272 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 Speed-Sensorless Estimation for Induction Motors Using Extended Kalman Filters Murat Barut, Student Member, IEEE, Seta Bogosyan, Member, IEEE, and Metin Gokasan, Member, IEEE Abstract—In this paper, extended-Kalman-filter-based estimation algorithms that could be used in combination with the speed-sensorless field-oriented control and direct-torque control of induction motors (IMs) are developed and implemented experimentally. The algorithms are designed aiming minimum estimation error in both transient and steady state over a wide velocity range, including very low and persistent zero-speed operation. A major challenge at very low and zero speed is the lost coupling effect from the rotor to the stator, which makes the information on rotor variables unobservable on the stator side. As a solution to this problem, in this paper, the load torque and the rotor angular velocity are simultaneously estimated, with the velocity taken into consideration via the equation of motion and not as a constant parameter, which is commonly the case in most past studies. The estimation of load torque, on the other hand, is performed as a constant parameter to account for Coulomb and viscous friction at steady state to improve the estimation performance at very low and zero speed. The estimation algorithms developed based on the rotor and stator fluxes are experimentally tested under challenging variations and reversals of the velocity and load torque (step-type and varying linearly with velocity) over a wide velocity range and at zero speed. In all the scenarios, the current estimation error has remained within a very narrow error band, also yielding acceptable velocity estimation errors, which motivate the use of the developed estimation method in sensorless control of IMs over a wide velocity range and persistent zero-speed operation. Index Terms—Extended Kalman filter (EKF), induction motor (IM), low/zero-speed operation, sensorless control. I. I NTRODUCTION T HERE has been extensive research in the sensorless fieldoriented control (FOC) and direct-torque control (DTC) of induction motors (IMs) for the last two decades. Both control methods require the accurate knowledge of the amplitude and angular position of the rotor or stator flux with reference to the stationary stator axis (in Cartesian coordinates). Additionally, information on the rotor angular velocity is required for velocity control over a wide speed range and in the low and zero-speed range for position-control applications. However, although speed sensorless drives are now well-established in industry for medium and high-speed operation [1], their persistent operation at very low and zero speed still constitutes a persisting Manuscript received July 20, 2004; revised July 31, 2006. Abstract published on the Internet September 15, 2006. M. Barut and S. Bogosyan are with the Electrical and Computer Engineering Department, University of Alaska Fairbanks, Fairbanks, AK 99775 USA (e-mail: [email protected]; [email protected]). M. Gokasan is with the Electrical and Electronics Engineering Department, Istanbul Technical University, Maslak, Istanbul, Turkey (e-mail: gokasan@itu. edu.tr). Digital Object Identifier 10.1109/TIE.2006.885123 challenge [2]. The problems are due to parameter uncertainties, signal acquisition errors, and noise in the very low speed range, with an additional difficulty encountered at zero speed in steady state, when the stator current ceases to convey information on the rotor angular velocity [3], [4]. Model-based methods using IM state equations and signalinjection methods [5] using the anisotropic properties of the machine have been competing for the improvement of the zero/low-speed performance of sensorless IMs [2]. Speed sensorless control methods based on signal injection are capable of long-term stability at zero stator frequency; however, they are highly sophisticated and require customized designs for a particular motor drive [3]. Recently, for the solution of the problem zero/very low speed, model-based estimation methods have been proposed, such as in [6]–[8], specifically addressing persistent operation zero speed. Among those studies [6] uses a total-least-squarebased speed adaptive flux observer which enables zero-statorfrequency operation over an interval of 60 s, with mean and maximum estimation error values of 1.34 and 38 r/min, respectively, at zero load. The