Speed Control for Induction

Transcription

1 I INTRODUCTION Robust Variable Structure Speed Control for Induction Motor Drive KUO-KAI SHYU National Central University Taiwan FAA-JENG LIN, Member, IEEE Chung Yuan Christian University Taiwan HSIN-JANG SHIEH BOR-SEN JUANG National Central University Taiwan In order to eliminate the effect of parameter variation on field-oriented control for induction motor drive, an adaptation algorithm for tuning the rotor time-constant is proposed Based on the adaptive observation of the rotor flux linkages, the rotor time-constant is adapted to obtain an exact indirect-field-oriented control (IFOC) In this proposed algorithm, a related function to the variation of the rotor time-constant is designed, then the accurate slip frequency needed for IFOC is obtained from this error function through a PI-type (proportional-integral) Wter Furthermore, a novel variable structure speed control with integral sliding surface is proposed under the adaptive field-oriented operation By means of the variable structure speed control, the dynamics of motor speed has the property of an exponentially convergent rate Using the proposed adaptive field-oriented control and the variable structure speed control, the IFOC is robust to the variation of the rotor time-constant and the speed control is insensitive to parameter uncertainty and load disturbance Finally, some simulation and experimental results are presented to validate the effectiveness Manuscript received May 19, 1997; revised February 17, March 17, and June 12, 1998 IEEE Log NO T-AES/35/1/01501 This work was supported by the National Science Council of the Republic of China under Contract NSC E , Authors current addresses: K-K Shyu and B3 Juang, Dept of Electrical Engineering, National Central University, Chung-Li 320, Taiwan, (kkshyu@eencuedutw); E-J Lin, Dept of Electrical Engineering, Chung Yuan Christian University, Chung-Li 320, Taiwan; H-J Shieh, Mechanical Industry Research Laboratories, Industrial Technology Research Institute, Chutung, Taiwan 1999 IEEE At present, there are two major methods of high-performance control of induction motor drives One is the direct field-oriented control (DFOC), and the other is indirect field-oriented control (IFOC) The IFOC is generally called slip frequency control It offers a feedforward control of decoupling torque and flux components for induction motor drive However, the IFOC is sensitive to the variation of rotor time-constant since the rotor time-constant of induction motor is utilized in the feedforward design of the slip frequency for IFOC [ 1, 21 Therefore, the research for improving the IFOC due to the problem of parameter deviation, especially the rotor time-constant or rotor resistance, has been developed [l, 3-71 In these researches, the reactive power function, flux observer method, Kalman filter method, and model-reference adaptive system method are, respectively, utilized to improve the robustness for the variation of rotor time-constant However, complex adaptation mechanism or spending much computation time is required On the other hand, the flux angle employed directly in decoupling the torque and flux components is called the DFOC which has been investigated in many studies [8-121 The stator-flux-based DFOC is properly operated in the high-speed control range due to the back-emf (electromotive force) voitage effect and is sensitive to the stator resistance deviation Moreover, the rotor-flux-based DFOC is also sensitive to the rotor time-constant deviation Therefore, the adaptive rotor flux observers were developed in [8-131 However, they are very sensitive to the offset of the stator voltage and resistance fluctuation And, moreover, in order to obtain a stable observer, a time-varying control gain of the flux observer is designed Consequently, the adaptive rotor-flux-observer-based DFOC is complex and needs much computation time In this work, a tuning function related to the decoupling angle of the rotor flux vector is designed to adaptively tune the rotor time-constant in IFOC The uncontrolled rotor flux observer based on current model is utilized and a simple adaptation algorithm is proposed to adapt the rotor time-constant of the current model-based rotor flux observer, simultaneously This results in that the completely decoupling control for IFOC is exactly established and the rotor time-constant can be accurately estimated Then, the induction motor drive operating as a dc motor is completed and the electromagnetic torque can be simply controlled by the torque-component current Moreover, using the variable structure control (VSC) to the speed control of induction motor has been presented in many publications [ 13-16] because of the property of a strong robustness of VSC However, in these researches, the acceleration is IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY

