Sensorless Control of a Linearized Induction Motor Drive

Transcription

1 International Review of Electrical Engineering (I.R.E.E.), Vol., N. 3 May June 7 Sensorless Control of a Linearized Induction Motor Drive K. B. Mohanty Abstract his paper presents an input-output linearizing and decoupling control scheme for speed control of an induction motor drive. In this scheme, the motor model is linearized, and torque and flux are decoupled by use of nonlinear control. Proportional-cum-integral controllers are used for the linear electrical and mechanical subsystems. A reduced order rotor flux observer is designed, eliminating the need of flux sensor for control purpose. A stator flux based algorithm is used to estimate the synchronous speed and then rotor speed, leading to sensorless control. Also, rotor flux and speed are estimated using Kalman filter. he control scheme is implemented and tested in laboratory. Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Linearizing control, Decoupling control, Sensorless control, Kalman filter Nomenclature dqs = i ds, iqs = ids jiqs i stator current, in real vector notation, or in complex vector notation (later) dqr = i dr, iqr = idr jiqr i rotor current vector dqs = v ds, vqs = vds jvqs v stator voltage vector Ψdqs = ψds, ψqs = ψds jψqs stator flux linkage Ψdqr = ψdr, ψqr = ψdr jψqr rotor flux linkage ω e angular electrical speed of reference frame (rad/s) ω r angular speed of rotor (rad/s) p number of pole pairs J ( β ) moment of inertia (friction coefficient) of drive R s (R r ) stator (rotor) resistance per phase. J = I = Ψ ˆ dqr the estimated rotor flux linkage G Flux observer gain matrix Ψ = Ψ Ψˆ error in the flux estimation dqr dqr dqr ω command electrical slip speed sl for decoupling ( k ) ψ command value of rotor flux dr linkage (V.s) k reference torque (N m) e s sampling time x(k) the state vector at the k-th sampling instant ( ) y(k) output at the k-th sampling instant F(k) the state transition matrix ( ) H(k) the measurement matrix ( ) x ˆ ( k ) estimate of x(k) from the measurement of y(k) ˆx priori estimate of x(k), or the initial guess x ( k ) extrapolated value of x(k) from x ˆ k P ( P ) covariance matrix of predicted P() state, xˆ ( x ) covariance matrix ( ) for ˆx Q covariance matrix ( ) of system disturbance input, u(k) R covariance of measurement noise, w(k) K the gain of Kalman filter ( ) I. Introduction One significant development in induction motor control over last three decades is the field oriented or vector control []. In vector control the torque and flux are decoupled by a suitable decoupling network. hen the flux component and the torque component (at quadrature to flux component) of the stator current, or in other words, the amplitude and phase angle of the stator current are controlled independently to control the Manuscript received and revised May 7, accepted June 7 Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved 386

