THE approach of sensorless speed control of induction motors

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 1039 An Adaptive Sliding-Mode Observer for Induction Motor Sensorless Speed Control Jingchuan Li, Longya Xu, Fellow, IEEE, and Zheng Zhang, Senior Member, IEEE Abstract An adaptive sliding-mode flux observer is proposed for sensorless speed control of induction motors in this paper. Two sliding-mode current observers are used in the method to make flux and speed estimation robust to parameter variations. The adaptive speed estimation is derived from the stability theory based on the current and flux observers. The system is first simulated by MATLAB and tested by hardware-in-the-loop. Then, it is implemented based on a TMS320F2812, a 32-bit fixed-point digital signal processor. Simulation and experimental results are presented to verify the principles and demonstrate the practicality of the approach. Index Terms Adaptive sliding-mode observer, induction motor, sensorless speed control. I. INTRODUCTION THE approach of sensorless speed control of induction motors can reduce cost, avoid fragility of a mechanical speed sensor, and eliminate the difficulty of installing the sensor in many applications. Thus, the approach has been receiving more and more attention. However, due to the high-order multiple variables and nonlinearity of induction motor dynamics, estimation of the rotor flux and speed is still very challenging. Over the years, many research efforts have been made and various sensorless speed control algorithms have been proposed in the literature. The model reference adaptive system (MRAS) methods [1], [2] are based on the comparison between the outputs of two estimates. The output errors are then used to drive a suitable adaptation mechanism that generates the estimated speed. These schemes require integration and the system performance is limited by parameter variations. The Kalman filter approaches [3] are known to be able to get accurate speed information, but have some inherent disadvantages, such as the influence of noise and large computational burden. Adaptive observer-based approaches [4], [5] have improved performance using an adaptive mechanism with relatively simple computation. Slidingmode observers [6] [9], due to their order reduction, disturbance rejection, and simple implementation, are recognized as the promising control methodology for electric motors. Other algorithms for sensorless speed control, such as artificial neural network [10] and artificial intelligence (AI) methods [11], can achieve high performance, but they are relatively complicated and require large computational time. In the sensorless speed control of induction motors with direct field orientation, the rotor flux and speed information are dependent on the observers. However, the exact values of the parameters that construct the observers are difficult to measure and changeable with respect to the operating conditions. When the motor parameters are changed and, thus, are different from the preset values, the estimated flux and speed will deviate from the real values. To make flux and speed estimation robust to parameter variations, a novel adaptive sliding-mode flux and speed observer is proposed in the paper. Two sliding-mode current observers are used in the proposed method. The effects of parameter deviations on the rotor flux observer can be alleviated by the interaction of these two current sliding-mode observers. The stability of the method is proven by Lyapunov theory. An adaptive speed estimation is also derived from the stability theory. II. SLIDING-MODE CURRENT AND FLUX OBSERVER DESIGN Induction motors can be modeled in various reference frames. Defining stator currents and rotor fluxes as the state variables, we can express the induction motor model in the stationary frame as (1) (2) are stator currents, are rotor fluxes, are stator voltages, Paper IPCSD-05-029, presented at the 2004 Industry Applications Society Annual Meeting, Seattle, WA, October 3 7, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript submitted for review September 25, 2004 and released for publication April 25, 2005. J. Li and L. Xu are with the Department of Electrical and Computer Engineering. The Ohio State University, Columbus, OH 43210-1272 USA (e-mail: li.407@osu.edu; xu.12@osu.edu). Z. Zhang is with the R&E Center, Whirpool Corporation, Benton Harbor, MI 49022 USA (e-mail: Zheng_Zhang@whirlpool.com). Digital Object Identifier 10.1109/TIA.2005.851585 are stator and rotor resistances, are total stator and rotor inductances, is magnetizing inductance, is the leakage coefficient,, is rotor time constant,, and is motor angular velocity. 0093-9994/$20.00 2005 IEEE

