Abstract-In this paper, we propose a nonlinear observer-based adaptive controller for induction motors with unknown load. With the use of the skew-symmetric ...
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 6, DECEMBER 1995
579
Nonlinear Observer-Based Adaptive Tracking Control for Induction Motors with Unknown Load Jung-Hua Yang, Wen-Hai Yu, and Li-Chen Fu, Member, ZEEE
Abstract-In this paper, we propose a nonlinear observer-based adaptive controller for induction motors with unknown load. With the use of the skew-symmetric property of induction motors, a two-stage design technique is applied to construct an observerbased controller for velocity tracking control. To demonstrate the effectiveness of the proposed scheme, a voltage-control type of drive system is set up to perform the task of velocity tracking. The main computing facility consists of two personal computers, PC 486 and PC 286, of which one is to perform the calculation of the control law and the other is to provide the function of pulse width modulation (PWM) and to generate the gating pulses. Satisfactory experimental results are shown in the paper.
1. INTRODUCTION
I
NDUCTION motors have been widely applied as the electromechanical actuators because of their ruggedness, low maintenance, and low cost. Advances in power electronics NOMENCLATURE and microprocessor technology make it feasible to use the induction motors in place of dc and synchronous motors in a U,, , 'Ubs , U,, (w,, , w b T , vcr) Stator (rotor) phase voltages. wide range of servo applications. However, it is very difficult i,,, i b s , ic,(iar,i b T , i c T ) Stator (rotor) phase currents. to achieve high performance with an induction motor, due to "Jds(Vqs) d-axis (q-axis) stator voltage. the intrinsic nonlinear coupling between the dynamics of the d-axis (q-axis) stator current. ids (iqs) electrical part and of the mechanical (torque) part. @dT(@qT) d-axis (q-axis) rotor flux. In a separate-excitation dc motor, the electromechanical Position of rotor flux vector. QS arrangement avoids the dynamics coupling between the stator QT Rotor angle. side and the rotor side, apparent from the torque dynamical Qsl Slip angle. equation. The dc motor can be linearly operated simply by ws Stator angular frequency. keeping the stator current constant. WT Rotor angular speed. However, for an induction motor, the stator windings will Wsl Slip angular speed. Leakage inductances of stator generate a flux which indirectly creates a rotor flux as well. L1s (LlT) Angular separation between the two fluxes results from the (rotor) windings. time delay inherent in the rotor circuit. Since the stator current Lms (Lmr) Magnetizing inductances of stahere is the only source of generating torque, obviously the tor (rotor) windings. LST Mutual inductances between stator and rotor effects will have to be tightly coupled. This should explain why the induction machine cannot be operated stator and rotor windings. as a linear device. Rs (RT) Stator (rotor) resistance. To overcome the problems mentioned above, the field LS(LT) Stator (rotor) self-inductance. M Stator/rotor mutual inductance. orientation control [12] is a widely adopted approach. This method uses a nonlinear feedback to obtain the approximate P Number of pole pairs. decoupling between signals in the stator side and in the rotor J Rotor inertia. side, and cause the dynamics of an induction motor to behave D Damping coefficient. KT Torque constant (= 3pM/2LT). like those of a separate-excitation dc motor. When the fullstate feedback is to be used, it is called direct field orientation TL Disturbance torque. control [8], [9]. But, this method requires accurate flux sensors c 7 Leakage coefficient (= 1 which not only are expensive but also suffer from drawbacks M 2 / L sL,). such as high temperature sensitivity and induced changes to Manuscript received March 28, 1994; revised March 20, 1995. This work the motor structure. Another approach is to use flux observers was supported by the National Science Council, R.O.C., under Grant NSC in place of the previous sensors. This method is called indirect 84-2622-E-01 1-005. J.-H. Yang and W.-H. Yu are with the Department of Electrical Engineering, field orientation control. Its stability, robustness, and related control properities are, however, not fully studied yet, although National Taiwan University, Taipei, Taiwan, R.O.C. L.-C. Fu is with the Department of Electrical Engineering and the De- the field orientation control performs well in practice. partment of Computer Science and Information Engineering, National Taiwan In the past few years, the advances in nonlinear control University, Taipei, Taiwan, R.O.C. theory have incurred a notable impact to the field of research IEEE Log Number 9415127. 0278-0046/95$04.00 0 1995 IEEE
580
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 6, DECEMBER 1995