2 induction motor (IM) as a separately excited DC motor. hough good dynamic current (or torque) and speed responses are obtained with conventional vector control, the torque is only asymptotically decoupled from the flux, i.e., decoupling is obtained only in steady state, when the flux amplitude is constant. Coupling is still present, when flux is weakened in order to operate the motor at higher speed within the input voltage saturation limits [], or when flux is adjusted in order to maximize power efficiency []. his has led to further research on application of differential geometry [3], [] to develop the control techniques for linearization and decoupling control. A current command input-output linearization controller is reported in [], where the IM drive is controlled for good dynamic performance and maximum power efficiency by linear decoupling of rotor flux and torque. On the basis of steady state errors, rotor resistance errors are computed and used in the output feedback control algorithm in order to reduce the errors. Differential geometry is applied in [5], to linearize the induction motor in field oriented coordinates. he decoupling of torque and flux is achieved by a static state feedback controller. he decoupling of torque and flux, using the amplitude and frequency of the supply voltage as inputs, is also obtained by a static state feedback controller in [6] and by a dynamic state feedback controller in [7]. Only the electromagnetic part is modeled, and mechanical dynamics is neglected in that study. Marino, Peresada and Valigi [8] have developed a voltage command input-output linearizing and decoupling controller for the induction motor drive. he linearizing controller is made adaptive to parameter variations. Linearizing control theory is applied to IM control in [9], after adding an integrator to one of the inputs. A globally stable controller is presented in [], for torque regulation of an induction motor with partial state feedback. Input-output linearizing control theory is also applied to IM drive in [], []-[]. A rotor flux observer is designed in [3], similar to that in [5]. hus the need of flux sensor for control purpose is eliminated. Although many speed estimation algorithms and sensorless control schemes [6] have been developed during the past few years, a simple and effective sensorless control scheme is presented in [7]. For the flux and speed estimation problem of induction motor, where parameter variation and measurement noise is present, Kalman filter [8], [9] is a good choice. In this paper, input-output linearization and decoupling control of induction motor is discussed in Section II. A rotor flux observer is designed in Section III. In Section IV, a speed estimation technique is presented, based on estimated stator flux components, leading to sensorless control. Kalman filter based flux and speed estimation is discussed in Section V. In Section VI, simulation and experimental results are presented and discussed. II. Linearizing and Decoupling Control A basic understanding of the decoupled flux and torque control resulting from field orientation or inputoutput linearization can be attained from the d-q axis model of an induction motor (IM) with the reference axis rotating at synchronous speed, ω e. he voltage equations of the IM in this synchronously rotating reference frame [] are: v = R i + Ψ + ω J Ψ () R dqs s dqs dqs e dqs ( ω pω ) i J () = r dqr + Ψ dqr + e r Ψdqr A state variable model of the induction motor with stator current and rotor flux vectors as state variables is obtained by simplification of (-) along with the fluxlinkage equations []. he model is as follows: where: ( a ω ) ( ω ) idqs = I ej idqs + a I pa J Ψ + cv 3 r dqr dqs { ( ω ω ) } dqr 5 dqs e r dqr (3) Ψ = a i + a I p J Ψ () c = L L L L, r s r m s r m r r m r a = c R + c R L / L, a = c R L / L, a3 = c L m / Lr, a = R r / Lr, a5 = Rr L m / Lr. he field orientation concept implies that the current components supplied to the motor should be oriented in phase (flux component) and in quadrature (torque component) to the rotor flux vector. his can be accomplished by choosing the speed of the reference frame ω e to be the instantaneous speed of ψ dqr and locking the phase of the reference system such that the rotor flux is entirely in the d-axis (flux axis). his results in the mathematical constraint: ψ = and ψ qr = (5) qr o achieve (5) the constraint on the synchronous speed is as follows (obtained from ()): ω = pω + a i / ψ (6) e r 5 qs dr When (5) is satisfied, the dynamic behavior of the induction motor is: i = a i + a ψ + ω i + c v (7) ds ds dr e qs ds Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

3 ω r ˆω r + PIC- i qs Flux-weakening Controller + i ds + PIC- PIC-3 u u Input-Output linearizing and decoupling controller v qs -Phase (d-q) to 3-Phase transformation v a v b v ds v c θ e 3-Phase PWM VSI M ˆψ dr i qs a 5 ˆ ψ i dr qs ω sl + + ˆω r i ds i qs 3-Phase to -Phase (d-q) transformation θ e vca v ba Speed and Flux Estimation (Observer-based or Kalman filter based) i b i c v ds i ds v qs i qs Fig.. Block diagram of the sensorless speed control scheme Fig.. Photograph of the experimental system i = ω i a i p a ω ψ + c v (8) qs e ds qs 3 r dr qs ψ = a ψ + a i (9) dr dr 5 ds he torque developed by the induction motor is: = K ψ i () e t dr qs where Kt = 3pL m / Lr = torque constant. he field oriented induction motor model, described by (7-), has nonlinearity. he speed emf term ( ωrψ dr ) appearing in (8) makes the current dynamics nonlinear and speed dependent. Equations (7-8) show that interaction between current components does exist, in the rotating reference frame. he transition from field oriented voltage components, v ds and v qs to current Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