1040 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 Fig. 1. Configuration of the flux and speed observer. The configuration of the proposed flux and speed estimators is shown in Fig. 1. The adaptive sliding-mode observer consists of two sliding-mode current observers and one rotor flux observer. The rotor flux observer is based on the current estimation from the two current observers. The rotor speed observer takes the outputs from the second current observer and the rotor flux observer as its inputs and generates the estimated rotor speed as the output. The estimated speed is then fed back to the second current observer for its adaptation. The estimation of the motor speed is derived from a Lyapunov function, which guarantees the system convergence and stability. Once the sliding functions of the current observers reach the sliding surfaces, the rotor flux will converge to the real value asymptotically. Each sub-observer of the overall adaptive sliding-mode observer is discussed in the following sections. A. Current Observer I The first sliding-mode current observer is defined as [6] Equation (5) indicates that the equivalent control equals the rotor flux multiplied by the matrix, which is the common part in (2). The rotor flux can be obtained by integrating this equivalent control without speed information as discussed in [6]. The flux estimation is accurate when the motor parameters, and are known. However, if the parameters in the observers are different from the real values, there will be some errors in the coefficients of the observers. Then, the estimated flux and speed will be incorrect. In order to compensate for this divergence, a second sliding-mode current observer is used for the flux estimation. B. Current Observer II The second sliding-mode current observer is designed differently from (3) as (6) are the first observer currents, are the first sliding functions, (3) are the second observer currents, are the observed rotor fluxes, the second sliding function, is The sliding-mode surface is defined as The sliding-mode surface is According to the above formulas, the current error equation is By subtracting (1) from (6), the error equation becomes (4). By selecting large enough, the sliding mode will occur, and then it follows that. From an equivalent control point of view, we have (7) (8) From the equivalent control concept [8], if the current trajectories reach the sliding manifold, we have (5). The second equivalent control equals to the negative multiplication of the estimated rotor flux error and the matrix. It is noticed that the second current observer needs the rotor speed as the input.

LI et al.: ADAPTIVE SLIDING-MODE OBSERVER FOR INDUCTION MOTOR SENSORLESS SPEED CONTROL 1041 C. Rotor Flux Observer Design Combining the results from (5) and (8), the rotor flux observer can be constructed as Let be an arbitrary positive constant. With this assumption, the above equation becomes (9) is the observer gain matrix to be decided such that the observer is asymptotically stable. From (3) and (6), the equivalent controls obtained individually by the two current observers will deviate from their real values if the motor parameters are incorrect. Consequently, the rotor flux estimation based on each individual control will also be inaccurate. To reduce this deviation on rotor flux estimation, the rotor flux observer is designed from the combination of two equivalent controls, the effects of parameter variations are largely cancelled. From (5) and (8), the error equation for the rotor flux is (14) Letting the second term be equal to the third term in (14), we can find the following adaptive scheme for rotor speed identification: (15) In practice, the speed can be found by the following proportional and integral adaptive scheme: (10) (16) III. ADAPTIVE SPEED ESTIMATION In order to derive the adaptive scheme, Lyapunov s stability theorem is utilized. If we consider the rotor speed as a variable parameter, the error equation of flux observer is described by the following equation: and are the positive gains. IV. STABLITY ANALYSIS Since the second term is equal to the third term in (14), the time derivative of becomes (11) is the estimated rotor speed The candidate Lyapunov function is defined as (12) is a positive constant. We know that is positive definite. The time derivative of becomes (13) (17) It is apparent that (17) is negative definite. From Lyapunov stability theory, the flux observer is asymptotically stable, guaranteeing the observed flux to converge to the real rotor flux. V. SIMULATION RESULTS To evaluate the proposed algorithm for the rotor flux and speed estimation, computer simulations have been conducted using MATLAB. The block diagram of the control system is shown in Fig. 2. To further investigate the implemental feasibility, the estimation and control algorithm are evaluated by hardware-in-the-loop (HIL) testing. A 1-hp induction motor was used in the simulation and also in the experiments. The motor parameters are as follows: 1 hp, four poles, 220 V, 5 A,,, mh, and mh. A. Simulation Results by MATLAB Figs. 3 and 4 show the induction motor response to a step speed command of 0.5 pu ( 900 r/min) the motor parameters are exactly known. The actual machine model is used