study in [7] uses model-referenceadaptive-system-based linear neural networks, presenting results with a maximum velocity estimation error of 95 r/min and a persistent operation interval of 60 s at zero speed. The study in [8] utilizes a continuous sliding-mode approach, for which zero-stator-frequency results are obtained under load and presented only for a very short interval of 4 s. In addition to the aforementioned group of studies taking a deterministic approach to the design of closed-loop observers, there are also extended-Kalman-filter (EKF)-based applications in the literature, taking a stochastic approach for the solution of the problem. Model uncertainties and nonlinearities inherent to IMs are well-suited for the stochastic nature of EKFs [9], [10]. With this method, it is possible to make the online estimation of states while simultaneously performing identification of parameters in a relatively short time interval [11]–[13], also taking system/process errors and measurement noises directly into account. The EKF is also known for its high convergence rate, which improves transient performance significantly. Additionally, accurate estimation and convergence in steady state requires high-frequency signals, which are also inherently met by EKFs with the model and measurement noises included in the model. These properties are the major advantages of the EKF over other estimation methods and are the reasons why the method finds wide application in sensorless estimation in spite of its computational complexity, which also ceases to be a problem with the developments in high-performance processor technology. 0278-0046/$25.00 © 2007 IEEE BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS There have been a large number of EKF applications for the sensorless control of IMs; studies using full-order [14], [15] and reduced order [16], [17] estimators have been presented with experimental results. The study in [18] compares the results of EKF and Extended Luenberger Observer (ELO) for high-speed operation using the IM model in the rotating axes, while the study in [19] performs a comparison of EKF and Sliding Mode Observer (SMO). A common feature in all these studies is the estimation of velocity, which is taken into consideration as a slow varying or constant parameter, except in [18]. Although good results have been obtained in those studies in the relatively low and high-speed operation region, the performance at zero stator frequency or at very low speed is not satisfactory or not addressed at all. The major contribution of this paper is the design and experimental implementation of EKF-based estimation algorithms developed for use with the speed sensorless DTC and direct FOC of IMs over a wide speed range, including zero speed. For this purpose, unlike previous EKF-based estimation studies, by taking the angular velocity into consideration as a constant parameter, ω is estimated as a state with the utilization of the equation of motion. The inclusion of the mechanical equation helps the estimation process by conveying the rotor–stator relationship when the stator currents cease to carry information on rotor variables at zero speed. Friction effects are also known to deteriorate performance at low velocity and position-control applications. To address this issue in this paper, the estimation of tL is performed as a constant to account for friction effects, particularly those of Coulomb and viscous friction at the steady state. In the proposed EKF algorithms, the stator and rotor flux amplitudes and positions are also estimated in addition to the stator currents (referred to the stator stationary frame), which are also measured as output. For improved estimation accuracy, the EKF algorithms also take into consideration the control input error arising due to the limited word length of the Analog Digital Converter (ADC) [13]. This paper aims to address problems related to sensorless estimation in IMs over a wide speed range, and closed-loop control of IMs is outside the scope of this paper. The evaluation procedure of an estimator without the use of a closed-loop control could, in a sense, be considered offline; to ensure a realistic evaluation of the online performance of the EKF estimator in spite of the fact, pulsewidth-modulation (PWM)-type input voltages have been applied to the IM via the ac drive, and the actual ds1104-based motion-control unit and motor are used to process the