2 always needed or an observer for rotor acceleration is designed In order to obtain the acceleration from the speed feedback-signal, an accurate observer or an differentiator for the acceleration signal has to be designed However, the observer and differentiator are very sensitive to system parameter variation and noise signals, respectively To remove these drawbacks of the presented VSC in speed control for induction motor, a novel sliding-surface with integral component for the VSC is proposed Using the proposed VSC with integral sliding-surface, the acceleration information for speed control is not required, and the insensitivity to the uncertainties and disturbances can be assured by theoretical discussion and experimental results Using the proposed speed controller, the exponential stability is obtained First, a novel sliding-surface corresponding to the error dynamics of the induction motor is designed, then the speed error signal is utilized in the VSC From the proposed sliding-surface, it can be seen that the convergent rate of speed error can be determined by a linear constant feedback-gain and the robustness to parametric uncertainties and disturbance load is guaranteed This work is organized as follows The conventional field-oriented control is briefly introduced in Section 11 Then, the adaptive field-oriented control with rotor time-constant adaptation is proposed in Section 111 The novel VSC with integral sliding-surface for speed control is presented in Section IV Finally, some simulation and experimental results are demonstrated in Section V -w, -- for stator and rotor, d and q are the components of a vector with respect to a fixed reference frame, wr is the rotor speed, L, and L, are the mutual and leakage inductances (L, = L, - Li/L,), q denotes the parametric uncertainty of Rr, and R,* is the nominal value of the rotor resistance From (3) and ) the current-model-based rotor flux observer can be designed as,, dadr - --Adr R,", -w A L, r qr + R,"-id, dt Lr Lr --A 7 - +q-iqs Lm L, qr L, A where Ad, and A,, are the estimates of the rotor flux Define the error variables of the rotor flux linkages as Taking the derivative of the error dynamic model with respect to time yields II FIELD-ORIENTED CONTROL OF INDUCTION MOTOR The dynamical model of an induction motor in the fixed reference frame can be described as follows: where is, 4,, V,, R, L denote stator current, rotor flux linkage, stator terminal voltage, resistance, and inductance, respectively The subscript s and r stand (6) It can be seen that the dynamic model (6) is not an asymptotically stable system with q # 0 And, moreover, the parametric uncertainty q usually exists since the rotor resistance is much sensitive to temperature variation Therefore, the complete DFOC via the current-model flux observation cannot be established On the other hand, the IFOC is also very sensitive to the variation of the rotor time-constant because the complete IFOC is entirely determined by the calculation of the slip frequency represented as follows 1 i;; WSl = -- T, iz where wsi denotes the slip frequency and iz4 and is: are the current commands in d and q axes, respectively When the rotor time-constant r, deviates from the nominal value, ie, _- - +A- TT,* r, the actual slip frequency for IFOC becomes w,/ = w;/ + aw,/ 216 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY 1999

3 This leads to problems with the failure of decoupling control in the field-oriented control In this operating condition of the induction motor drive, the power efficiency and the controlled performance are degenerated Therefore, in order to compensate the influence of the variation of rotor time-constant on IFOC, a novel adaptive field-oriented control with rotor time-constant tuning is proposed in Section 111 Ill ADAPTIVE FIELD-ORIENTED CONTROL WITH ROTOR TIME-CONSTANT TUNING First, we introduce the rotor voltage equations of the induction motor in the synchronous reference frame as V$ = Rri;, + PA:, - (we- wr)air v,"r = Rri& + PA:, + (we- w,)a;, (7a) (7b) Due to the feature of the squirrel-cage induction motor, the v,oltage equation (7) in rotor can be written as 0 = Rri$, + PA$ - (we - wr)xir 0 = Rriir + PA:, + (we - wr)a& (84 (8b) Because the detuning is mainly caused by changes in the rotor resistance that occur at a slow rate, it is a reasonable approximation to assume that the terms PAS, and PA;, are close to zeros Hence, the above (8) can be written as 0 = Rri& - (we- wr)air 0 = Rri$ + (we - w,)a& Substituting the following equalities (94 (9b) When a detuning condition occurs, an error in the parameter estimates appears as well as in the rotor flux components, such that the slip frequency given by (12) becomes 1 - wsl = -{(e + AQ)[(AZ + AA;,)i:, Ar2 - (A:; + AA;,)i&]) 1 - = -{(e + A6)[A~i~, + AA;,i;, At - - AA;,i&]} A where 1/T, = 0 and 1/T, = 6 Since As equals A, Ai: = 0 under completely decoupling control, the following equation can be obtained and wsi = L{t?Af;*,is + e^aa$,i& - e^aai,i:, + AQAf;*,i;, At + AOAA$ii, - AQAA:,i&} (13) Moreover, the slip frequency described in (13) can be reinterpreted as 1 - wx1 = w:* + --(QAA$,ig, - 0AA&i:, + AQAgi;, Xr2 + Ab'AA&ii, - At?AAari&} Therefore, the following equality must be guaranteed if the slip command equals actual slip e^aa:,i;, - e^aa:,i;, + ABAgi:, + A0 AA;,ii, - AOAAgri5, = 0 (14) Neglecting both A6 Ax:, and A0 Ax;, and dividing (14) by w:l = ;(Ag)-li;,, (14) is reduced to into (9) yields Under the current-regulated inverter, ig = i;, and i;: = i;,, (15) can be further described where wsr = we - wr is the slip frequency Multiplying (10) by the terms A:r and A;r results in 1 T, dr qr 0 = - L A C ie -w qr ds sl qr ('la) T Subtracting (11 a) from (11 b) and rearranging terms, we have Lm Us/ = m(a$rias - Airi;r)* (12) r r Based on (16), we define an error function Ed = AA:,i& - AAirig, (17) From (16) and (17) it is obviously viewed that the detuning of rotor time-constant can be found through the defined function (16) That is, the actual parameter B can be calculated by e^ + A@ Then, the accurate slip frequency for complete IFOC can be given Moreover, in order to simply regulate the error function (1 7) to obtain the deviation A8, the PI-type filter is used to regulate the error function (17) SHYU ET AL: ROBUST VARIABLE STRUCTURE SPEED CONTROL FOR INDUCTION MOTOR DRIVE 217