1042 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 Fig. 2. System configuration for simulation and implementation. Fig. 3. Real and estimated speed at a step speed command. Fig. 4. Real and estimated rotor flux. to calculate the current, flux, and speed of the motor. The observer model as described above is used to estimate the rotor flux and speed. Fig. 3 shows the speed command, real speed, estimated speed, and the speed estimation error. Fig. 4 shows the real and estimated rotor flux and the flux estimation error. It can be seen that the estimated speed and flux converge to the real values very quickly. To study the effects of parameter variation on the speed and flux observers, the parameters in the observers are changed on purpose in the simulation. Fig. 5 shows the simulation results when the coefficient in the observers is changed by 20% from its actual value, the flux and speed are estimated by the proposed method, and and by the previous method using only one current

LI et al.: ADAPTIVE SLIDING-MODE OBSERVER FOR INDUCTION MOTOR SENSORLESS SPEED CONTROL 1043 Fig. 5. Coefficient k in the observer is increased by 20%. (a) : real rotor flux; : estimated by the proposed method; : estimated by previous method. (b)! : real rotor speed;! : estimated by the proposed method;! : estimated by previous method. sliding-mode observer as in [6]. It is noticed that even if is incorrect, the estimated rotor flux and speed by the new observer still converge to the real values, but in the previous model, there is an offset in the rotor flux estimation and fluctuation in the rotor speed estimation. The dc offset of flux estimation by the previous method is caused by the incorrect equivalent control. If changes, the equivalent control will detune. The integration of incorrect causes dc offset on the flux estimation, as in the new flux observer, this dc offset is cancelled by using two current observers. The effects of coefficient variation on the flux and speed estimation are shown in Fig. 6. We can also observe obvious fluctuations in speed estimation. There is still an error on the rotor flux estimation by the proposed method as shown in Fig. 6(a), but the new method eliminates the dc offset caused by the parameter variation, which can be observed in results simulated by the previous model. Fig. 6. Coefficient in the observer is increased by 20%. (a) : real rotor flux; : estimated by the proposed method; : estimated by previous method. (b)! : real rotor flux;! : estimated by the proposed method;! : estimated by previous method. B. HIL Evaluation Results by TI 2812 DSP HIL evaluation is to use a computer model of the process as the real target hardware, and on the other hand, the control and estimation algorithm are implemented in real time. The purpose of HIL is to make evaluation of the proposed algorithm as close as possible to that which would be encountered in the real-time implementation. In this paper, the evaluation is performed using a TMS320F2812 DSP. The dynamics of the electric machine are modeled by five differential equations. The control and estimated algorithms are implemented in 32-bit Q-math approach, interacting with the motor model rather than the real targeted physical system. The main advantages of this evaluation are: 1) the control software is implemented and evaluated in real time and can be debugged very easily in the absence of motor and 2) the control software can be easily transferred to the real drive system with only minor changes.

