive control system track a

second-order reference model, the error dynamic canbe modified as follows:

_e =Ace + BcK 1

K(uQTw)(s +p)(s +p)1

=Ace + Bc11

K(u1Q

Tw)(s +p): (62)

From (62), we can observe that

Bc1= BcK (63)

u1= (s +p)1u (64)

w= (s +p)1w: (65)

In the real world, Q is unknown. As a result, thecontrol input is selected as

u = QTw: (66)

Then, from (64)(66), we can observe

u1=QTw: (67)

By substituting (67) into (62), we can derive that theerror dynamic equations are expressed as

_e =Ace + Bc11

KQTw(s +p): (68)

In addition, by substituting (65) and (66) into (61), wecan derive

e1= 1

KWm(s)

QTw(s +p) (69)

where QT is the error between QT andQT.By comparing (64) and (67), we can obtain

u = (s +p)u1

= (s +p)QTw

= _QTw +QTw: (70)

The parameter _QT is obtained from adaptation law. In

order to derive the adaptation law, selecting a suitableLyapunov function is required. To define a Lyapunovfunction, a new parameter e is defined as

e = eBc11

KQTw: (71)

Taking the differential value of (71) and substituting itinto (68), we can obtain

_e =Ace + (AcBc1+ Bc1p) 1

KQTw: (72)



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Fig. 4. Implemented system.

Fig. 5. Measured square-wave position responses for thee different controllers. (a) Position (b) Speed.

Rearranging (71) and substituting it into (58), we canobtain

e1= CTce: (73)

Next, we select a Lyapunov function

V=eTPce +1

2QT1Q

1K (74)

andPc satisfies the following two equations:

ATc Pc+ PcAc= Q (75)

and

PcBc1= Cc: (76)



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Fig. 6. Measured sinusoidal-wave responses. (a) Position. (b) Speed.

Taking the derivative of (74), and substituting(75)(76) into the derivative result, we can obtain

_V=eTQe +QT

e11

Kw + 1

_Q

1K

: (77)

In this paper, finally, we choose the adaption law as

_Q= we1sgn

1

K

: (78)

In (78), we define

sgn

1

K

=K

K : (79)


_V=eTQe 0: (80)

Equation (80) shows that thee is a nonincreasingvariable. The proposed system, therefore, is a stableposition-control system.

IV. IMPLEMENTATION

The implemented system is shown in Fig. 4.The control system includes four major parts: thelinear motor, the inverter, the personal computer,and the sensing and pulsewidth modulation (PWM)circuits. The personal computer is used to executethe control algorithms. The feedback signals and thecontrol inputs are connected between the hardwarecircuits and the personal computer through theinterfacing card. The sensing circuits include theposition sensing circuit and the current sensing circuit.The PWM signals are obtained by using a 5 kHztriangular waveform to modulate the three-phasecurrent deviations. The lock-out circuit and the delaycircuit are implemented to avoid the short-circuitbetween the upper leg and lower leg of the inverter.The three-phase linear motor is driven by the inverter,which is implemented by using six insulated gatebipolar transistors (IGBTs). The input voltage ofthe inverter is around 154 V dc voltage, which is



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Fig. 7. Measured triangular-wave responses. (a) Position. (b) Speed.

obtained from an ac 110 V with a full-wave rectifierand a 1000F filtering capacitance. As a result, theinput voltage of the inverter is a smooth dc voltagesource. The motor is a 3-phase, 4-pole PMLSM.The parameters of the motor are: Rs= 1:05 -,

Ld=Lq= 0:4 mH, Kt= 14:3 Nt/A,M= 1:8 Kg, andB= 5 Nt.s/m. After suitable feedback of the currentand position sensing signals of the linear motor,the three-phase currents of the linear motor can beadjusted. As a result, a closed-loop control system isachieved.