4 components as in (7-8) involves leakage time constants and interactions. During the flux transient period (given by (9)) coupling of flux and torque is obvious from (7- ). he interaction between current components, and nonlinearity in the overall system are eliminated by using input-output linearization and decoupling control [], [5], [8], []-[]. he present approach consists of change of coordinates and use of nonlinear inputs to linearize the system equations. Developed torque e is considered as a state variable, replacing i qs to describe the motor dynamics. Using (8), (9), () and (6), the torque dynamic equation is expressed as: = e ( a a ) Kψ cv pω ( i aψ ) e t dr qs r ds 3 dr () he nonlinearities in (7), and () are put together and then replaced by nonlinear functions of the form u and u respectively. Equation (7) and () are then modified as follows: i = a i + a ψ + u () ds ds dr e = a + a + u (3) e he electrical subsystem given by (9) and () is linear, and a Proportional-cum-Integral (P-I) controller is used to obtain u. he mechanical subsystem given by (3), and the speed dynamic equation: ( βω ) ω = / J () r e L r is linear, and two P-I controllers are used in a nested manner to control the torque and speed. With these linearizing inputs u and u, the flux and torque are decoupled. Controllers are designed to obtain u and u, which maintain decoupling and linearization under all conditions. he stator input voltage components v ds and v qs in terms of u and u are: ( ω ) v = i + u / c (5) ds e qs vqs = pωr ids + a3ψdr + u / K t ψdr /c (6) of rotor flux. However, rotor flux of induction motor cannot be measured practically, and it is difficult to measure the airgap flux, also. herefore, the rotor flux is to be estimated from the measured values of speed, stator current and voltage. he IM model described by (3-) is written in the form: where: i = A i + A Ψ + B v (7) dqs dqs dqr dqs Ψ = A i + A Ψ (8) dqr dqs dqr ω A = a I ej ; = a 3 r = a5 A I pa ω J ; A I ; = a ( ω pω ) A I J ; e r B = c From (8), the flux observer equation with an error correction term is derived [5] as follows: ˆ Ψdqr = A ˆ idqs + AΨ dqr + G i A i + A + Bv I ( Ψ ˆ ) dqs dqs dqr dqs (9) Subtracting (9) from (8), the flux error dynamics for this observer is: Ψ dqr = A G A Ψ () It is verified that the matrix pair (A, A ) is observable for all real ω r. So, by choosing suitable gain matrix G, the eigen-values of the flux error dynamic matrix ( A G A ) can be placed in the left half of s- plane, so that the estimated flux Ψ ˆ dqr approaches the actual flux Ψ dqr asymptotically. It is desirable to eliminate the differential term of the current in (9). So a dummy variable defined by () is chosen. he algorithm for implementing observer (9) is as follows: dqr dqs dqr ˆ ξ = Ψˆ Gi () he block diagram of the induction motor drive with this input-output linearizing control scheme is shown in Fig.. he design procedure for the P-I controllers is detailed in []. he gains are: K pd = 5., K id = 36, K pw =.6, K iw =.98, K pq =, K iq = ˆ ξ = ( A GA ) ξ + A GA + A GA G i GB v dqs ˆ dqs () III. Rotor Flux Estimation he input-output linearization and decoupling control algorithm given by (6), (5-6) requires the knowledge o place the eigen-values of the matrix A G A ) at ( x ± jy) rad/s, the required ( observer gain matrix G is given by ( g I + g J ) [3], where: Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