1044 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 Fig. 7. Speed step response from 00.5 pu to 0.5 pu (curve 1: speed command!, 0.606 pu/div; curve 2: real speed!, 0.606 pu/div; curve 3: estimated speed ~!, 0.606 pu/div). Fig. 9. Trapezoidal speed at 60.5 pu (curve 1: phase current i, 0.6 pu/div; curve 2: torque current i, 0.3 pu/div; curve 3: estimated speed ~!, 1.212 pu/div). Fig. 10. Experimental setup. Fig. 8. Rotor flux estimation (curve 1: real flux ; curve 2: estimated flux ~ ; curve 3: estimated flux angle ~ ). The results evaluated by HIL are shown in Figs. 7 9. Fig. 7 shows the motor step response to a speed command at 0.5 pu ( 900 r/min). Fig. 8 shows the real and estimated rotor flux and the estimated flux angle. Fig. 9 shows the motor response to a trapezoidal speed command. The results show that the method can be successfully implemented by the fixed-point DSP. VI. EXPERIMETAL RESULTS In order to evaluate the performance of the proposed algorithm experimentally, an induction motor drive system was set up. The setup consists of a 1-hp induction motor, a power drive board, and a DSP controller board. The external load is imposed by a hysteresis dynamometer. The experimental setup is shown in Fig. 10. The control algorithm is implemented by a Texas Instruments TMS320F2812 32-bit fixed-point DSP. It has the following features: high-performance static CMOS technology, 150 MHz (6.67-ns cycle time); high-performance 32-bit CPU; Flash devices: up to 128 K 16 Flash; 12-bit ADC, 16 channels. The test was first performed on the motor in four-quadrant operation. Fig. 11 shows the motor response to a commanded step change speed at 900 r/min. Fig. 12 shows the measured current and two sliding-mode observer currents. It is seen that the sliding-mode functions enforce the two observed currents to the measured ones very closely. Once these two observer currents converge to the measured ones, the estimated rotor flux converges to the real rotor flux. The motor responses to a trapezoidal speed command when the motor runs at no load are shown in Fig. 13. To further investigate the motor transient performance at load conditions, an external torque pu is applied when the motor runs at the same trapezoidal speed command as in Fig. 13. The waveform of speed command, estimated speed, torque current, and phase current are shown in Fig. 14. The estimated rotor speed response to a step change of command from 360 to 1260 r/min with a load torque of

LI et al.: ADAPTIVE SLIDING-MODE OBSERVER FOR INDUCTION MOTOR SENSORLESS SPEED CONTROL 1045 Fig. 11. Transient response to speed step command 6900 r/min at no load (curve1: speed command!, 1091 r/min/div; curve 2: estimated speed ~!, 1091 r/min/div; curve 3: torque current i, 1.5 A/div; curve 4: phase current i, 5 A/div). Fig. 13. Transient response due to trapezoidal speed command (6 900 r/min) at no load (curve 1: speed command!, 2182 r/min/div; curve 2: estimated speed ~!, 2182 r/min/div; curve 3: torque current i, 1.5 A/div; curve 4: phase current i, 5 A/div). Fig. 12. Real and estimated currents (curve 1: measured current i, 3 A/div; curve 2: observed current ^i, 3 A/div; curve 3: observed current ~ i, 3 A/div). pu is shown in Fig. 15. To investigate the speed robustness, a step disturbance torque pu is applied and then removed at motor speed r/min. Fig. 16 shows the estimated rotor speed response and the torque current response. As evidenced by the testing results, the induction motor drive functions very well by the proposed algorithm. VII. CONCLUSION A novel adaptive sliding-mode observer for sensorless speed control of an induction motor has been presented in this paper. The proposed algorithm consists of two current observers and one rotor flux observer. The two sliding-mode current observers Fig. 14. Transient response due to trapezoidal speed command (6900 r/min) at T =0:5pu (curve 1: speed command!, 1091 r/min/div; curve 2: estimated speed ~!, 1091 r/min/div; curve 3: torque current i, 1.5 A/div; curve 4: phase current i, 5 A/div). are utilized to compensate for the effects of parameter variations on the rotor flux estimation. When the motor parameters are deviated from initial values by temperature or operation conditions, the errors of two equivalent controls from current observers will be largely cancelled, which make the flux estimation more accurate and insensitive to parameter variations. Although an additional sliding-mode current observer is used, the complexity of the method is not increased too much. The stability and convergence of the estimated flux to real rotor flux are proved by the Lyapunov stability theory. Digital simulation