V. EXPERIMENTAL RESULTS

In this paper, the linear permanent magnetsynchronous motor was made by KollmorgenCompany, typed IL 6-050. The accuracy of theposition sensor is 1 m. The current limit of theproposed system is10 A. The sampling intervalof the position control is 1 ms. Some measured

waveforms are provided here to validate thetheoretical analysis. Fig. 5(a)(b) show the measuredsquare-wave position responses for three differentcontrollers. Fig. 5(a) is the measured position responseand Fig. 5(b) is the relative speed response. As youcan observe, the three different controllers havesimilar responses. Fig. 6(a)(b) show the measuredsinusoidal-wave command responses. Fig. 6(a) isthe position response. Fig. 6(b) is the relative speedresponse. The three different controllers performdifferent phase-lags; however, they are very close.Fig. 7(a)(b) show the measured triangular-waveposition responses. Fig. 7(a) shows the positionresponses and Fig. 7(b) shows the relative speedresponses. Again, the three different controllers havesimilar position and speed responses. In Fig. 6(b)and Fig. 7(b), there are several spikes. The majorreason is that the speed signal is the derivation ofthe position signal. As a result, a small noise inposition signal can generate a large spike in the speed



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Fig. 8. Measured square-wave position responses. (a) With a 20 Nt load. (b) With a 10 times inertia.

Fig. 9. Measured short-distance position responses.

signal. Fig. 8(a) shows the measured square-waveposition response under an external load of 20 Nt.The proposed controllers have good load disturbance

rejection capability. Fig. 8(b) shows the measuredsquare-wave position response when the inertia ofthe system in increased to 10 times. According to the



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Fig. 10. Measured long-distance position responses.

Fig. 11. Steady-state waveforms of a triangular position command. (a) Current. (b) Voltage.



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Fig. 12. Waveforms of square-wave command using backstepping adaptive controller. (a) Position. (b) Position error. (c) q-axis current.

(d) Uncertainty d1.

experimental results, the differences of the position

responses are more obvious when the inertia of thesystem is varied. In addition, the self-tuning adaptivecontroller and the model reference adaptive controller

perform better than the backstepping adaptivecontroller. Fig. 9 shows the measured short-distance

position responses at a 0.1 cm movement. Fig. 10shows the measured long-distance position responsesat a 30 cm movement. Figs. 11(a)(b) show the

measured steady-state current and voltage waveforms

of a triangular position command. Fig. 11(a) isthe measured a-phase current; Fig. 11(b) is the

measured line-to-line voltage between the a-phase andb-phase. The measured current is near a sinusoidalwaveform and the line-to-line voltage amplitude is

around 150 V. Figs. 12(a)(d) show the measured

waveforms of a square-wave command using theproposed backstepping adaptive controller. Fig. 12(a)is the measured position response of a square-wavecommand. Fig. 12(b) is the relative position error.Fig. 12(c) is the measured q-axis current. Fig. 12(d)

is the estimated uncertainty d1. Figs. 13(a)(d) show

the measured waveforms of a square-wave commandby using a model reference controller. Fig. 13(a) isthe position response; Fig. 13(b) is the position errorresponse. Fig. 13(c) is the q-axis current response.Some parameters of the model reference controller arealso measured. Fig. 13(d) is the measured parameter

of K. Fig. 13(e)(g) show the measured parameters

ofQ3,Q2, and

Q1 respectively. As you can see, theparameters converge to near constant values as timeincreases. According to the experimental results,



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Fig. 13. Square-wave position responses using model reference controller. (a) Position. (b) Position error. (c) q-axis current.(d) Parameter K.