5 g ( ) + ( + ) a + ( p a ω ) x a a y ω pω p a ω e r 3 r = 3 r (3) 3 iα s = ( ic ib) ( ic ib) 3 = 3 (3) g ( ) ωr ( + ωe ωr) a + ( p a ω ) x a p a y p a 3 = 3 r () Selection of values for x and y is a compromise between sensitivity to measurement error and rapid recovery of initial error. A fast observer converges quickly, but it is also sensitive to measurement error. he rotor flux is estimated by solving for ξˆ from (), and then substituting in (). IV. Speed Estimation In the speed estimation scheme described here, the synchronous speed is estimated and the slip speed is assumed to be command value. So, the estimated rotor speed is given by: ˆ ω = ˆ ω ω / p (5) r e sl he principle of synchronous speed estimation is as follows. If ψ αs and ψ β s are the two components of the stator flux vector in the stationary (α β ) reference frame, the electrical angle of the stator flux vector is defined as: ψ tan s βs / αs θ = ψ ψ (6) he time derivative of stator flux angle gives the instantaneous electrical synchronous speed: ψ ψ ψ ψ ω = θ = (7) e ψ s α s βs βs αs ψαs + ψβs From the voltage equations of the induction motor in the stationary ( α β ) reference frame [], the components of stator flux linkage are given by: t ( v R i ) dt (8) ψ = αs αs s αs t βs βs s βs ψ = v R i dt (9) he current components in the stationary (α β ) reference frame are calculated from the measured phase currents i b and i c : iβ = i i i = i + i 3 s a b c b c (3) Similarly the voltage components in the stationary (α β ) reference frame are calculated from the measured line voltages v ab and v ac : 3 vα s = ( vc vb) ( vab vac) 3 = 3 (3) vβ = v v v = v + v 3 3 s a b c ab ac (33) After the stationary reference frame components of measured voltages and currents are obtained by (3-33) in every sampling interval, the rate of change of the stator flux components are obtained in the discrete domain, using (3-35) obtained from (8-9): ( k) v ( k) R i ( k) ψ = (3) αs αs s αs ( k) v ( k) R i ( k) ψ = (35) βs βs s βs he stator flux components are then obtained from their derivatives as follows: ( ) ψ k = ψ k + ψ k (36) αs αs αs s ( ) ψ k = ψ k + ψ k (37) βs βs βs s he estimated synchronous speed is obtained from (7), using (3-37). hen rotor speed is estimated using (5), in which the command value of slip speed, ω sl is : ω ( ) 3 ψ k = R k / p k sl r e dr (38) In the calculation of the rotor angular speed, the sampling time is set at the same value ( s ) as used in the current control loop, to obtain a fast dynamic response. However, in this way the estimated speed is also corrupted by the current ripples. In practical conditions, the time constant of current loop is much smaller than that of the speed loop. In other words, the current loop bandwidth is much wider than the speed loop bandwidth. herefore, a moving average algorithm [7] is used to smooth the estimated speed as follows: ˆ ω r N r (39) N k = ( n) = ˆ ω ( n k) Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N. 3 39

6 where: - N = / - = sampling time of the current control loop - = sampling time of the speed control loop In the simulation study presented, the values of and are. ms and 5ms, respectively. V. Kalman Filter for Flux and Speed Estimation he Kalman filter [8] is one of the most well known and often used tools for stochastic estimation, where parameter variation and measurement noise is present. It is essentially a set of mathematical equations that implement a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance when some presumed conditions are met. For the flux and speed estimation problem of the induction motor drive, Kalman filter is used. he decoupled induction motor drive has two linear subsystems: (i) electrical subsystem described by () and (9), (ii) mechanical subsystem given by (3-). he discrete time model of both electrical subsystem and mechanical subsystem is: ( k + ) = ( k) ( k) + ( k) x F x u () = + y k H k x k w k () where, u(k) is the random disturbance input. It is the sum of physical input and the system noise. w(k) is the measurement noise. Both u(k) and w(k) are assumed to be white noise with zero mean. For the electrical subsystem: x ( k) = i ds k ψ dr k, and y ( k ) = i ds k. For the mechanical subsystem: x ( k) = ( k) ω ( k), and y ( k ) ( k ) e r =. he first step of Kalman s algorithm in estimating x() is to determine the extrapolated value as follows: () = ( ) ˆ x F x For a general notation at any sampling instant, dropping the arguments: x = F x ˆ () where, ˆx is the previous estimate, and x is the present extrapolated value based on previous estimate. he error covariance matrix of the new x is: e ( ) P = F P F + Q Again dropping arguments for a general notation: P = F P F + Q (3) Dr. Kalman says the new optimal estimate is: ( y ) xˆ = x + K H x () he optimal gain of Kalman filter is given by [8] : K = P H H P H + R (5) he new estimate ˆx has an error covariance matrix, which is given by: P= I KH P I KH + KRK (6) he Kalman filter consists of repeated use of eqns.(-6) for each measurement [8], [9]. VI. Results and Discussions he input-output linearization and decoupling controller, flux and speed observers were implemented on an IGB based PWM inverter fed induction motor drive. Photograph of the experimental setup is shown in Fig.. A 75 MHz Pentium processor based PC housed with moderately priced add-on cards, such as A/D card (PCL-8) and D/A card (PCL-76) from Dynalog Microsystems, India is used in the experimental rig. he software controller was implemented in C language. Sampling time was fixed at 5 µs by using 85 timer of the PC. Once the timer has finished, the interrupt controller calls the channel interrupt, that is used for reading the A/D converter data each 5 µs. he time required by the PC to execute the control loop once has been found to be 86 µs approximately. For closed loop control, the motor is initially started on open loop in constant Volts/Hertz mode. After the motor achieves the steady state operation at a desired frequency, the control algorithm is switched on for closed loop operation. he 3-phase induction motor used in the experimental study has the following rating and parameters:.75 kw, V, 3A, 5 Hz, rpm, R s = 6.37 ohms, R r =.3 ohms, L s = L r =.6 H, L m =. H, J =.88 Kg m, β =.3 N m s/rad. Fig. 3 shows performance of the real time flux simulator. Simulation study is carried out in a stationary reference frame, when the motor is started from standstill. Speed, actual and estimated rotor flux, and flux estimation error are shown. Flux and estimated flux are sinusoidal because of the stationary reference frame. Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N. 3 39