on induction motor control. Input-output decoupling control via geometric techniques was presented in 131 and [41. In [4], a simplified model is used, i.e., only the electromagnetic part is considered and the speed is assumed to be a slowly varying parameter. Exact decoupling of the control of electric torque from that of flux amplitude by taking the amplitude and the frequency of the voltage supply as inputs are achieved through a static state feedback. On the other hand, the results in [21], [22] are based on the adaptive control theories of linear systems so that linearized models of induction motors are used for controller design and for stability analysis. In contrast, the work in [I81 proposed an adaptive tracking control scheme based on the nonlinear model. Moreover, Marino [5], [6] proposed a direct adaptive controller for speed regulation, in which the motor model is input-output decoupled by a feedback-linearizingtechnique while the load torque and rotor resistance are adapted in time. The results of that is the insurance of asymptotic convergence of the system states and the estimated parameters. In all the aforementioned results [4]-[6], [1&1,however, the condition to have the full states available is needed. But, practical implementations will require the use of flux observers [IO], and hence a good deal of research efforts have been directed toward the design of such overall nonlinear controllers. Some results such as [5] and [6] have been proposed to build controllers in combination with the flux observers of [lo]; however, no proof of stability was given for the resulting closed-loop system yet. In [5], the observer-based adaptive controller was designed and the closed-loop stability was provided under several restrictive assumptions. In [151, closed-loop stability is ensured by use of the techniques for designing nonlinear feedback control [ 161, but suffer from the singularity problem of the control laws as in [3]-[6], [15], and [18]. The globally stable controller for regulating torque and flux amplitudes was presented in [171 and [25]. Using the skew-symmetricproperties of the model of induction motors, a controller without singularity is designed by using a flux observer, but only torque regulation and flux regulation are achieved. In this paper, we propose a nonlinear observer-based adaptive controller for induction motors. Via the use of skewsymmetric properties of the model [17], the two-stage design technique [18] is applied to construct an observer-based controller for velocity tracking control. The parameters of the load torque do not have to be known prior to the design. To demonstrate the effectiveness of the proposed scheme, an experiment on the velocity tracking control is performed. In order to implement the proposed scheme for experiment, a voltage-control type of drive system [131, [141 has been set up. The main computing facility consists of two personal computers, namely, PC 486 and PC 286. One is taken to perform the calculation of the control laws whereas the other is to provide the function of pulse width modulation (PWM) and to generate gating pulses. The layout of this paper is as follows. The nonlinear model of the induction motors is shown in Section II. Such a model is then rearranged for the controller design, in which torque load is taken into more realistic considerations. In Section 111,
the controller is proposed and the main results of this paper are derived as well. Experimental setup as well as the results are presented in Section IV. Finally, the conclusions are provided in Section V. 11. MODELOF INDUCTION MOTORS With the notations in [I] and [31, the dynamics of a balanced 3-phase Y-connected induction motor that has symmetric, and linear magnetic circuits can be described as a fifth-order statespace dynamical system. Let the motor have p poles, then, after a coordinate transform onto the dq coordinate frame rotating synchronously with an angular speed w,, the dynamical system can be re-expressed as follows: ids
=-alids
iqs = - U s i d s
+ wsiqs+
UZ@d,
- aliqs
a3W,@d,
&dT
= -a4@dT f
a,,
= -a4Qqr
WT =
+
+
+ + a2@qr +
a3w,@qr
CVdS
(1)
CVqs
a5ids
+
(WS - pur)@,,
(2) (3)
a5iqs
- ( U , - pw,)@&.
(4)
-
-Dw,+ Te - TL
(5)
J
Te = k T ( @ d r i q s
(6)
- Qqrids)
v,,,
where v d s , ws are control inputs and T, is the generated torque. The definitions of the notations and symbols are given in the Nomenclature. It can be seen shortly that the dynamical model described by (1)-(6) possesses a skew-symmetric property, which will be used subsequently in the design of the controller. In order to manifest this property, we first rearrange the dynamical equations by using more compact notations as follows. DenotingzT =[$I xz x3 5 4 ] = [ids zqs ad, @*,I,
XT u2
z5]=
=[ZT
= V,,,
u3
[id,
@qr
ip
UT],
+
+
f
a3Z5x4
22
= - U 3 2 1 - a122 - a 3 x 5 2 3
a2x4
23
=-a423
21 =-alxl
i 4 x5
UI
=
I&,
= w s , we can rewrite (1)-(6) as u3xZ
a253
+ + + - D x ~+ Te - TL = -a4x4
+
-I)Z5)24
a551
(U3
a5%2
(U3 -P 2 5 ) 2 3
f
CUI
+
Cu2
(7) (8) (9)
.T
T, = kT(53ZZ - 5 4 x 1 ) .