4 IV VARIABLE STRUCTURE SPEED CONTROL Based on the complete IFOC via the proposed field orientation, the variable structure speed control with integral sliding-surface is proposed in this section In order to possess the robustness to the variation of motor parameters, especially the motor inertia, and disturbance load-torque, the VSC is utilized to the speed control of the induction motor Moreover, a novel sliding-surface with integral component is designed to remove the need of acceleration of the conventional variable structure speed control for induction motor Under the complete field-oriented control, the mechanical equation can be equivalently described as J- dum + Bw, + TL = KTiis dt where J and B denote the moment of inertia and viscous friction coefficient, respectively, T, is the external disturbance-load, w, is the rotor mechanical speed in angular frequency, and Kt is defined K ---A* 3P L, T - 4 L, (18) where P is the number of poles in the induction motor Furthermore, consider the mechanical equation (1 8) with uncertainties d, = (a+ Aa)w, + (b+ Ab)i;, + d (19) where = -B/J, b = KT/J, and d = -T,/J; Aa and Ab are denoted as the parameter uncertainties defined Aa = A(B/J), Ab = A(K,/J) We further define the speed error as x(t) = w,(t) - w; (20) where wlr, is the speed command Taking the derivative of (20) with respect to time yields where and i(t) = ax(t) + b[u,(t) + 21 (21) - a u,(t) = ie + =wk qs b - Aa Ab d d = -w,(t) + -le + = b b " b According to the uncertain system (21), the sliding-surface with integral component is designed as follows: "+ 1 (22) S(t) = ~ (t) - (a + gk)x(-r)d~ = 0 (23) where k is linear feedback gain When the sliding mode occurs, S(t) = s(t) = 0, the dynamical behavior of the controlled system can be equivalently expressed as i(t) = (3 + bk)x(t) (24) From (24) it is evident that the speed error x(t) will converge to zero exponentially In other words, the controlled rotor speed w, can track the desired speed command asymptotically First, the following assumption is given - Id1 5 P (25) Le, the lumped uncertainty 2 has an upper bound p Then, based on the uncertain system (21) and the designed sliding-surface (23), the variable structure speed controller is designed u,(t) = kx(t) - 0 sgn[s(t)] (26) where sgn() is a sign function defined as THEOREM 1 Using the proposed speed controller (26), the uncertain system (19) is asymptotically stabilized PROOF According to [17], the existence of the sliding mode of the proposed speed control can be derived as: S(t)S(t) = S(t)(X(t) - (a + bk)x(t)} Substituting (21) and (26) into the above equation, we obtain W>S(t> I -151 IS(t>l(P - Jdl) IO Therefore, using the speed controller of (26) the existence condition of the sliding mode in [17] is satisfied And when the state x(t) is trapped on the sliding-surface, the dynamics of the system are determined by (24) which is always stable, so the state x(t) will slide into the origin REMARK The final output of the proposed speed controller (26) for the torque-current component i;s of field orientation is derived by substituting (26) into (22) V SIMULATION AND EXPERIMENTAL RESULTS The block diagram of the experimental induction motor drive is shown in Fig 1 In Fig 1, the voltage-source inverter-fed is utilized The stator currents are sensed by Hall-effect current sensors, LEM module, and regulated by bang-bang controller Equation (17) is used in the error function calculation block Then the output passes through a PI-type filter to estimate the inverse rotor time-constant The proposed adaptation algorithm of estimating the rotor time-constant and the speed control are implemented by microcomputer and TMS320C3 1 DSP-board The 218 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY 1999