7 5.6 Speed (rpm) 5 Rotor Flux Linkage (V.s) Estimated Flux Linkage (V.s) Error in Estimated Flux Linkage (V.s) Fig. 3. Simulation response with flux observer when staring from standstill, in a stationary reference frame Rotor speed Actual rotor flux linkage Estimated rotor flux linkage of observer Flux estimation error 9.6 Speed and reference speed (rpm) Ref. speed Speed Rotor Flux Linkage (V.s) Estimated Flux Linkage (V.s) % Error in Estimated Flux Linkage Fig.. Simulation response of the proposed drive with controller and flux observer (in a synchronously rotating reference frame) Reference and actual rotor speed Actual rotor flux linkage Estimated rotor flux linkage of observer Percentage error in flux estimation Fig. shows rotating reference frame simulation of the proposed drive system with designed controllers and flux observer. Reference speed is changed in steps from to 5 rpm, then to 8 rpm with flux weakening and finally to rpm. Speed response shows some overshoot, while flux response proves that the decoupling of flux and torque (or speed) is obtained. Flux changes only when there is a change in flux command, i.e., change in sped from 5 to 8 rpm and then to rpm. Estimated flux and percentage error in flux estimation are also shown. he control scheme uses three PI regulators. One PI regulator is used for the electrical subsystem to control the (d-axis) rotor flux and excitation current i ds. Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N. 3 39

8 5 5 Speed (rpm) Estimated Speed (rpm) d- and q-axis currents (A) i qs i ds Phase current, ia (A) Fig. 5. Simulation response for step change in speed with speed estimation: Speed, Estimated speed, d- and q-axis stator currents, Stator phase current 5.6. Speed (rpm) 3 Rotor Flux linkage (V.s) Estimated Speed (rpm) Estimated Rotor Flux linkage (V.s) % Error in Speed Estimation % Error in Flux Estimation (e) (f) Fig. 6. Simulation response for speed and flux estimation with Kalman Filter: Speed, Rotor Flux Linkage, Estimated Speed, Estimated Rotor Flux Linkage, (e) % Error in Speed Estimation, (f) % Error in Rotor Flux Estimation Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

9 8 Speed (rpm) 5 5 Phase Current, ia (A) Speed: 39.5 rpm/div ime: 5 ms/div Phase Current: A/div ime: ms/div Fig. 7. Simulation and experimental responses for step increase in reference speed from to 8 r/min (reference flux linkage =.5 V.s): (i) Simulation response Speed Phase current (ii) Experimental response Speed Phase current Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N. 3 39

10 Speed (rpm) Phase Crrent, ia (A) Phase Current: A/div Speed: 39.5 rpm/div ime: 5 ms/div ime: ms/div Fig. 8. Simulation and experimental responses for step decrease in reference speed from to 9 r/min (reference flux linkage =.5 V.s): (i) Simulation response Speed Phase current (ii) Experimental response Speed Phase current Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