algorithm. The estimation schemes are thus tested experimentally under instantaneous load (linear with velocity and step-type) and velocity variations to evaluate the performance over a wide speed range, as well as during persistent operation at zero speed. Very low current and velocity estimation errors have been obtained under the developed scenarios, motivating the utilization of the developed estimation approach in the sensorless control of IMs. The paper is organized as follows: after the introduction in Section I, the derivation of the extended models is discussed in Section II for the estimation algorithms; Section III describes the development of the EKF algorithm for both models; Section IV gives the hardware configuration, with Section V presenting and discussing the experimental results for all three 273 scenarios. Finally, the conclusions and suggestions for future improvements are given in Section VI. II. E XTENDED M ATHEMATICAL M ODEL OF THE IM As it is well known, IM is described by a fifth-order differential equation with two inputs and only three state variables available for measurement [20]. For speed sensorless control, the model consists of differential equations based on the stator and/or rotor electrical circuits considering the measurement of stator current and/or voltages. Being different from previous EKF-based estimators, which estimate the rotor velocity using the aforementioned equations, the extended IM model derived in this paper also includes the equation of motion to be utilized for the estimation of the rotor velocity. The EKF-based estimators designed for FOC and DTC are based on the extended IM models in the following general form: ẋe (t) = f e (xe (t), ue (t)) + wx1 (t) = Ae (xe (t)) xe (t) + B e ue (t) + wx1 (t) (1) Z(t) = he (xe (t)) + wx2 (t) (measurement equation) = H e xe (t) + wx2 (t). (2) Here, the extended state vector xe represents the estimated states and load torque tL , which is included in the extended state vector as a constant state with the assumption of a slow variation with time. f e : nonlinear function of the states and inputs. Ae : system matrix. ue : control input vector. B e : input matrix. wx1 : process noise. he : function of the outputs. H e : measurement matrix. wx2 : measurement noise. Based on the general form in (1) and (2), the detailed matrix representation of the two IM models can be given as below. Model 1: Extended model of IM based on the stator flux is shown by (3) and (4) at the bottom of the next page. Model 2: Extended model of IM based on the rotor flux is shown by (5) and (6) at the bottom of the next page. The following are defined for (3)–(6). pp : number of pole pairs. Lσ = σLs : stator transient inductance. σ: leakage or coupling factor. Ls and Rs : stator inductance and resistance, respectively. Lr and Rr : rotor inductance and resistance referred to the stator side, respectively. νsα and νsβ : stator stationary axis components of stator voltages. isα and isβ : stator stationary axis components of stator currents. ψsα and ψsβ : stator stationary axis components of stator flux. ψrα and ψrβ : rotor stationary axis components of stator flux. JL : total inertia of the IM and load. ωm : angular velocity. III. D EVELOPMENT OF THE EKF A LGORITHM An EKF algorithm is developed for the estimation of the states in the extended IM model given in (3) and (4), or (5) and (6), to be used in the sensorless control of the IM. The KF method used for this purpose is a well-known recursive algorithm that takes the stochastic state space model of the system into account together with the measured outputs to achieve the optimal estimation of states [19] in multi-input multi-output systems. The system and measurement noises are considered to be in the form of white noise. The optimality of 274 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 the state estimation is achieved with the minimization of the covariance of the estimation error. For nonlinear problems, the KF is not strictly applicable since linearity plays an important role in its derivation and performance as an optimal filter. The EKF attempts to overcome this difficulty by using a linearized approximation where the linearization is performed about the current state estimate [21]. This process requires the discretization of (3) and (4), or (5) and (6), as below xe (k + 1) = f e (xe (k), ue (k)) + wx1 (k) Thus, the EKF algorithm can be given in the following recursive relations: N (k) = F e (k)P (k)F e (k)T + F u (k)Du F u (k)T + Q (11a) T P (k + 1) = N (k) − N (k)H e −1 × Dξ + H e N (k)H T H e N (k) (11b) e x̂e (k + 1) = fˆ (xe (k), ûe (k)) + P (k + 1)H T D−1 Z(k) = H e xe (k) + wx2 (k). e ∂f e (xe (k), ue (k)) F u (k) = ∂ue (k) (8) i̇sα i̇sβ ψ̇sα ψ̇sβ = ω̇m ṫL − Rs Lσ + Rr Ls Lr Lσ −pp ωm −Rs 0 p − 23 JLp ψsβ 0 − ẋe (9) −pp ωm Rr Ls +L L r σ 0 −Rs 3 pp 2 JL ψsα 0 Rs Lσ . (10) Rr Lr Lσ p ω − pLσm pp ωm Lσ 0 0 0 0 0 0 0 0 Rr Lr Lσ 0 0 0 0 0 1 i Lσ sα 0 i sβ 0 ψ 1 0 sα + ψ 0 0 sβ 0 ωm − J1L tL 0 0 0 xe Ae 0 Ae isα isβ 1 0 0 0 0 0 ψsα isα = + w12 0 1 0 0 0 0 ψsβ isβ ωm Z He tL R 2 Rr Lm r Lm − Lσs + R 0 L2 L2 r Lσ r Lσ i̇sα 2 R L R L s m r m i̇sβ − Lσ L pp ωm 0 − Lσ + L2 Lσ r r ψ̇rα Rr Rr = L 0 − m Lr Lr ψ̇rβ Rr 0 pp ω m ω̇m Lr Lm − 3 pp Lm ψ 3 pp Lm 0 ṫL 2 JL Lr rβ 2 JL Lr ψrα 0 0 0 ẋe isα i sβ 1 0 0 0 0 0 ψrα isα = + w22 0 1 0 0 0 0 ψrβ isβ ωm Z He tL (11c) Here, Q: covariance matrix of the system noise, namely model error. Dξ : covariance matrix of the output noise, namely measurement noise. Du : covariance matrix of the control input noise (νsα and νsβ ), namely, input noise. P and N : covariance matrix of state estimation error and extrapolation error, respectively. The algorithm involves two main stages: prediction and filtering. In the prediction stage, the next predicted states fˆe (·) and predicted state error covariance matrices P (·) and N (·) are processed, while in the filtering stage, next estimated states x̂e (k + 1) obtained as the sum of the next predicted states and x̂e (k),ûe (k) x̂e (k),ûe (k) ξ × (Z(k) − H e x̂e (k)) . As mentioned before, EKF involves the linearized approximation of the nonlinear model [(7) and (8)] and uses the current estimation of states x̂e (k) and inputs ûe (k) in linearization by using ∂f e (xe (k), ue (k)) F e (k) = ∂x (k) e e (7) 0 0 νsα +w11 (t) 1 νsβ 0 u e 0 1 Lσ (3) Be (4) Lm Lσ Lr pp ωm 0 Rr Lm L2 r Lσ 0 −pp ωm 0 r −R Lr 0 0 0 0 0 1 isα Lσ 0 isβ 0 ψ 0 rα 0 + ψrβ 0 0 0 ωm − J1L tL 0 0 x 0 e 0 0 νsα +w21 (t) 0 νsβ 0 u e 0 1 Lσ Be (5) (6) BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS 275 TABLE I RATED VALUES AND PARAMETERS OF THE IM USED IN THIS PAPER Fig. 1. Structure of the EKF algorithm. Fig. 2. Schematic representation of the experimental setup. the correction term [second term in (11c)] are calculated. The schematic representation of the algorithm is given in Fig. 1. The algorithm utilizes the extended or augmented model in (3) and (4), or (5) and (6), to generate all states required for the sensorless control system, in addition to the load torque tL , using the measured phase currents and voltages. IV. H ARDWARE C ONFIGURATION The experimental test-bed for the EKF-based estimators is given in Fig. 2. The IM in consideration is a three-phase fourpole 4-kW motor; the detailed specifications of which will be given in the experimental results section. The EKF algorithm and all analog signals are developed and processed on a Power PC-based DS1104 Controller Board, offering a four-channel 16-bit (multiplexed) ADC and four 12-bit ADC units. The controller board processes floating-point operations at a rate of 250 MHz. A torque transducer rated at 50 N · m and an encoder with 1024 counts/r are also used for the evaluation and verification of the load torque and velocity estimates. The phase voltages and currents are measured with high band voltage and current sensors. In the experiments, the IM is fed via an ac drive with a constant V/f PWM voltage instead of a sinusoidal input voltage to achieve a more realistic performance test. Although the ac drive is used in open loop, voltages with different frequency values can be varied linearly with the acceleration and deceleration times of the driver, which also allows velocity reversal. The load is generated through a dc machine operating in generator mode coupled to the IM. An array resistor connected to the armature terminals of the dc machine is used to vary the load torque applied to the IM, based on tL = kt2 ω/R, where kt is the torque constant of dc machine, ω is the angular velocity, and R is the total resistance (switched array + armature). The value of the resistance is adjusted to 14.3 Ω to generate a load torque tL of 18 N · m at approximately 1400–1420 r/min, while for a tL of 10.4 N · m, the resistance is set to 29.4 Ω and to its maximum value, respectively. Finally, the total inertia of the system does not change in this application and is assumed to be