(12)
Note that (7)-(10) can be further rewritten in a more compact symbolic form as
YANG er al.: NONLINEAR OBSERVER-BASED ADAPTIVE TRACKING CONTROL FOR INDUCTION MOTORS WITH UNKNOWN LOAD
581
A. First Stage Controller Design
Referring to (ll), i.e.
to
and
B e
0
[i i].
It should be noted that
AiT
=
0
0
1
+ D x +~ TL = T,,
J k 5
the output signal in this stage is w, and the generated torque T, is viewed as the input. If we want the output signal x5 to track X 5 d , a sufficient condition is to have the input signal T, be equal to the desired torque T d as follows: A 1
is a skew-symmetric matrix, i.e.,
-Al.
In the following, we assume that the torque load is a known function of the rotor speed with unknown constant parameters. This assumption is more realistic than the one with constant load [15], [17], [18]. It is well-known that the bearings and lots of viscous forces vary linearly with the speed, while the largescale fluid systems such as pumps and fans have loads that typically vary in a way proportional to the square of the speed [19]. Hence, the torque load is assumed to be in the form of
Td
+ k1e5 + f i o f
= J55d
(fi1
+ 0 ) X 5 + fizz;
where e5 = 2 5 - X 5 d and jh,j i 1 , f i 2 are estimates of PO, pi, p 2 , respectively. If TL is replaced by (14), we then have
J15 + k l e 5 = T, - T d - wTe"
(16)
where e" = 8 - 8 denotes the parameter estimation error. Since T, is not the actual exogenous input and the parameters are not accurately known, the right hand side of (16) can not be made identically zero. B. Second Stage Controller Design
Where Po, P I , P 2 are Some Unknown constants, [I, 2 5 , and dT = [ p i , ~ 2 ~ ,3 1 .
WT(Z5)
=
111. CONTROL OF INDUCTION MOTORS
Given the dynamic model of an induction motor described in the previous section, the control problem is stated subjected to some prior assumptions about the system in the following. Assumptions: 1) The motor parameters are known in advance. 2) Rotor speed 2 5 and stator currents xi, 2 2 are measurable. 3) The desired rotor speed w d E C 2 , i.e., w$), the ith derivative of W d , i = 1, 2, exist and are continuous. Control Objective: Given a desired rotor speed trajectory determine the control inputs U I , u 2 , U 3 such that the rotor speed w, can track the desired trajectory exponentially in time t, i.e.
In this stage, we just take (7)-(10) into consideration. Here, the generated torque T, is viewed as the output, and the input signals are u l , u2, and ~ 3 It. is easy to show that as X 4 = X 4 d = 0, X 3 = x 3 d = p, 2 2 X 2 d = T d / k ~ , i 3the , generated torque will coincide with T d from (12). Note that the desired trajectory X l d for 2 1 can be arbitrarily chosen without affecting the desired output torque T d , whereby an additional control input to the system can be obtained by appropriately specifying X l d as will be shown. Let e = x - X d , where X: = [ z l d , X 2 d , x 3 d , Q d ] , zT = [ X 3 2 4 1 , iT= [ 2 3 241, and .ZT = zT - ET = [53, 5 4 1 = [z3- 23 x4 - 241, where 23, 24 are the estimates of the flux states 2 3 and X4, resPectivelY. From (131, we have
6 = (A0 + A i
---f
X5d,
as t
-+
00
+
- (a2
a151d
+
U2
= [;2d
-+@, as t
---f
00
and
xld
Gqr + O ,
as t
-+ 00.
In the following, the proposed controller is motivated by the two-stage analysis first presented in [18]. The model of an induction motor can be viewed as a cascade of two subsystem, or in other words as a two-stage system.