the three different controllers have a very similarsteady-state position error, which is 1 m. For alinear motor drive, both steady-state performance andtransient response are important. In order to evaluatethe dynamic performance, the different performanceindices, which are the integration of the square ofthe position error, are shown in Table I. The unit

of Table I is cm2.s. As you can observe, the threecontrollers have different performance indices. Forthe time-varying sinusoidal-wave command, thetriangular-wave command, and the inertia varyingcase, the model reference adaptive controller performsbetter than the other controllers. On the other hand,for square-wave command, the self-tuning adaptivecontroller has the best performance. Generallyspeaking, the backstepping adaptive controller has thesimplest computing process; however, its performance

is a little worse as compared with the two othercontrollers. According to the results of Table I, thedesigner can select different adaptive controller tosatisfy their real applications. For example, if theapplications focus on triangular-command positioncontrol, the model reference adaptive controller isthe best choice. On the other hand, if the applications

focus on square-wave control or step-input control, theself-tuning adaptive controller is the best candidate.The detailed design procedures of the controllersare clearly discussed and proved here. In the realworld, there are some difficulties that should be faced.The selection of the tuning parameters relies on thedesigners experience. For example, the designershould properly choose the following parameters: D,

F,G, and of the backstepping adaptive controller,1, 2, and 1 of the self-tuning controller, andp,h,



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Fig. 13. Continued. (e) Parameter Q3

. (f) Parameter Q2

. (g) Parameter Q1

.

TABLE IIntegration of Square of Position Error for Different Controllers

ControllerCommand Backstepping STC MRAC

square 10 cm 0.003801 0.001097 0.004646

sinusoidal 5 cm 0.000934 0.000785 0.000028

triangular 10 cm 0.000442 0.000624 0.000042

square 10 cm and20 Nt

0.018698 0.002218 0.011230

square 10 cm and10 times inertia

2.975864 1.616673 0.870155

square 0.1 cm 0.0000036 0.00000072 0.000026

square 30 cm 21.876602 22.876022 25.184871

of the model reference controller. As a result, doingcomputer simulation is required before executing theimplementation. By using this way, a lot time in trialand error can be reduced.

VII. CONCLUSIONS

In this paper, three different adaptive controltechniques have been applied to a PMLSM. Thesystematic design procedures have been discussed. Byusing the proposed controllers, the PMLSM controlsystem has satisfactory performance in transientresponse, load disturbance rejection capability, andtracking ability. Several varying commands areused to evaluate the proposed PMLSM system. Thispaper proposes three design methods of the adaptivecontroller for a PMLSM position control system.

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Tian-Hua Liu (S85M89SM99) was born in Tao Yuan, Taiwan, Republicof China, on November 26, 1953. He received the B.S., M.S., and Ph.D. degreesfrom National Taiwan University of Science and Technology, Taipei, Taiwan, in1980, 1982, and 1989, respectively, all in electrical engineering.

From August 1984 to July 1989, he was an instructor in the Department ofElectrical Engineering, National Taiwan University of Science and Technology.He was a visiting scholar in the Wisconsin Electric Machines and PowerElectronics Consortium (WEMPEC) at the University of Wisconsin, Madison,

from September 1990 to August 1991, and in the Center of Power ElectronicsSystems (CPES) at Virginia Tech from July 1999 to January 2000. From August1989 to January 1996, he was an associate professor in the Department ofElectrical Engineering, National Taiwan University of Science and Technology,where since February 1996, he has been a professor. His research interestsinclude motor controls, power electronics, and microprocessor-based controlsystems.

Yung-Ching Lee received the B.S. degree in automatic control engineering fromFeng Chia University, Taichung, Taiwan, in 2000 and the M.S. degree in electricalengineering from National Taiwan University of Science and Technology, Taipei,Taiwan, in 2002.

He is now working for Mustek, Hsinchu, Taiwan, where he is involved withthe development of the servo control for DVD player applications. His researchinterests include TV tuner module design, high-performance ac and dc motordrives, and single-chip applications for consumer products.

Yih-Hua Chang was born in Taipei, Taiwan, Republic of China, on November16, 1973. He received the B.S. degree in electronic engineering from Fu JenUniversity, Taiwan, in 1997 and the M.S. degree in electrical engineeringfrom National Taiwan University of Science and Technology, Taiwan, in 1999,respectively.

Currently, he is a Ph.D. student at National Taiwan University of Science andTechnology. His research interests include electric-machine drives and powerconverter technology.


adaptive controller design for a linear motor control systems

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