5 ~~ 3 phasc 220 v 60 Hz With adaptation ' Without adaptation Encodcr Fig 1 Block diagram of DSP-implemented indirect-field-oriented induction motor drive with rotor time-constant adaptation (b) 0 4 secldiv Fig 4 (a) Adaptive and nonadaptive tuning behaviors of rotor time-constant in speed transient operation (b) Corresponding step speed responses from r/min I Time (sec) 40C-----~~tual inverse rotor time-constant I 30-2o -Estimated inverse rotor time-constant 1; secidiv Fig 5 Speed responses from dmin using VSC and PI controller with and without parameter uncertainty (l/t) = (3/Tn) rotor time-constant with conditions of (a) (1/T7) = and (b) (1/7;) = (3/Tn) under estimate initial (I/?) = vsc with uncertainty Witlmut adaptation z6001 ' wi<t+n 'Without adaptation K 500 (b) ' 04 secldiv 0 4 secidiv Fig 3 (a) Adaptive and nonadaptive tuning behaviors of rotor time-constant in speed transient operation (b) Corresponding step speed responses from dmin insulated gate bipolar transistor (IGBT) module is used in PWM inverter block The induction motor used in this drive system is three-phase Y-connected two-pole 08 KW The characteristics of the experimental induction motor are given as follows Rated stator current = 54 A Rated stator voltage = 120 V Rated load torque = 38 Nm 04 secidiv Fig 6 Speed responses from r/min using VSC and PI controller with and without parameter uncertainty U/q) = (3/T,) Rated speed = 2000 rhin Stator resistance: R, = 117 fl Rotor resistance: R, = Stator inductance: L, = 119 mh Rotor inductance: L, = 11 8 mh Mutual inductance: L, = 113 mh Number of poles P = 2 Motor inertia: J = Nms2/rad Viscous friction coefficient: B = Nms/rad Now, the computer simulation is carried out The dynamical estimation behaviors of inverse rotor time-constant by proposed adaptation algorithms with assumption of 1/T, = 1/T,* and 1/T, = 3/T,, are shown in Fig 2 In this figure, the estimate initials SHYU ET AL: ROBUST VARIABLE STRUCTURE SPEED CONTROL FOR INDUCTION MOTOR DRIVE 219

6 ~ c3 0 5sec : : : 0ssec: CHI=ZV j CHSZV : : : 5oompldiv DG la1 i : Dd 103 i i i (500mPldiv) -1! Rotor Speed ---i-,c,-- Fig 7 Adaptation dynamics of inverse rotor time-constant with operating the motor speed (a) r/min (b) dmin are all set at 1/?(0) = 5 and the speed is controlled from r/min without load torque From Fig 2 it is evident that the estimate of the inverse rotor time-constant can be tuned to the actual value by proposed technique even though the actual inverse rotor time-constant is three times as large as nominal value Furthermore, Figs 3 and 4 show the effect of speed changes on the adaptation of the rotor time-constant and the transient performance for step speed response controlled by the proposed variable structure speed controller from r/min and r/min with and without rotor time-constant adaptation From Figs 3 and 4 one can see that with the adaptation of rotor time-constant the transient performance is better and the proposed adaptation technique for rotor time-constant is not affected by the changes of motor speed Figs 5 and 6 demonstrate the goodness compared with the PI speed controller and the robustness with respect to uncertainties due to the variations of rotor time-constant and step changes in load torque from 0-2 Nm for the proposed VSC speed controller Moreover, Figs show the experimental results of utilizing the proposed adaptation and control techniques to an induction motor drive Fig 7 shows the adaptive tuning of the inverse rotor time-constant under operating the motor speed from and ; + ; : : : j : : * : OSseci (b) Fig 8 Step speed responses from r/min (a) Without adaptive field-oriented control (b) With adaptive field-oriented control r/min, respectively From Fig 7 it reveals that the rotor time-constant can be adaptively and stably estimated The goodness for the adaptive tuning of rotor time-constant is depicted by the transient speed responses in Figs 8 and 9 In these two figures, the operated value of the inverse rotor time-constant A is purposely given as 5, Le, 1/T, = 5, which is much lower than the real value of the inverse rotor time-constant in operation process and the motor speed is controlled in step responses from and r/min by means of the proposed VSC speed controller which the effect of the parameter uncertainties and external load torque are not taken into account in design Considering the parameter uncertainties and external load torque in VSC design, Fig 10 shows the VSC speed regulation due to step load resistance change of the dc generator (DCG) which is about 06 Nm disturbance torque in steady state The proposed VSC speed controller is used in Figs 10(a) and (b) and the conventional PI speed controller is used in Fig lo(c) Fig 11 depicts the experimental results of the step speed responses from r/min by VSC speed control without and with parameter uncertainty, 1/T, = 5, subjected to constant load resistance (approximately steady state 220 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY 1999