-
a4
Zld)
+
a553d
+
Vl]/C
a5)(24 - X4d)
a5
-5 2 d
P
1
= - p f - 213 a5 a5
so that
+
- ( a 2 a5)X3d - X3d) - a325(24 - z 4 d )
- U3X2d
(18)
+alX2d +U3Xld +a3z5X3d + a 3 z 5 ( 2 3 - X3d)
- (a2 f U3 =px5 f
@?dr
- k d + (A0 + A 1 + A 2 ) X d + BU (17)
a5)(23
-k2(zl
assuming that the signals xi, 2 2 , and z5 are available. Furthermore, the rotor fluxes are also regulated according to the desired commands, i.e.
A2)e
which motivates us to design the control inputs u l , u2,us, and X l d as U1 = [ i l d
ic5
+
1
-
- 214
P
- k 3 ( 5 2 - X 2 d ) f .2]/.
(19) (20) (21)
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 6, DECEMBER 1995
582
where
Here, ,512, E22 are some correction terms chosen for the purpose of canceling the coupling terms in (23), namely, R(t, Z), whereas G I , are designed for canceling the coupling terms in the overall closed-loop dynamics.
C. Main Results Theorem 1: Consider an induction motor whose dynamics are governed by (1)-(6) under the assumptions (Al)-(A3). Then, the control objective can be achieved provided the observer-based controller is designed according to (18)-(21) with
and
1
= -( J 2 5 d
KTP
+ (bi +
+
+ ,& + + +
kik5
O ) i 5
ji2.g
{ H 2 ( 2 5 d , k5dr
KTP + [kl
+
(fil
1 -Hz+KTP '
[-D25
bo,
,&, &,
H 3 ( b 1 , b2, 2 . 5 )
+K T ( 2 3 2 2 -5 4 x 1 )
-
WT6]
and
H2 = J 5 5 , H 3 =ki
-
klk5d
+ & + /&25 +
+ +D) + (ji1
,&22
2b2X5.
Note that i l d , & ? d are compensated signals yet to be defined, k 2 , k3 are feedback control gains, and vz, i = 1, 2, 3, 4, are additional control terms used for cancelling the coupling terms in the subsequent closed-loop stability analysis. Remarks: 1) In the above derivation for x z d , k 5 has been replaced by (1/J)[-D25 K T ( 2 3 2 2 - 2 4 2 1 ) - WT6]from (111, (12). 2) In the proposed control law (181, i l d and & d , respectively, denote the estimation of i l d and k 2 d which may be unknown due to the unavailability of Aux signals and load parameters. 1) Observer Design: In order to estimate the flux signals, we design a nonlinear observer as follows:
+
!3 = - a 4 8 3
84
= -U484
+ a 5 2 1 + (us + U522
+t i 1 + 612 P X 5 ) 2 3 + ( 2 1 f (22
-P
- (U3 -
25)24
(25) (26)
where tzJ, 1 I i, j 5 2, are some suitable functions to be specified in the following. Then, the estimation errors satisfy
z" = - a 4 1 2 5
=k T X l d e 5
(31)
U4 x5)
+D)+2b2X5125)
1 KTPJ
(28) (29) (30)
=k
~ 2 4 e 5
v2
2@225k;;5
1
=
=- k ~ 2 3 e 5 v3 = - k ~ x 2 d e 5
v1 &z5
- ( ~ -3 p 2 5 ) J2zX
where
a 12 = diag[1, 11
+E
(27)
YANG et al.: NONLINEAR OBSERVER-BASED ADAPTIVE TRACKING CONTROL FOR INDUCTION MOTORS WITH UNKNOWN LOAD
583
where
where a0
= min ( a 1
+
k2, a2
+ k3,
Furthermore, by substituting the definitions of (36), we obtain V
By applying 8, 5 1 2 , and established:
a4). 213
and
v4
122,
the following inequality can be
into
5 -aallel12 - a 4 1 1 , ~ 1 1-~ kle; + eTR(t,z")- t 1 2 5 3 given that QO, a 4 , k1 are positive constants. Consequently, all - t 2 2 2 . 4 - e 5 w ~+08Tr-G. (37) signals in the closed-loop system remain bounded, i.e., Ilell,
It should be noted that T d which needs to be used for implementing k 2 d and k 1 d includes the term i s . This is the and $ld. reason why we design i 2 d and i l d instead of Accordingly, the more detailed expressions of k l d and x 2 d are derived in the following. Since
we then have
11211, and e 5 E L , from Lyapunov theory. Besides, due to the boundedness of all state variables and control inputs we can further guarantee &, b, 65 E L,. Furthermore, if we take V d t = V(m) - V ( 0 )< integration of V , we can obtain CO which, in turn, implies Ilell, 11i?(1, and e 5 E La. All together, we conclude that Ilell, 1)211, and e 5 -+ 0 asymptotically via Barbalat's lemma [23]. IV. EXPERIMENTAL RESULTS
