1. Department of Electrical Engineering Southern Taiwan University Robot and Servo Drive Lab. 2016/3/14 Implementation Of Finite-State Model Predictive Control For Commutation Torque Ripple Minimization Of Permanent-Magnet Brushless DC Motor Professor ： Ming-Shyan Wang Student ： Shih-Yu Wu IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 3, Page.896~Page.905, MARCH 2013, By Changliang Xia, Senior Member, IEEE, Yingfa Wang, and Tingna Shi

2. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 2 Outline Analysis Of Commutation Process Reduction Of Commutation Torque Ripple Numerical Simulations And Analysis Experimental Result And Analysis Conclusion References

3. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 3 Abstract This method proposes a unified approach for suppressing commutation torque ripple over the entire speed range without distinguishing high speed and low speed and overcomes the difficulties of commutated-phase-current control, avoiding complex current controllers or modulation models. A discrete-time noncommutated-phase-current predictive model of BLDCM during commutation is established. According to the predefined cost function, the optimal switching state is directly selected and applied during the next sampling period so as to make the slope rates of incoming and outgoing phase currents match in the course of commutation, thus ensuring the minimization of commutation torque ripple.

4. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 4 Mathematical Model Of Commutation Torque Permanent-magnet BLDCM conventionally operates in two phase (electrical) conducting mode, and this conducting mode includes a commutation region and a noncommutation region. This paper focuses on the commutation region, aiming at reducing commutation torque ripple

5. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 5 Mathematical Model Of Commutation Torque The mathematical model of BLDCM can be expressed as : 3 phase balanced :,, and are the terminal voltages of the three phase winding,, and are the phase currents of the three-phase winding,, and are the back EMFs of the three-phase winding is the neutral point voltage R and are the phase resistance and equivalent phase inductance

6. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 6 Mathematical Model Of Commutation Torque The commutation of the motor from phase A → C conduction to phase B → C conduction is taken as an example of commutation process A phase is floating phase C phase is noncommutated phase

7. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 7 Mathematical Model Of Commutation Torque Generally, the electromagnetic torque developed by BLDCM is given by : is the rotor mechanical angular velocity is the electromagnetic torque. Supposing that back EMF maintains constant value E during commutation, the commutation torque of BLDCM can be expressed as

8. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 8 Mathematical Model Of Commutation Torque where E is the flap top value of the trapezoidal back EMF, is the torque constant, is the noncommutated phase current. It can be seen from the aforementioned analysis that the commutation torque developed in the commutation process is proportional to noncommutated phase current. Therefore, noncommutated phase current can be taken as the evaluation criterion of commutation torque.

9. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 9 Mathematical Model Of Commutation Torque As known in [11], the relationship between the slope rate of falling current and that of rising current indicates that there exist three different cases of commutating current in the winding

10. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 10 Noncommutated-Phasecurrent Constant = 4E Known from the analysis in [11], the necessary and sufficient condition for eliminating commutation torque ripple is The following result is derived:

11. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 11 Noncommutated-Phasecurrent Constant = 4E 3 phase balance 、 phase resistance neglected 、 、 、 代入公式 (5.4) (5.5) 代入 (5.1) (5.5) 代入 (5.2) (5.5) 代入 (5.3)

12. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 12 Noncommutated-Phasecurrent Constant = 4E Taking the beginning of the commutation as the time origin, the initial phase currents are given by ， ，

13. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 13 Noncommutated-Phasecurrent Constant = 4E Current vanishes at the same time the current reaches its final value I

14. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 14 Noncommutated-phase-current dips: With the presence of during commutation, the conduction status of the inverter Noncommutated-Phase-Current Dips floating Phase A

15. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 15 Noncommutated-Phase-Current Dips 3 phase balance 、 phase resistance neglected 、 、 、 The following result is derived:

16. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 16 Noncommutated-Phase-Current Dips The sum of the slope rates of phase A current and phase B current can satisfy condition (5) by correctly switching power switch between conduction and shutdown. Hence, commutation torque ripple can be reduced. As shown in Figure, improved commutating phase current is given in broken lines.

17. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 17 Noncommutated-Phase-Current Spikes : With the presence of during commutation, the conduction status of the inverter Noncommutated-Phase-Current Spikes

18. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 18 Noncommutated-Phase-Current Spikes 3 phase balance 、 phase resistance neglected 、 、 、 The following result is derived:

19. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 19 Noncommutated-Phase-Current Spikes Therefore, the sum of the slope rates of phase A current and phase B current can satisfy condition (5) by correctly switching power switches and between conduction and shutdown. Hence, commutation torque ripple can be reduced. As shown in Figure, improved commutating phase current is given in broken lines.

20. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 20 FS-MPC Making full use of the inherent discrete nature of power inverters, by computation of a discrete model, FS-MPC predicts the future behavior of the system in the next sampling period under each possible state of power switches. In addition, it makes use of predictive behavior to evaluate the predefined cost function and finally selects and generates the optimal state of power switches. A control objective, cost function which is a scalar criterion measuring

21. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 21 FS-MPC The cost function of noncommutated phase current during commutation is defined as: usually the output of the speed loop, is the reference current is the predictive value of noncommutated phase current during commutation k + 1 is the (k + 1)th sampling time

22. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 22 Noncommutated-Phase-Current Predictive Model As known from the preceding section, noncommutated phase current is taken as the evaluation criterion of commutation torque. Hence, only noncommutated phase current needs to be measured, while there is no need to consider the slope rates of falling current and rising current. Noncommutated-phase-current predictive model in different commutation processes is established as follows. 1. Phase C as noncommutation phase: From (1) and (2), the following equations are derived:

23. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 23 Noncommutated-Phase-Current Predictive Model From (9) and (10), the following expression is obtained: Approximating the derivative by and then replacing it in (11), the discrete model of (11) is obtained as is the sampling time

24. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 24 Noncommutated-Phase-Current Predictive Model The discrete model (12) needs to be iterated for the (k + 1)th prediction. Then, the predictive current of phase C is given as 2. Phase B as noncommutation phase: Similarly, the predictive current of phase B is given as

25. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 25 Noncommutated-Phase-Current Predictive Model 3. Phase A as noncommutation phase: Similarly, the predictive current of phase A is given as

26. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 26 Numerical Simulation Results-Low Speed when the motor runs at low speed, the rising current increases quickly. Consequently, noncommutated phase- current spikes are generated. Hence, commutation torque increases, and commutation torque ripple is generated. In Fig. 8(b), phase B current is regulated by power switch at the moment of commutation, and the rise of phase B current slows down. Then, the rising current and falling current are matched, and constant noncommutated phase current is ensured.

27. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 27 Numerical Simulation Results-High Speed which leads to the appearance of noncommutated-phase-current dips and the decrease of commutation torque, hence generating commutation torque ripple. In Fig. 9(b), the slope rate of phase A current decreases via regulating power switch at the moment of commutation. Consequently, the rising current and falling current are matched, and constant noncommutated phase current is ensured during commutation.

28. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 28 Experimental Result And Analysis Texas Instruments floatpoint DSP TMS320F28335 with 32-bit CPU System clock rate is 150 MHz Switching frequency and ADC sampling frequency 40 kHz The most relevant prototype parameters of BLDCM are presented in

29. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 29 Experimental Result And Analysis At Low Speed Fig. 13(a), at low speed n = 200 r/min, the rising current in phase B goes faster, and noncommutated-phase- current spikes occur in phase C. In Fig. 13(b), when the proposed FS- MPC approach is adopted at the speed n = 200 r/min, phase B current is adjusted by power switch, and consequently, the rising current and falling current are matched. Hence, noncommutated phase current is kept constant. CH1:phase A current CH4:control signal of power switching T3 CH2:phase B current CH5:control signal of power switching T1 CH3:phase C current A(T1)C→B(T3)C

30. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 30 Experimental Result And Analysis At Low Speed Fig. 14(a), at high speed n = 2000 r/min, the slope rate of rising current in phase B gets lower, and the rising current and falling current are mismatched. noncommutated phase current generates current dips. Furthermore, commutation torque ripple is generated. In Fig. 14(b),when the proposed FS-MPC approach is adopted at the speed n = 2000 r/min, the actions of during commutation properly adjust the current slope of phase A. CH1:phase C current CH4:control signal of power switching T3 CH2:phase A current CH5:control signal of power switching T1 CH3:phase B current A(T1)C→B(T3)C

31. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 31 Experimental Result And Analysis In Dynamic Process Figure shows the three-phase current and speed response at low speed in dynamic process Figure(a), when the motor runs at low speed in dynamic process, the slope rate of rising current goes higher, and noncommutated-phase winding generates current spikes. Then, commutation torque increases. (a) Without the proposed approach. CH1:speed response CH4: phase C current CH2:phase A current CH3: phase B current

32. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 32 Experimental Result And Analysis In Dynamic Process Figure shows the three-phase current and speed response at low speed in dynamic process Fig. 15(b), the rising current and falling current are matched when the proposed FS-MPC approach is adopted at low speed in dynamic process. (b) With the proposed approach CH1:speed response CH4: phase C current CH2:phase A current CH3: phase B current

33. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 33 Experimental Result And Analysis In Dynamic Process Figure shows the three-phase current and speed response at high speed in dynamic process In Fig. 16(a), when the speed is greatly increased, noncommutated phase current generates current dips, and commutation torque decreases. (a)Without the proposed approach. CH1:speed response CH4: phase C current CH2:phase A current CH3: phase B current

34. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 34 Experimental Result And Analysis In Dynamic Process Figure shows the three-phase current and speed response at high speed in dynamic process The proposed method gives a unified approach for suppressing commutation torque ripple over the entire speed range without distinguishing high speed and low speed. (a)With the proposed approach. CH1:speed response CH4: phase C current CH2:phase A current CH3: phase B current

35. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 35 Conclusion This paper has proposed a unified approach, which can effectively reduce commutation torque ripple over the whole speed range, without considering different current cases at high speed and low speed, respectively, and overcome the difficulties of commutated-phase-current control, avoiding complex current controllers or modulation models. The study in this paper has demonstrated that commutation torque ripple can be effectively reduced by properly switching three conduction statuses of the power inverter during commutation.

36. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 36 References [11] R. Carlson, M. Lajoie-Mazenc, and J. C. D. S. Fagundes, “ Analysis of torque ripple due to phase commutation in brushless dc machines, ” IEEE Trans. Ind. Appl., vol. 28, no. 3, pp. 632 – 638, May 1992. [12] G.-H. Kim, S.-J. Kang, and J.-S. Won, “ Analysis of the commutation torque ripple effect for BLDCM fed by HCRPWM-VSI, ” in Proc. Appl. Power Electron. Conf. Expo., 1992, pp. 277 – 284. [13] Y. Murai, Y. Kawase, K. Ohashi, K. Nagatake, and K. Okuyama, “ Torque ripple improvement for brushless dc miniature motors, ” IEEE Trans. Ind. Appl., vol. 25, no. 3, pp. 441 – 450, May/Jun. 1989. [14] D.-K. Kim, K.-W. Lee, and B.-I. Kwon, “ Commutation torque ripple reduction in a position sensorless brushless dc motor drive, ” IEEE Trans. Power Electron., vol. 21, no. 6, pp. 1762 – 1768, Nov. 2006. [15] K.-Y. Nam,W.-T. Lee, C.-M. Lee, and J.-P. Hong, “ Reducing torque ripple of brushless dc motor by varying input voltage, ” IEEE Trans. Magn., vol. 42, no. 4, pp. 1307 – 1310, Apr. 2006. [16] J.-H. Song and I. Choy, “ Commutation torque ripple reduction in brushless dc motor drives using a single dc current sensor, ” IEEE Trans. Power Electron., vol. 19, no. 2, pp. 312 – 319, Mar. 2004. [17] T. N. Shi, Y. T. Guo, P. Song, and C. L. Xia, “ A new approach of minimizing commutation torque ripple for brushless dc motor based on dc – dc converter, ” IEEE Trans. Ind. Electron., vol. 57, no. 10, pp. 3483 – 3490, Oct. 2010. [19] J. Rodriguez, J. Pontt, C. Silva, and M. Salgado, “ Predictive control of three-phase inverter, ” Electron. Lett., vol. 40, no. 9, pp. 561 – 563, Apr. 2004. [20] J. Rodriguez, J. Pontt, C. A. Silva, and P. Correa, “ Predictive current control of a voltage source inverter, ” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 495 – 503, Feb. 2007.

37. Department of Electrical Engineering Southern Taiwan University 2016/3/14 Robot and Servo Drive Lab. 37 Thanks for listening!