7 ::ie--*i I j :OSsecj CHl?V : CqZV : : : SOOms/aiv DC: 10:l : ' : DF 10:l j i i [500m$/div) i i i : i i i i'o!mzls/f : : : : I ; ; ; ; : : : : i i j ; ; ; ; 1 : I! : : :, : : : i (b) e* 0 Ssec Fig 9 Step speed responses from r/min (a) Without adaptive field-oriented control (b) With adaptive field-oriented control : :: : : + : " I j j-j,,, I ~, : i0sseci (b) load torque 06 Nm) In view of Fig 11 one can find that the robustness of the proposed controller can be obtained in practical applications To verify the decoupled effect, three torque responses for a) 1/T, = 5, b) 1/? = 1135 and c) adaptive 1/k are presented in Figs 12(a), (b), and (c), respectively, when a step change in torque command is applied It can be seen that the results coincide with the decoupled effect as expected From these simulation and experimental results it reveals that the effectiveness of the proposed adaptation algorithms about rotor time-constant and the proposed VSC speed control is validated by experimentations VI CONCLUSIONS In this paper, a simple and robust method to tune the rotor time-constant for IFOC and a variable structure speed controller with integral sliding-surface for the servo control of induction motor drive have been developed With the adaptation algorithm, the IFOC is robust to the deviation of the rotor time-constant needed for decoupling control in indirect field orientation An error function related Fig 10 Speed regulations at (a) 1000 r/min by VSC, (b) 1500 r/min by VSC, and (c) 1000 r/min by PI controller due to step load resistance (approximately steady state torque 06 Nm) to the deviated rotor time-constant is proposed to estimate the deviated value of the rotor time-constant through a PI-type filter By the adaptive tuning of the rotor time-constant, the IFOC can be completely achieved Moreover, based on the adaptive field-oriented control, the variable structure speed control with integral sliding-surface is presented Due to the property of the design of an integral sliding-surface, the acceleration signal needed for the conventional variable structure speed controller is removed Using the proposed variable structure speed control, the robustness for uncertainty and SHYU ET AL: ROBUST VARIABLE STRUCTURE SPEED CONTROL FOR INDUCTION MOTOR DRIVE 22 1

8 I 7 CH1:ZV CH*V ' 50om?/div DC 1O:l : oq 10:1 i, ' (50Oms/div) ' : NORM:ZkS/s i Com&nd j j ', looqiqm i i : t ' : 7 T : Rotorspeed i rr I i : : - : Orpm: ' : j, j eri I t j i :OSseci i ' f : : : : j ie--c i j io5secj CHlpZV ' C&ZV : : : 5OOw/div DC l0:l i i i (500msldiV) : j ;; ;!y?sle : : : : + : j &&and 1 ;,, : looorpm l i j j :!4** RotprSpied 1 j j i t++jtt~ + ~-~-f*l*"'-rct-c+---r-!-~+~f~-+~~-~ -- * a, 4 ;, ; t : " T : t- : { ; ; ; : J 'Orpmi i : i i +-+ disturbance load is provided and the controlled rotor speed has the exponential stability Finally, simulation and experimental results are presented to verify the validity REFERENCES [l] Nordin, K B, Novotny, D W, and Zinger, D S (1984) The influence of motor parameter deviations in feedforward field orientation drive systems In IEEE IAS Annual Meeting Record, 1984, [2] Bose, B K (1986) Power Electronics and ac Drives Englewood Cliffs, NJ: Prentice-Hall, 1986 [3] Graces, L J (1980) Parameter adaptation for the speed controlled static ac drive with a squirrel cage induction motor IEEE Transactions on Industrial Applications, 16, 2 (1980), [4] Kubota, H, Matsuse, K, and Nakano, T (1990) New adaptive flux observer of induction motor for wide speed range motor drives In Proceedings of IEEE IECON International Conference, 1990, [5] Zai, L C, and Lipo, T A (1987) An extended Kalman filter approach to rotor time-constant measurement in PWM induction motor drives In IEEE IAS Annual Meeting Record, 1987, (c) Fig 12 Torque responses for (a) l/c = 5, (b) l/t = 1135, and (c) adaptive l/q subjected to step change torque command [6] Atkinson, D J, Acarnley, P P, and Finch, J W (1991) Observer for induction motor state and parameter estimation IEEE Transactions on Industrial Applications, 27, 6 (1991), [7] Rowan, T, Kerkman, R, and Leggate, D (1991) A simple on-line adaptation for indirect field orientation of an induction machine IEEE Transactions on Industry Applications, 37 (1991), [8] Tajima, H, and Hori, Y (1993) Speed sensorless field-orientation control of the induction machine IEEE Transactions on Industry Applications, 29, 1 (1993), IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY 1999