The proposed controller is tested in a squirrel-cage motor system rated one horse power (HP) and with an optical encoder attached to its shaft, a PWM transistor inverter, and two personal computers (PC486 with 16 bits A/D D/A card and PC286) communicating through 8255 cards. The configuration of the system is shown in Fig. 1. where
A. Rotor Position and Current Detection The rotor position is detected by a dual-pulse (with complementary outputs) optical encoder with two phases set apart by 90". The resolution is 1024 pulses per revolution. The pulses pass through a digital circuit, which aims to accumulate the number of passing pulses with 12 bit counter. The corresponding speed is calculated by PC486. Because of the balanced three phases, i.e., i,, + i b s +i,, = 0, two currents are adequate for the coordinate transformation. Currents are measured with Hall effect transducers (LB-1OGA) and low-pass filters. B. Control Algorithm Processing
The control algorithm runs on PC486. In each period of 2 ms, the program performs the following tasks: rotor position acquisition and current sampling, speed calculation, coordinate transformation, control algorithm execution, data fetching to the common memory for PC286, and informing PC286.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 6, DECEMBER 1995
584
Rotor Speed
1EE
1
80286
AT-BUS
I Fig. 2. Velocity tracking for
W d
= 8O(I - e-1.5t) radis.
8255 (2) Fluxes respanse
8.2,
I
r----l
Fig. 3. q-axis flux estimation.
us
t
Fig. I. Configuration of experimental system.
C. Gating Pulse Generator
The gating pulses are generated by comparing the carrier signals with the three-phase sine waves, which are precalculated and stored in memory as look-up tables in PC286. Each sine wave (there are totally 128 sine waves with different magnitudes) is recorded in a look-up table with 1024 entries, which store the values of the sine wave at 1024 different phase angles. The reference frequency determines the time interval between two pieces of data as 1
AT=1024f s where AT is the interval between every two pieces of sine wave data, and f a [ = (w,/2n)] is the stator frequency. The time interval is controlled by the interrupt service routine which is generated by the timer 8253. The amplitude and phase angle of the stator voltage, v, and 4,respectively, are determined from V d s and uqS as: 21,
=Jm
4 = arctan -.vq s vds
D. Communication Between Two PC's
The PC286 is used to generate the proper sine wave data according to the desired amplitude v,, the required initial 4,and the time interval phase angle of stator voltage 0, AT. For the limitation of the interrupt interval, the output data
+
-+-
are generated every n steps ( n = [ f s / 2 0 ] 1).Therefore, the practical time interval equals to AT = n/1024fs. Moreover, U,, f,, and 4 are calculated in PC486 and are stored into common memory. As soon as the new data are ready, the PC486 sends a semaphore to PC286, which then fetches them and produces the proper data.
E. Results The squirrel-cage motor used in the experiment is manufactured by ELMA MOTOR'S CO. with delta-connected stator. The parameters of the motor are shown below: I 1) Rated power = 0.75 kW 2) Rated current = 4 A 3) Rated voltage = 220 V 4) Rated frequency = 60 Hz 5 ) Rated speed = 1120 r/min 6) poles = 6 7) R, = 3.745 n 8) R, = 3.583 0 9) L, = 163.3 mH 10) LT = 163.3 mH 11) L, = 154.67 mH Two desired trajectories for velocity tracking control are presented in the experiment. The first desired trajectory is Wd = 80(1 - e-' 5 t ) rads, or equivalently, W d = 80(1 e-l 5 t ) x ( 6 0 / 2 ~ ) rpm, and the tracking result is shown in Fig. 2 where the unit on the horizontal axis is 7.2 ms. The flux estimations 2s and are plotted in Fig. 3 and Fig. 4, respectively. Moreover, for demonstration of sinusoidal tracking capability the second trajectory is chosen as Wd = 80 sin ( t ) 20 sin ( 3 t ) radsec. Similarly, the plot for velocity tracking is shown in Fig. 5 whereas the flux estimations are shown in Figs. 6 and 7.