11 Speed (rpm) Flux linkages (V.s) and torque (N.m) ψ qr e ψ dr d- and q-axis currents (A) i qs i ds Phase current, ia (A) Fig. 9. Simulation response for step change in load torque: speed d- and q-axis rotor flux linkages and developed torque d- and q-axis stator currents Stator phase current wo PI regulators are used in the mechanical subsystem in a nested manner. As the speed response with one PI speed regulator is unsatisfactory, twp PI regulators are used one in the speed (external) loop and another in the torque (internal) loop. Because of the significant difference in the time constants of speed and electromagnetic torque, or torque component of current i qs, two PI regulators give better response. Additionally, a pure integrator is used to give shaft position angle, θ e from the rotor speed, ω r. he simulation result of the speed observer presented in section-iv, is shown in Fig. 5, for a step change in speed command from rpm to 3 rpm. he command flux linkage is.5 V s, i.e., the command d-axis stator current is.863 A. he speed response exhibits an overshoot of 9 rpm and % settling time of.3 s. he estimated speed response is similar to the actual speed response, except the fact that it contains ripple of peak-to-peak value, 5 rpm (.36% rms) about the steady state value. he d-axis stator current exhibits overshoot of.5 A and oscillation for.8 s. he q-axis stator current exhibits overshoot of 5.7 A and oscillation for.5 s. Peak phase current of stator increases from A to 6 A and exhibits oscillation for. s during the transient period. he simulation result for flux and speed estimation with Kalman Filter, presented in section-v, is shown in Fig. 6. Speed command is given a step decrease from 5 rpm to rpm. he command flux linkage is.5 V s. he estimated speed is similar to the actual speed response, except the temporary deep of 7rpm (.7%), which occurs at the moment of change in command speed. he actual rotor flux, estimated rotor flux and percentage error in speed and flux estimation are also shown. Maximum error in flux estimation is 8%, which occurs at the beginning, and decays to zero in.3s. Convergence of the Kalman Filter is obtained by appropriate choice of covariance of system and measurement noises. he speed observer presented in section-iv has sever problem at low speeds. But simulation studies carried out, establish that Kalman Filter estimates both flux and speed accurately at all speeds. Fig. 7 shows the simulated and experimental responses for a step increase in speed reference from rpm to 8 rpm with linearizing control. here are some differences in the transient responses, though the steady state values are equal. Settling time for current is approximately 6 ms from the experimental result, and ms from the simulation one. Settling time for speed is approximately 3 ms from the experimental result, and 65 ms from the simulation one. he difference in the transient response is due to several factors, such as ceiling in the inverter voltages, inverter nonlinearity, measurement noise, magnetic saturation etc. Fig. 8 shows the simulated and experimental responses for a step decrease in speed reference from rpm to 9 rpm. Settling time for current is approximately ms from the experimental result, and ms from the simulation one. Settling time for speed is approximately ms from the experimental result, and 6 ms from the simulation one. Fig. 9 shows the simulation response for a step change in load torque from to 3 N m. Developed torque response exhibits an overshoot of. N m (6.67%). he d-axis rotor flux linkage remains constant at.5 V s and q-axis rotor flux linkage remains constant at zero. During the transient period of torque change, speed drops by 78 rpm (7.8%) and settles to 3% of reference value in.37 s. Decoupling of torque and flux, or in other words, torque and flux components of stator current is apparent from Fig. 9. Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N

