Department of Electrical Engineering Southern Taiwan University of Science and Technology Robot and Servo Drive Lab. 2016/3/14 Sensorless Control Method for PMSM Based on Frequency-Adaptive Disturbance Observer IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 2, NO. 2, JUNE 2014 Yongsoon Park, Student Member, IEEE, and Seung-Ki Sul, Fellow, IEEE 學生 : 林信佑 指導教授 : 王明賢

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 2 outline Abstract Introduction DISTURBANCE OBSERVER FOR FLUX ESTIMATION Gain Settings of the Disturbance Observer Experiments Conclusion References

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 3 Abstract In this paper, a frequency-adaptive disturbance observer has been proposed to remove the disturbances in estimating the stator flux and to enhance the accuracy of the rotor angle estimation. The performance of the proposed sensorless method has been mainly assessed through experiments at low speed operations, where the sensorless drive of PMSM is regarded as being extremely difficult without the signal injection.

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 4 Introduction FOR HIGH performance servo drive, the rotor angle of permanent magnet synchronous motor (PMSM) should be detected without time delay. The rotor angle indicates the direction of rotor flux originated from the permanent magnet, and the position sensor is normally used to detect it. However, the position sensor may cause some problems related to extended axial length, extra cost, reliability concern, and electromagnetic interference of signal.

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 5 In general, the estimation of stator flux is based on (1) which is derived from the stator voltage equation in (2) Rs is the stator resistance, λ f refers to the flux linkage of permanent magnet, and θr to the rotor angle.

Department of Electrical Engineering Southern Taiwan University of Science and Technology The stator flux can be calculated through integration according to (1), which is based on (2). When considering the current model in (1) with (3), the stator flux in the stationary reference frame can be described as 2016/3/14 Robot and Servo Drive Lab. 6

Department of Electrical Engineering Southern Taiwan University of Science and Technology T2S for the estimation of angle and speed If λem is always positive under operation, (6) can be used to calculate the rotor angle.For the most cases of PMSM, λem may have positive value even with the maximum id. 2016/3/14 Robot and Servo Drive Lab. 7

Department of Electrical Engineering Southern Taiwan University of Science and Technology State Equation to Design the Disturbance Observer When λm refers to the magnitude of stator flux in the α−β frame, the stator flux estimated by the integration in a practical system can be modeled as Disturbances are mainly low-frequency phenomenon, which can be modeled by step signal model [22]. In addition, if λm is also assumed to be step varying, the derivative of (7) can be derived as 2016/3/14 Robot and Servo Drive Lab. 8

Department of Electrical Engineering Southern Taiwan University of Science and Technology where ω f means the rotating speed of stator flux. Based on (8), the state equation on the estimated stator flux can be derived as 2016/3/14 Robot and Servo Drive Lab. 9

Department of Electrical Engineering Southern Taiwan University of Science and Technology Luenberger observe can be designed as The hat “ ∧ ” indicates estimated value hereafter, and the variables in Lm are the observer gains. 2016/3/14 Robot and Servo Drive Lab. 10

Department of Electrical Engineering Southern Taiwan University of Science and Technology Gain Settings of the Disturbance Observer For the gain settings, the internal transfer functions of the observer can be discussed. These transfer functions are derived as (11), as explained in [16] 2016/3/14 Robot and Servo Drive Lab. 11

Department of Electrical Engineering Southern Taiwan University of Science and Technology Gain Settings of the Disturbance Observer 2016/3/14 Robot and Servo Drive Lab. 12

Department of Electrical Engineering Southern Taiwan University of Science and Technology Gain Settings of the Disturbance Observer Pt=det[SIm-Am+LmCm] 2016/3/14 Robot and Servo Drive Lab. 13

Department of Electrical Engineering Southern Taiwan University of Science and Technology By the setting of (14), ω f only appears as the form of its square in the coefficients of the internal transfer functions. That is, the poles and zeros at a certain speed are the same with those at the reversed speed. Then, the observer poles can be placed by considering the positive case only. In addition, the condition of (15) can be adopted to make the observer structure symmetric in the α − β frame 2016/3/14 Robot and Servo Drive Lab. 14