+
V. CONCLUSIONS
From the skew-symmetric property of induction motors, the observer-based adaptive controller is proposed via Lyapunov
..
YANG et al.: NONLINEAR OBSERVER-BASED ADAPTIVE TRACKING CONTROL FOR INDUCTION MOTORS WITH UNKNOWN LOAD
-8.2
L
E
188 (
388
288
488
one point = 7 . 2 ” s 1
588
788
CBE
888
I 988
Sampling tine = 8.24”s
Fig. 4. d-axis flux estimation. Rotor Speed
188 r
-188
I
E
I
I 188
288
388
488
588
688
788
888
988
Fig. 5. Velocity tracking for wd = 80 sin ( t )+ 20 sin ( 3 t ) rad/s. F l u x e s response
i
8 -8.85
p E
188
ZER
r 388
488
588
688
588
688
788
888
988
888 8.24~s
988
Fig. 6. q-axis flux estimation.
8.1
-6.1
E
188 (
288
388
488
one point = 7.2ns 1
788
Sampling time
3
Fig. 7. d-axis flux estimation.
analysis. Without the measurement of fluxes, velocity tracking can be achieved under the assumptions that the motor parameters are known but without the knowledge of load parameters. The experimental results have shown the effectiveness of the proposed controller in combination with the flux observer. The future theoretical work will attempt to enhance the robustness of the controller and/or to add parameter estimation with an adaptive observer.
585
[5] R. Marino, S. Pereada, and P. Valigi, “Adaptive partial feedback linearization of induction motors,” in Proc. 29th CDC, 1990, pp. 33 13-33 18. [6] -, “Adaptive input-output linearizing control of induction motors,” IEEE Trans. Automat. Contr., vol. 38, no. 2, pp. 208-221, Feb. 1993. [7] W. Leonhard, “Microcomputer control of high dynamic performance AC-drives-A survey,” Automatica, vol. 22, no. 1, pp. 1-19, 1986. [8] A. B. Plunkett, “Direct flux and torque regulation in a PWM inverterinduction motor drive,” IEEE Trans. Ind. Applicat., vol. IA-13, no. 2, Mar./Apr. 1977. [9] T. A. Lip0 and K. C. Chang, “A new approach to flux and torquesensing in induction machines,” IEEE Trans. Znd. Applicat., vol. IA-22, no. 4, July/Aug. 1986. [lo] G. C . Verghese and S. R. Sanders, “Observers for flux estimation in induction machines,” IEEE Trans. Ind. Electron., vol. 35, no. 1, Feb. 1988. [11] A. Bellini, G. Figalli, and G. Ulivi, “Analysis and design of a microcomputer-based observer for an induction machine,” Automatica, vol. 24, no. 4, pp. 549-555, 1988. [12] R. Gabriel, W. Leonhard, and C. Nordby, “Field-oriented control of a standard AC motor using mircoprocessors,” ZEEE Trans. Znd. Applicat., vol. IA-16, no. 2, Mar./Apr. 1980. [13] Z. K. Wu and E. G. Strangas, “Feed forward field orientation control of an induction motor using a PWM voltage source inverter and standardized single-board computers,” ZEEE Trans. Ind. Electron., vol. 35, no. 1, Feb. 1988. [14] K. Kubo, M. Watanabe, T. Ohmae, and K. Kamiyama, “A fully digitized speed regulator using multimicroprocessor system for induction motor drives,” IEEE Trans. Ind. Applicat., vol. IA-21, no. 4, pp. 1001-1008, July/Aug. 1985. [15] I. Kanellakopoulos, P. T. Krein, and F. Disilvestro, “Nonlinear fluxobserver based control of induction motors,” in Proc. 1992 ACC, pp. 1700-1704. [16] I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “A toolkit for nonlinear feedback design,” Syst. Contr. Lett., vol. 18, no. 2, pp. 83-92, 1992. [17] R. Ortega, C. Canudas, and S. I. Seleme, “Nonlinear control of induction motors torque tracking with unknown load disturbance,” in Proc. 1992 ACC, pp. 206-210. [18] J.-H. Jean and L.