constant. It consists of the motor and generator inertia, which are both determined accurately and reflected to the EKF algorithms, as given in Tables I and II. V. E XPERIMENTAL R ESULTS The parameters for the IM and dc generator are listed in Tables I and II. The values of system parameters and covariance matrix elements are very effective on the performance of the EKF estimation. In this paper, to avoid computational complexity, the covariance matrix of the system noise Q is chosen in diagonal form, also satisfying the condition of positive definiteness. According to the KF theory, the Q, the Dξ (measurement error covariance matrix), and the Du (input error covariance matrix) have to be obtained by considering the stochastic properties of the corresponding noises [22], [23]. However, since these are usually not known, in most cases, the covariance matrix elements are used as weighting factor or tuning parameters. In general, while the tuning of the initial values of the P (estimation error covariance matrix) and the Q is done by experimental trial-and-error to achieve a rapid initial convergence and the desired transient and steady-state behaviors of the estimated states and parameters, the Dξ and Du are determined taking into account the measurement errors of the current and voltage sensors and the quantization errors of the ADCs, as given below. For Model 1 Q = diag 1.4 × 10−12 A2 1.4 × 10−12 A2 × 1.3 × 10−12 (V · s)2 1.3 × 10−12 (V · s)2 × 9.6 × 10−14 (rad/s)2 1.7 × 10−12 (N · m)2 P = diag 10 A2 10 A2 10 (V · s)2 10 (V · s)2 × 10 (rad/s)2 10 (N · m)2 . 276 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 TABLE II RATED VALUES AND PARAMETERS OF THE DC MACHINE USED IN THIS PAPER Fig. 3. Stator currents and voltages applied to the IM through the ac drive. For Model 2 Q = diag 1.5 × 10−11 A2 1.5×10−11 A2 10−15 (V · s)2 ×10−15 (V · s)2 10−15 (rad/s)2 10−15 (N · m)2 P = diag 1 A2 1 A2 1 (V · s)2 1 (V · s)2 1 (rad/s)2 1 (N · m)2 . For both models Dξ = diag 1.5 × 10−7 A2 1.5 × 10−7 A2 Du = diag 10−10 V2 10−10 V2 . Fig. 3 demonstrates the transformed currents and voltages at 50 Hz and 380 V for a tL of approximately 20 N · m. The performance of the IM is tested in open loop with PWM input voltages/currents given in Fig. 3. The EKF algorithm takes as the input of the transformed components of the current and voltage. The following is a generalized description of this transformation xα = xa ; 1 xβ = √ (xb − xc ) 3 torque values. The application considered in this paper does not involve a change in the inertia; therefore, its rated value is used in the models. To evaluate the performance of the developed EKF schemes for the stator and rotor oriented IM models—namely, Model 1 and Model 2, respectively—three scenarios are implemented experimentally, with different variations given to the load torque and velocity references. Besides the output current, the velocity and induced torque are also measured in all three cases to provide a basis of evaluation for the performance of EKF schemes. The results are presented in Figs. 4–6. In these figures, tind &t̂L , nm &n̂m , ψ̂sα , ψ̂sβ , ψ̂rα , and ψ̂rβ illustrate the induced torque as obtained from the torque transducer and estimated load torque, the actual and estimated velocity, and the estimated α and β components of the stator and rotor fluxes, respectively. e(·) error signals demonstrate the deviations between the actual and the estimated components of the stator current. The sampling rate used for the EKF estimation in the experiments is Tsample = 100 µs. The estimation of states is started with the assumption of no a priori information and with initial values of zero. (12) where x: i and ν for current and voltage, respectively. Due to the importance of system parameter values, prior to the performance tests, the dc resistance is measured, and no load and short circuit experiments are performed to calculate the initial values of the parameters. These parameters are tuned to obtain minimum error of the current, velocity, and output torque between the actual system and its model. By applying the same voltage inputs to the actual system, its model is running simultaneously on the computer. The tuning process is performed over a wide velocity range and for a variety of load A. Scenario I—Step-Type Changes in tL (Fig. 4) In this scenario, the EKF schemes for both models are tested under step-type variations of the load torque, as can be seen in Fig. 4. These step variations are created by switching the load resistors ON and OFF. Inspecting the results for both models, it can be noted that, in spite of the instantaneous switching effects, isα and isβ peaks and variations remain within a very low error band. The small value of this estimation error is an important indicator for the good performance of the EKF in the high-velocity range under load and no load. The estimated BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS Fig. 4. 