Department of Electrical Engineering Southern Taiwan University of Science and Technology The observer gains are finally determined as When the gains in (16) are used, the transfer functions pertaining to the disturbances are derived as 2016/3/14 Robot and Servo Drive Lab. 15

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 16 Disturbance Observer for Stator Flux Estimation

Department of Electrical Engineering Southern Taiwan University of Science and Technology Frequency response of proposed observer when ω f is 2π10 rad/s. 2016/3/14 Robot and Servo Drive Lab. 17

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 18

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 19

Department of Electrical Engineering Southern Taiwan University of Science and Technology EXPERIMENTS Initially, the rotor angle is directly calculated from the stator flux by using (6) and (20) that is indicated by θˆr in Fig /3/14 Robot and Servo Drive Lab. 20

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 21 Equation (25) can be derived from (24)

Department of Electrical Engineering Southern Taiwan University of Science and Technology EXPERIMENTS 2016/3/14 Robot and Servo Drive Lab. 22 where the ratings of the eight-pole SMPMSM are 11.5 N-m and 1500 r/min. The induction machine (IM) in Fig. 8(a) was employed to apply load torque to the SMPMSM during driving.

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 23 EXPERIMENTS

Department of Electrical Engineering Southern Taiwan University of Science and Technology EXPERIMENTS 2016/3/14 Robot and Servo Drive Lab. 24 The angle error θd was <0.25 rad near zero speed as shown in Fig. 13.

Department of Electrical Engineering Southern Taiwan University of Science and Technology EXPERIMENTS 2016/3/14 Robot and Servo Drive Lab. 25 As explained earlier, the SMPMSM cannot be stopped indefinitely at standstill under heavy loads with the proposed method. However, as shown in Fig. 14, it has been confirmed that the test motor can be repeatedly stayed at standstill for 300 ms under 7.5-N-m load, which corresponds to 65.2% of the rated torque.

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 26 Conclusion The frequency-adaptive disturbance observer has been proposedin this paper to enhance the performance of the sensorless control method based on the stator flux model of PMSM. Although the proposed method could not ensure its performance over all operating conditions, the speed of the test motor could be repeatedly reversed by the proposed method less than ±10% of its rated speed under 65.2% load. And,the test motor can stay at zero speed with partial load without instability issues for several hundred milliseconds.

Department of Electrical Engineering Southern Taiwan University of Science and Technology 2016/3/14 Robot and Servo Drive Lab. 27 References [1] Y.-D. Yoon, S.-K. Sul, S. Morimoto, and K. Ide, “High-bandwidth sensorless algorithm for AC machines based on square-wave-type voltage injection,” IEEE Trans. Ind. Appl., vol. 47, no. 3, pp. 1361–1370,May/Jun [2] J. Holtz, “Sensorless control of induction machines—With or without signal injection,” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 7–30,Feb [3] M. Schroedl, “Sensorless control of AC machines at low speed and standstill based on the ‘INFORM’ method,” in Proc. Ind. Appl. Conf.31st IAS Annu. Meeting, vol. 1. Oct. 1996, pp. 270–277. [4] P. L. Jansen and R. D. Lorenz, “Transducer less position and velocity estimation in introduction and salient AC machines,” IEEE Trans. Ind.Appl., vol. 31, no. 2, pp. 240–247, Mar./Apr [5] M. Linke, R. Kennel, and J. Holtz, “Sensorless position control of permanent magnet synchronous machines without limitation at zero speed,” in Proc. 28th Annu. Conf. Ind. Electron. Soc., Nov. 2002,pp. 674–679.

Department of Electrical Engineering Southern Taiwan University of Science and Technology References [6] Z. Q. Zhu and L. M. Gong, “Investigation of effectiveness of sensorless operation in carrier-signal-injection-based sensorless-control methods,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3431–3439, Aug [7] R. Mizutani, T. Takeshita, and N. Matsui, “Current model-based sensorless drives of salient-pole PMSM at low speed and standstill,” IEEE Trans. Ind. Appl., vol. 34, no. 4, pp. 841–846, Jul./Aug [8] S. Morimoto, K. Kawamoto, M. Sanada, and Y. Takeda, “Sensorless control strategy for salient-pole PMSM based on extended EMF in rotating reference frame,” IEEE Trans. Ind. Appl., vol. 38, no. 4, pp. 1054–1061, Jul./Aug [9] P. Kshirsagar, R. P. Burgos, J. Jang, A. Lidozzi, F. Wang, D. Boroyevich, et al., “Implementation and sensorless vector-control design and tuning strategy for SMPM machines in fan-type applications,” IEEE Trans. Ind. Appl., vol. 48, no. 6, pp. 2402–2413, Nov./Dec /3/14 Robot and Servo Drive Lab. 28