1046 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 [5] G. Yang and T. H. Chin, Adaptive-speed identification scheme for a vector-controlled speed sensorless inverter-induction motor drive, IEEE Trans. Ind. Appl., vol. 29, no. 4, pp. 820 825, Jul./Aug. 1993. [6] A. Derdiyok, M. K. Guven, H. Rehman, N. Inanc, and L. Xu, Design and implementation of a new sliding-mode observer for speed-sensorless control of induction machine, IEEE Trans. Ind. Electron., vol. 49, no. 5, pp. 1177 1182, Oct. 2002. [7] H. Rehman, A. Derdiyok, M. K. Guven, and L. Xu, A new current model flux observer for wide speed reange sensorless control of an induction machine, IEEE Trans. Ind. Electron., vol. 49, no. 6, pp. 1041 1048, Dec. 2002. [8] V. I. Utkin, Sliding mode control design principles and applications to electric drives, IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 23 36, Feb. 1993. [9] C. Lascu, I. Boldea, and F. Blaabjerg, Direct torque control of sensorless induction motor drives: A sliding-mode approach, IEEE Trans. Ind. Appl., vol. 40, no. 2, pp. 582 590, Mar./Apr. 2004. [10] P. Mehrotra, J. E. Quaico, and R. Venkatesan, Speed estimation of induction motor using artificial neural networks, in Proc. IEEE IECON 96, 1996, pp. 881 886. [11] D. Schroder, C. Schaffner, and U. Lenz, Neural-net based observers for sensorless drives, in Proc. IEEE IECON 94, 1994, pp. 1599 1610. Fig. 15. Speed response due to step change command from 360 to 1260 r/min at T = 0:5 pu (curve1: real speed, 1091 r/min/div; curve 2: estimated speed ~!, 1091 r/min/div; curve 3: torque current i, 1.5 A/div; curve 4: phase current i, 5 A/div). Jingchuan Li received the B.S. degree from Xi an Jiaotong University, Xi an, China, in 1993. He is currently working toward the Ph.D. degree in the Department of Electrical and Computer Engineering, The Ohio State University, Columbus. His research interests include power electronics, design and control of electrical machines, and finiteelement analysis of electromagnetic devices. Fig. 16. Transient response for step disturbance torque (curve1: real speed!, 1091 r/min/div; curve 2: estimated speed ~!, 1091 r/min/div; curve 3: torque current i, 1.5 A/div). and experiments have been performed. The effectiveness of the approach is demonstrated by the results. REFERENCES [1] C. Schauder, Adaptive speed identification for vector control of induction motors without rotational transducers, IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054 1061, Sep./Oct. 1992. [2] F. Z. Peng and T. Fukao, Robust speed identification for speed-sensorless vector control of induction motors, IIEEE Trans. Ind. Appl., vol. 30, no. 5, pp. 1234 1240, Sep./Oct. 1994. [3] Y. R. Kim, S. K. Sul, and M.-H. Park, Speed sensorless vector control of an induction motor using an extended Kalman filter, in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, Oct. 4 9, 1992, pp. 594 599. [4] H. Kubota, K. Matsuse, and T. Nakano, DSP-based speed adaptive flux observer of induction motor, IEEE Trans. Ind. Appl., vol. 29, no. 2, pp. 344 348, Mar./Apr. 1993. Longya Xu (S 89 M 90 SM 93 F 04) received the M.S. and Ph.D. degrees in electrical engineering from the University of Wisconsin, Madison, in 1986 and 1990, respectively. In 1990, he joined the Department of Electrical and Computer Engineering, The Ohio State University, Columbus, he is presently a Professor. He has served as a Consultant to several industrial companies, including Raytheon Company, US Wind Power Company, General Motors, Ford, and Unique Mobility Inc. His research and teaching interests include dynamic modeling and optimized design of electrical machines and power converters for variable-speed generating and drive systems, application of advanced control theory, and digital signal processors for control of motion and distributed power systems in super-high-speed operation. Dr. Xu received the 1990 First Prize Paper Award from the Industrial Drives Committee of the IEEE Industry Applications Society (IAS). In 1991, he received a Research Initiation Award from the National Science Foundation. He was also a recipient of 1995, 1999, and 2004 Lumley Research Awards from the College of Engineering, The Ohio State University, for his research accomplishments. He has served as Chairman of the IAS Electric Machines Committee and as an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS. Zheng Zhang (M 98 SM 99) received the B.S.E.E. degree from Hefei University of Technology, Hefei, China, in 1982, the M.S.E.E. degree from Chongqing University, Chongqing, China, in 1985, and the Ph.D. degree from the Politecnico di Torino, Turin, Italy in 1997, all in electrical engineering. From 1985 to 1992, he was with the University of Shandong, Jinan, China, he taught several courses and conducted research. From 1993 to 1995, he was with the Electronics Division of the FIAT Research Center, Turin, Italy, as an Intern Researcher. While there, he was involved in the development of motor and drive systems for electric vehicle applications. He is currently with the R&E Center, Whirlpool Corporation, Benton Harbor, MI. His research interests include special motors, advanced motor controls for low-cost electronic devices, and diagnostics of appliances by use of motor drive information. He has authored more than 30 published technical papers.