277 Experimental results for step-type load torque variations at constant high velocity. (a) Model 1. (b) Model 2. values of velocity and load torque also track their measured values more closely throughout the operation range. again, the current errors remain within the previously defined error band, indicating the good performance of the algorithm over a wide velocity range. B. Scenario II—Velocity and Load Torque Reversal (Fig. 5) In this scenario tested for both models, the velocity/load torque (varying linearly with velocity) is reversed by changing the input frequency from 50 to −50 Hz, while the motor is running under a load torque of 19 N · m. The slope of this variation is determined with the arbitrary choice of the acceleration/deceleration rate given as an option on the ac drive. By inspecting the results of this scenario, it can be noted that the estimated load torque/velocity tracks the linear variation of the measured torque/velocity through 1450 to −1450 r/min. Once C. Scenario III—Zero and Low Velocities (Fig. 6) In this scenario, while the motor is running at 10 r/min, at t = 20 s, nm is stepped down to 0 r/min and is kept at zero for 64 s; at the end of this interval, nm is stepped up to 10 r/min for Model 1. A similar scenario with the same duration of zerospeed operation is implemented for Model 2. The variations are obtained by changing the speed reference on the ac drive. As a result, the stator-based estimator yields a velocity error of −4 r/min, while for the rotor-based estimator, this error remains 278 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 Fig. 5. Experimental results for reversed load torque and velocity. (a) Model 1. (b) Model 2. within −2 r/min. Also, a very low current error is obtained in both models. Additionally, the flux amplitude and position estimates for both the stator and rotor-based models at zero speed appear to be stable and constant as expected, indicating the good performance of the developed algorithm. The errors obtained in the velocity and load torque estimates, on the other hand, are mainly due to parameter uncertainties related to Ls and Rs , stator inductance and resistance, respectively, and Lr and Rr , rotor inductance and resistance, respectively, as discussed in Section I. An indication of this fact is the bigger velocity estimation error obtained with the EKF scheme developed for the stator-oriented model, Model 1. The well- known temperature-based variations of Rs at very low velocity are more effective than Rr variations at low speed, thereby explaining the larger estimation errors in the flux with Model 1 at low/zero speed, which in turn causes larger velocity estimation errors. However, estimation errors in both cases remain within an acceptable band, motivating the use of estimation scheme in sensorless IM control. VI. C ONCLUSION In this paper, EKF-based sensorless estimation algorithms are developed for the stator- and rotor-oriented models of IMs. BARUT et al.: SPEED-SENSORLESS ESTIMATION FOR INDUCTION MOTORS USING EXTENDED KALMAN FILTERS Fig. 6. 279 Experimental results for very low and zero velocity operation. (a) Model 1. (b) Model 2. The load torque and velocity estimations are performed simultaneously, with the velocity taken into consideration using the equation of motion and not as a constant parameter as in most past studies. The stator (or the rotor) flux is estimated as well, in addition to the stator currents, which are also measured as output. The estimation algorithms are tested experimentally under challenging variations of load torque and velocity, also including persistent operation at zero speed. For all tested scenarios, the current (estimation) errors have remained within a band for both models, indicating the good performance of the proposed method. Satisfactory velocity estimation errors ranging within 2–4 r/min have also been obtained for persistent operation of zero speed. The advantage of the proposed estimation scheme is that it does not require change of algorithms or adjustment of gains/parameter signals for convergence at steady state. In that sense, the developed EKF scheme offers a more generalized and yet effective solution for the sensorless estimation of IMs 280 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 over a wide speed range and at zero speed, motivating the use of the estimation method with sensorless FOC and DTC of IMs. The results can be further improved with the estimation of temperature and frequency dependent uncertainties of stator and rotor resistances and other system parameters based on the application. 