Department of Electrical Engineering Southern Taiwan University of Science and Technology References [10] K.-W. Lee and J.-I. Ha, “Evaluation of back-EMF estimators for sensorless control of permanent magnet synchronous motors,” J. Power Electron., vol. 12, no. 4, pp. 604–614, Jul [11] A. Khlaief, M. Bendjedia, M. Boussak, and M. Gossa, “A nonlinear observer for high-performance sensorless speed control of IPMSM drive,” IEEE Trans. Power Electron., vol. 27, no. 6, pp. 3028–3040,Jun [12] I. Boldea, M. C. Paicu, and G.-D. Andreescu, “Active flux concept for motion- sensorless unified AC drives,” IEEE Trans. Power Electron., vol. 23, no. 5, pp. 2612–2618, Sep [13] G. Foo and M. F. Rahman, “Sensorless direct torque and flux-controlled IPM synchronous motor drive at very low speed without signal injection,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 395–403, Jan [14] Y. Park, S.-K. Sul, J.-K. Ji, and Y.-J. Park, “Analysis of estimation errors in rotor position for a sensorless control system using a PMSM,” J. Power Electron., vol. 12, no. 5, pp. 748–757, Sep /3/14 Robot and Servo Drive Lab. 29

Department of Electrical Engineering Southern Taiwan University of Science and Technology References [15] D. G. Luenberger, “An introduction to observers,” IEEE Trans. Autom. Control, vol. 16, no. 6, pp. 596–602, Dec [16] Y. Park, S.-K. Sul, W.-C. Kim, and H.-Y. Lee, “Phase locked loop based on an observer for grid synchronization,” in Proc. IEEE 28th APEC, Mar. 2013, pp. 308– 315. [17] Y.-C. Son, B.-H. Bae, and S.-K. Sul, “Sensorless operation of permanent magnet motor using direct voltage sensing circuit,” in Proc. Conf. Rec. IEEE IAS Annu. Meeting, Oct. 2002, pp. 1674– ] B.-H. Bae and S.-K. Sul, “A compensation method for time delay of full-digital synchronous frame current regulator of PWM AC drives,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 802–810, May/Jun [19] Y. Park and S.-K. Sul, “A novel method utilizing trapezoidal voltage to compensate for inverter nonlinearity,” IEEE Trans. Power Electron., vol. 27, no. 12, pp. 4837–4846, Dec /3/14 Robot and Servo Drive Lab. 30

Department of Electrical Engineering Southern Taiwan University of Science and Technology References [20] Y. Park and S.-K. Sul, “Compensation of inverter nonlinearity based on trapezoidal voltage,” in Proc. IEEE ECCE, Sep. 2012, pp. 2292–2299. [21] D.-W. Chung, J.-S. Kim, and S.-K. Sul, “Unified voltage modulation technique for real-time three-phase power conversion,” IEEE Trans. Ind. Appl., vol. 34, no. 2, pp. 374–380, Mar./Apr [22] M. A. Johnson and M. H. Moradi, “Some PID control fundamentals,” in PID Control: New Identification and Design Methods. New York, NY, USA: Springer- Verlag, 2005, ch. 2. [23] Y. Peng, D. Vrancic, and R. Hanus, “Anti-windup, bumpless, and conditioned transfer techniques for PID controllers,” IEEE Control Syst., vol. 16, no. 4, pp. 48– 57, Aug [24] J.-P. Lee, B.-D. Min, T.-J. Kim, D.-W. Yoo, and J.-Y. Yoo, “Active frequency with a positive feedback anti-islanding method based on a robust PLL algorithm for grid-connected PV PCS,” J. Power Electron., vol. 11, no. 3, pp. 360–368, May /3/14 Robot and Servo Drive Lab. 31