12 VII. Conclusions he concept of input-output linearization and decoupling control as applied to the induction motor drive is clearly presented. A speed adaptive reduced order observer for estimation of rotor flux has been developed. A simple speed estimation scheme, based on estimated stator flux components, is discussed for sensorless control. Even if the estimated speed contains ripples, the actual speed response, with the controller using the estimated speed, is ripple free. he ripple in the estimated speed may be reduced by increasing the sampling time of the speed estimation. But, it increases the overshoot and settling time of the actual speed response. Rotor flux and speed are also estimated by Kalman filter. Simulation results with Kalman filter show very good and fast estimation of flux and speed in the presence of system and measurement noise. he designed controller and flux observer are implemented in the laboratory, on an IGB based PWM inverter fed IM drive, and tested. he experimental results of the drive are compared with corresponding simulation results. Within the limitations of the experimental set-up, satisfactory agreement is found among them thus validating the control algorithm. References [] W. Leonhard, Control of Electrical Drives (Springer-Verlag: Berlin, Germany, 99). [] D. I. Kim, I. J. Ha and M. S. Ko, Control of induction motors via feedback linearization with input-output decoupling, Int. Journal of Control, vol. 5, no., pp , 99. [3] A. Isidori, A. J. Krener, C. Gori-Giorgi, and S. Monaco, Nonlinear decoupling via feedback: A differential-geometric approach, IEEE rans. AC, vol. 6, pp , 98. []. J. arn, A. K. Bejczy, A. Isidori and Y. Chen, Nonlinear feedback in robot arm control, Proc. of 3 rd Conf. on Decision and Control, Dec. 98, pp [5] Z. Krzeminski, Nonlinear control of induction motor, Proc. of th IFAC World Congress on Automatic Control, vol. 3, Munich, 987, pp [6] A. De Luca, and G. Ulivi, Design of exact nonlinear controller for induction motors, IEEE rans. AC, vol. 3, no., pp 3-37, Dec [7] A. De Luca, and G. Ulivi, Dynamic decoupling of voltage frequency controlled induction motors, 8 th Int. Conf. on Analysis and Optimization of Systems, Antibes, June 988, pp [8] R. Marino, S. Peresada, and P. Valigi, Adaptive input-output linearizing control of induction motors, IEEE rans. AC, vol. 38, no., pp. 8-, 993. [9] J. Chiasson, Dynamic feedback linearization of the induction motor, IEEE rans. AC, vol. 38, no., pp , Oct [] R. Ortega and G. Espinosa, A controller design methodology for systems with physical structures: Applications to induction motors, Automatica, vol. 9, no. 3, pp , 993. [] M. Bodson, J. Chiasson and R. Novotnak, High perfomance induction motor control via input-output linearization, IEEE Control Systems Magazine, pp. 5-33, Aug. 99. [] K. B. Mohanty and N. K. De, Nonlinear controller for induction motor drive, Proc. of IEEE Int. Conf. on Industrial echnology (ICI), Goa, Jan., pp [3] K. B. Mohanty, Input-Output linearizing and decoupling control of an induction motor drive, Procc. of H International Power Electronics and Motion Control Conf., Riga, Sept., Vol., pp [] K. B. Mohanty and N. K. De, Linearizing control of an induction motor, Proc. of IEEE Int. Conf. on Industrial echnology (ICI), Mumbai, Dec. 6, pp [5] Y. Hori, V. Cotter, and Y. Kaya, Control theoretical considerations relating to an induction machine flux observer, IEE Proc., 6-B, pp. -8, 986. [6] K. Rajashekara, A. Kawamura, and K. Matsuse, Sensorless Control of AC Motor Drives (Piscataway, NJ, IEEE Press, 996). [7] K. B. Mohanty, A. Routray, N. K. De, Rotor flux oriented sensorless induction motor drive for low power applications, Procc. of Int. Conf. on Computer Applications in Electrical Engg.: Recent Advances, Roorkee, Feb., pp [8] R. E. Kalman, A new approach to linear filtering and prediction problems, rans. of ASME, Journal of Basic Engg., vol. 8-D, pp. 35-5, 96. [9] K. B. Mohanty and A. Patra Flux and speed estimation in decoupled induction motor drive using Kalman filter, Procc. of 9 H National Systems Conference (NSC), Mumbai, Dec. 5, pp. -9. [] P. C. Krause, Analysis of Electrical Machine (McGraw-Hill, New York, 986). Author s information Kanungo Barada Mohanty is born at Orissa on th June 968, has received B.E. degree from Sambalpur Univ., M.ech. and Ph.D. degrees from Indian Institute of echnology (II), Kharagpur in the years 989, 99 and respectively, all in Electrical Engineering. He is a faculty member of Electrical Engg. Dept, National Institute of echnology, Rourkela since 99, and currently holding the post of Assistant Professor. From 997 to, he was on deputation to Electrical Engg. Dept of II Kharagpur, where he was a doctoral student. He has five journal publications and more than fifteen papers in various international and national conferences, all in the field of power electronic drives, and mostly in control and estimation of induction motor drives. His research interests include control and estimation in induction motor drive, wind turbine driven induction generator, and fuzzy control. Dr. Mohanty is a member of he Institution of Engineers (India), Solar Energy Society of India, and System Society of India. Copyright 7 Praise Worthy Prize S.r.l. - All rights reserved International Review of Electrical Engineering, Vol., N