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Dunnigan, “Comparative study of a sliding-mode observer and Kalman filters for full state estimation in an induction machine,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 149, no. 1, pp. 53–64, Jan. 2002. [20] R. Ortega, N. Barabanov, G. Escobar, and E. Valderrama, “Direct torque control of induction motors: Stability analysis and performance improvement,” IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1209–1222, Aug. 2001. [21] G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984. [22] P. Vas, Sensorless Vector and Direct Torque Control. New York: Oxford Univ. Press, 1998. [23] Q. Ge and Z. Feng, “Speed estimated for vector control of induction motor using reduced-order extended Kalman filter,” in Proc. IEEE PIEMC, Beijing, China, 2000, vol. 1, pp. 138–142. Murat Barut (S’06) was born in Gaziantep, Turkey, in 1973. He received the B.Sc. degree in electronics engineering from Erciyes University, Kayseri, Turkey, in 1995, the M.Sc. degree in electrical and electronics engineering from Nigde University, Nigde, Turkey, in 1997, and the Ph.D. degree (with Siemens Excellence Award) in computer and control engineering from Istanbul Technical University, Istanbul, Turkey, in 2005. Since August 2004, he has been conducting his Ph.D. research studies at the Department of Electrical and Computer Engineering, University of Alaska Fairbanks, Fairbanks. He is currently an Assistant Professor with the Department of Electrical and Electronics Engineering, Nigde University. His current research interests include power electronics, electrical drives, mechatronics, and motion control. Prof. Barut is a Student Member of the IEEE Industrial Electronics Society. Seta Bogosyan (M’95) received the B.Sc., M.Sc., and Ph.D. degrees in electrical and control engineering from Istanbul Technical University, Istanbul, Turkey, in 1981, 1983, and 1991, respectively. She conducted her Ph.D. studies at the Center for Robotics, University of California, Santa Barbara, where she was a Researcher and a Lecturer from 1987 to 1991. Within the last decade, she was an Associate Professor at Istanbul Technical University. She is currently a faculty member of the Department of Electrical and Computer Engineering, University of Alaska Fairbanks, Fairbanks. She is also the Principal Investigator of several National Science Foundation and other federally funded projects. Her research interests include motion control, sensorless control of induction motors, control of hybrid electric vehicles, remote robotics, and applications of nonlinear control/estimation techniques to electromechanical systems in general. Prof. Bogosyan is an AdCom Member and the Vice President in Membership Activities of the IEEE Industrial Electronics Society (IES). She is an Associate Editor of the International Journal of Intelligent Automation and Soft Computing and the IEEE IES Magazine. Metin Gokasan (S’82–M’88) received the B.Sc., M.Sc., and Ph.D. degrees from Istanbul Technical University, Istanbul, Turkey, in 1980, 1982, and 1990, respectively, all in electrical and control engineering. He is currently an Associate Professor with the Department of Electrical and Electronics Engineering, Istanbul Technical University. From 2004 to 2006, he conducted research at the University of Alaska Fairbanks, Fairbanks, as a Visiting Scholar and worked in several projects involving the control of HEVs and sensorless control of induction motors. His research interests include the control of electrical machinery, power electronics and electrical drives, control of hybrid electric vehicles, and mechatronics systems. Prof. Gokasan is a Member of the IEEE Industrial Electronics Society (IES) and the Technical Committee on Education in Engineering and Industrial Technologies within the IEEE IES.