-C. Fu, “A new adaptive control scheme for induction motors,” in 15th Nat. Symp. Automat. Contr., Taiwan, R.O.C., 1991, pp. 593-601. [19] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design. New York Wiley, 1989. [20] J. Holtz, “Pulsewidth modulation-A survey,” ZEEE Trans. Ind. Electron., vol. 39, no. 5, Dec., 1992, pp. 410-420. [21] C. M. Liaw, C. T. Pan, and Y. C. Chen, “An adaptive controller for current-fed induction motor,” ZEEE Trans. on Aerosp. Elect. Syst., vol. 24, no. 3, pp. 250-262, 1988. [22] C. C . Chan, W. S. Leung, and C . W. Ng, “Adaptive decoupling control of induction motor drives,” IEEE Znd. Electron., vol. IE-37, no. 1, pp. 4 1 4 7 , Feb. 1990. [23] M. Vidyasagar, Nonlinear System Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1992. [24] I. Kanellakopoulos and P. T. Krein, “Integral-action nonlinear control of induction motors,” in Proc. IFAC, vol. 7 , 1993, p. 251. [25] G. Espinosa-Perez and R. Ortega, “An output feedback globally stable controller for induction motors,” ZEEE Trans. Automat. Contr., vol. 40, pp. 138-143, Jan. 1995.
REFERENCES
._
111 P. C . Krause. Analysis of Electric Machinery. ~~
New York: McGraw-
Hill, 1986. [2] B. K. Bose, Power Electronics and AC Drives. Englewood Cliffs, NJ: Prentice-Hall, 1986. [3] D . 4 Kim, 1.4. Ha, and M.-S. KO, “Control of induction motors via feedback linearization with input-output decoupling,” Znt. J. Contr., vol. 51, no. 4, pp. 863-883, 1990. [4] A. De Luca and G. Ulivi, “Design of an exact nonlinear controller for induction motors,” ZEEE Trans. Automat. Contr., vol. 34, no. 12, Dec. 1989.
Jung-Hua Yang was born in Kaohsiung, Taiwan, R.O.C., in 1867. He received the B.S. degree from the Chung-Yaun Christian Univesity, Chung-Li, Taiwan, R.O.C., in 1989, and the M.S. and Ph.D. degrees from the National Taiwan University, Taipei, Taiwan, R.O.C., in 1991 and 1995, respectively, all in electrical engineering. His research interests include nonlinear adaptive control, flexible structure control, motor control, and robotics.
.
.., ._ .
586
,
. . . . ... .. - -
.
.
. .-._ - .. . .
.
. .
.
. _. . . .
. .
.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 42, NO. 6, DECEMBER Wen-Wai Yu received the B.S. degree in control engineering from the Chiao Tung University, Hsingchu, Taiwan, R.O.C., and the M.S. degree from the National Taiwan Univerity, Taipei, in 1991 and 1993, respectively. His research interests include nonlinear control of motor systems and microprocessor-based control systems.
-.. ~
._
I
1995
Li-Chen Fu (S’85-M’S8) was bom in Taipei, Taiwan, R.O.C., in 1959. He received the B.S. degree from National Taiwan University in 1981, and the M.S. and Ph.D. degrees from the University of Califomia, Berkeley, in 1985 and 1987, respectively. Since 1987, he has been on the faculty and is currently a professor in both the Department of Electrical Engineering and the Department of Computer Science and Information Engineering of National Taiwan University. His areas of research interest are adaptive control and systems identification, nonlinear system control, robot motion planning, multisensing, control of robots, FMS scheduling, and neural networks for pattem recognition. Dr. Fu is a member in both the control system and robotics and automation societies of IEEE as well as a board member of the Chinese Automatic Control Society and the Chinese Institute of Automation Technology. He is also an OF CONTROL SYSTEMS AND TECHNOLOGY. He associate editor of the JOURNAL received the Excellent Research Award and the Outstanding Research Award from the National Science Council in 199&1993 and 1994-1995, respectively, the Outstanding Youth Medal in 1991, and the Outstanding Engineering Professor Award in 1994.
t
