1. Department of Electrical Engineering Southern Taiwan University of Science and Technology Robot and Servo Drive Lab. 2015/10/27 DSP-Based Control of Sensorless IPMSM Drives for Wide-Speed-Range Operation 學生 : Guan-Ting Lin 指導老師 : Ming Shyan Wang IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, p720-727,FEBRUARY 2013 Gaolin Wang, Rongfeng Yang, and Dianguo Xu, Member, IEEE

2. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 2 Outline Introduction Control scheme Sensorless IPMSM Control Scheme Based on DSP Mathematical Model of the Interior PMSM Position estimation at low-speed Position estimation at high-speed Design of Sliding-Mode Position Observer Dead-Time Compensation Strategy Experimental results Conclusion

3. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 3 Introduction The first class is based on the electromotive force(EMF) machine model for the middle- and the high-speed operation. The other class is the high frequency (HF) signal injection estimation for low-speed operation. The hybrid position observer combines the HF signal injection at low speed with the extended EMF observer at higher speed. To improve the performance, a dead-time compensation strategy are adequately considered.

4. Department of Electrical Engineering Southern Taiwan University of Science and Technology Control scheme Sensorless IPMSM Control Scheme Based on DSP 2015/10/27 Robot and Servo Drive Lab. 4 Fig. 1. Control scheme of sensorless IPMSM based on DSP. Vector control scheme drive based on the HF signal injection and the sliding- mode observer. The HF voltage signal is superimposed to the voltage reference from the PI current controller. A sliding-mode observer based on the extended EMF is designed to obtain the rotor position. A software phase-locked loop (PLL) and a dead-time compensation method are adopted

5. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 5 Mathematical Model of the Interior PMSM Define a d–q frame, which corresponds to the synchronous rotating reference frame. the voltage model can be given by By using the rotating inverse coordinate transformation,(1) can be transformed to the stationary frame (α–β):

6. Department of Electrical Engineering Southern Taiwan University of Science and Technology Then, the electromagnetic torque can be expressed as: 2015/10/27 Robot and Servo Drive Lab. 6 The electromagnetic torque of the IPMSM consists of two terms: the magnetic reaction and the reluctance torque. The mechanical motion equation of IPMSM is given as:

7. Department of Electrical Engineering Southern Taiwan University of Science and Technology Position estimation at low-speed 2015/10/27 Robot and Servo Drive Lab. 7 Assuming that the frequency is far higher than the fundamental frequency the HF voltage model can be expressed as: (3) To analyze the characteristic of the HF voltage model conveniently, (3) can be rewritten as follows: (4)

8. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 8 transform (4) to the d–q rotating reference frame, and the expression can be given as: Defining the estimated rotating frame as,then (5) can be transformed into the estimated frame as: (5) where the subscript “e” means the corresponding component in the estimated rotating frame and Δθe means the position estimation error. (6)

9. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 9 In order to extract the rotor position from the HF current, a measured frame is defined. The frame lags the frame with. Moreover, (5) can be transformed to the measured frame as follows: (7) In a special case, if the measured frame lags the estimation frame with 0.25π, then (7) can be simplified to (8)

10. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 10 If the rotor position estimation error Δθe is sufficiently small, then (8) can be approximated as (9) As a result, the equivalent estimation error signal ε for the rotor position observer can be obtained from the magnitude of the measured HF current components according to (9), which is given by (10)

11. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 11 Fig. 2. Signal process for rotor position estimation using HF signal injection. the position estimation error signal can be acquired from the magnitude of HF current components in the measured axes.

12. Department of Electrical Engineering Southern Taiwan University of Science and Technology Position estimation at high-speed 2015/10/27 Robot and Servo Drive Lab. 12 A sliding-mode observer is designed using an equivalent extended EMF model of IPMSM. It can provide fast convergence and low sensitivity to parameter variations. It can be expressed as: Design of Sliding-Mode Position Observer Where A 2 = B 2 =, z is the sliding-mode control function. z eq is the equivalent control function. l is the equivalent feedback gain. (11)

13. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 13 From (11), the difference between the actual stator current and the estimated one is used to establish the sliding-mode control function z. Due to the action of the sliding-mode controller, the current difference can be reduced to zero. Moreover, the position estimation value will converge to the actual one.

14. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 14 From fig.3, It can be seen that the α–β-axis components of z eq contain the sine and cosine functions of the rotor position signal, respectively. Conventionally, the position can be calculated directly through the arc-tangent function Fig. 3. EMF-based sliding-mode observer adopting a software PLL. However, the existence of noise signal may influence the accurate estimation of position. In particular, during the EMF crossing zero, using the arc-tangent function will cause obvious estimation error.

15. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 15 a software PLL is used to acquire rotor position according to the estimated EMF information. In this way, the equivalent position error signal from the EMF model can be obtained as: Therefore, the position observer based on software PLL can be expressed as: where ξ 1 and ξ 2 are the gain coefficients of the PLL.

16. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 16 Dead-Time Compensation Strategy To prevent the two insulated gate bipolar transistors (IGBTs) in an inverter leg from conducting simultaneously, a small delay time is added to the IGBT turn-on/turn-off. Since no voltage sensors adopted to detect the stator voltage, the voltage reference is used for the sliding-mode observer as the input. The dead-time setting will produce an additional position estimation error. Therefore, the dead-time compensation is important for the sensorless control.

17. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 17 The equivalent dead time ( ) can be expressed as: where sign( i af ) = is the dead-time set value. is the turn-on delay time. is the turn-off delay time. is the equivalent error time, representing the average voltage drops of the IGBTs and the diodes

18. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 18 u s is the collector-emitter saturation voltage of the IGBT. u d is the forward voltage of the freewheeling diode. As a result, the average voltage error in one carrier period can be expressed as: where T s is the PWM control period.

19. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 19 An average dead-time compensation scheme based on the voltage-error vector is adopted. the voltage errors in the three-phase a-b-c stationary frame can be obtained. Moreover, the voltage errors in the two-phase α–β stationary frame can be calculated from The voltage-error vectors in the α–β reference frame can be described as Fig. 4. Fig. 4. Voltage-error vector in the stationary coordinate scheme.

20. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 20 The dead-time compensation is carried out in the α–β reference frame according to and. The relation between the voltage references ( and ) and the compensated voltage references ( and ) can be described as: ＊ ＊ ＊ ＊ Where can be expressed as: where m is a small constant value related to the rated stator current; it can be selected experimentally.

21. Department of Electrical Engineering Southern Taiwan University of Science and Technology Experimental results 2015/10/27 Robot and Servo Drive Lab. 21 Fig. 5. Platform of 2.2-kW IPMSM sensorless control system based on DSP. (a) Drivers with dc-bus connection. (b) Load test platform. The rated parameters of the IPMSM are listed as follows: The PWM switching frequency of the inverter is10K Hz. The dead time is set as 3.2 μs. The magnitude and the frequency of the injected HF voltage are 57 V and 1 kHz.

22. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 22 The two switching points of the hybrid position observer are set as 150 and 300 r/min. The parameters of the current PI regulator K p2 = 4, K i2 = 25. The parameters of the speed PI regulator K p1 = 35, K i1 = 10. The parameter of the sliding-mode observer is l = 1 The parameter of dead-time compensation m is selected as 2% rated stator current value.

23. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 23 Fig. 6 shows, According to the sample value of stator current, the HF current signal is obtained through the digital filters, and the estimated position can be got. Fig. 6. Signal process results of the HF signal injection at 50 r/min with 25% rated load.

24. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 24 Fig. 7 shows, It can be seen that the speed estimation error is within ±10 r/min during the transients, and the estimated speed tracks the actual speed well. The IPMSM sensorless drive can operate at zero speed with full load disturbance. Fig. 7. Zero-speed sensorless operation with step rated load disturbance

25. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 25 Fig. 8. Motoring and regenerating sensorless operation at ±20 r/min with rated load. (a) Actual speed and position. (b) Speed and position estimation error. The estimation error is within ±0.05π. Moreover, the speed estimation error is within ±8 r/min during the transients and the steady state.

26. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 26 Fig. 9. Position and speed estimation error during the switch-over area from 0 to 400 r/min with rated load. From the dotted line area, the transient of the estimation errors during the switch-over area is obvious. According to the actual speed, it can be seen that the switching of the two different estimation methods is smooth.

27. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 27 Fig. 10. Sensorless operation from 1 to 1500 r/min, then back to 1 r/min with 50% rated load. Fig. 10 shows, It can be seen that the sensorless IPMSM can operate at full- speed range. The estimation error is within ±12 r/min in the whole speed range.

28. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2015/10/27 Robot and Servo Drive Lab. 28 At the beginning, the dead-time compensation is disabled, and the stator current is distorted obviously. The dead-time effect results in large position estimation error reaching 0.055π. Then, the dead-time compensation is enabled. The aximum position estimation error is decreased to within 0.035 π. Fig. 11. Dead-time compensation results at 600 r/min with 75% rated load.

29. Department of Electrical Engineering Southern Taiwan University of Science and Technology Conclusion A position estimation method combining the HF signal injection and the sliding- mode observer based on the EMF model for sensorless IPMSM. The robust characteristic of the hybrid position observer can be achieved at full- speed range. The software PLL and the dead-time compensation method are effective for the position estimation. Even at the zero-speed operation, the sensorless IPMSM drive has strong robustness to step rated load disturbance. 2015/10/27 Robot and Servo Drive Lab. 29