9 [9] Kubota, H, Matsuse, K, and Nakano, T (1994) DSP-based speed adaptive flux observer of induction motor IEEE Transactions on Industry Applications, 30, 4 (1994), [lo] Huang, L, Tadokoro, Y, and Matsuse, K (1994) Deadbeat flux level control of direct-field-oriented high-horsepower induction servo motor using adaptive rotor flux observer IEEE Trunsactions on Industry Applications, 30, 4 (1994), [ll] Lorenz, R D, Lipo, T A,, and Novotny, D W (1994) Motion control with induction motors IEEE Proceedings, 82 (1994), [12] Yang, G, and Chin, T H (1993) Adaptive speed identification scheme for a vector-controlled speed sensorless inverter-induction motor drive IEEE Transactions on Industry Applications, 29, 4 (19Y3), [13] Nandam, P K, and Sen, P C (1990) A comparative study of Luenberger observer and adaptive observer-based variable structure speed control system using self-controlled synchronous motor IEEE Trunsactions on Industrial Electronics, 37, 2 (1990), [14] Ho, E Y Y, and Sen, P C (1990) A microcontroller-based induction motor drive system using variable structure strategy with decoupling IEEE Transactions on Industrial Electronics, 31, 3 (1990), [15] Ho, E Y Y, and Sen, P C (1991) Control dynamics of speed drive system using sliding mode controllers with integral compensation IEEE Transactions on Industrial Applications, 27, 5 (1991), [16] Utkin, V I (1993) Sliding mode control design principles and applications to electric drives IEEE Transactions on Industrial Electronics, 40, 1 (1 993), [17] Itkis, U (1976) Control Systems of Variable Structure New York: Wiley, 1976 Kuo-Kai Shyu was born in Hsin-Chu, Taiwan, ROC, in 1957 He received the BS degree from the Tatung Institute of Technology, Taipei, Taiwan, in 1979, and the MS and PhD degrees from the National Cheng-Kung University, Tainan, Taiwan, in 1984 and 1987, respectively, all in electrical engineering He is currently Professor in the Department of Electrical Engineering, National Central University, Chung-Li, Taiwan His research interests are in the areas of variable structure control and ac servo motor drive control Faa-Jeng Lin (M'93) received the BS and MS degrees in electrical engineering from the National Cheng Kung University, Taiwan, and the PhD degree in electrical engineering from the National Tsing Hua University, Taiwan, in 1983, 1985, and 1993, respectively During he was with the Chung-Shan Institute of Science and Technology as a group leader of automatic test equipment and microcomputer system design division He is currently Professor in the Department of Electrical Engineering, Chung Yuan Christian University, Taiwan His research interests include motor servo drives, computer-based control systems, control theory applications, and power electronics SHYU ET AL: ROBUST VARIABLE STRUCTURE SPEED CONTROL FOR INDUCTION MOTOR DRIVE 223

10 Hsin-Jang Shieh was born in Taiwan, ROC, on March 7, 1970 He received the BS and PhD degrees in electrical engineering from National Central University, Chung-Li, Taiwan, in 1992 and 1997, respectively He is currently with the Mechanical Industry Research Laboratories, Industrial Technology Research Institute, Chutung, Taiwan His research interests are in the areas of motor drive control, power electronics control, and control theory application Bor-Sen Juang received his BS and MS degrees in electrical engineering from National Central University, Chung-Li, Taiwan His current work is in the field of high-speed transmission lines 224 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL 35, NO 1 JANUARY 1999