1. Hybrid Terminal Sliding-Mode Observer Design Method for a Permanent-Magnet Synchronous Motor Control System 教授 : 王明賢 學生 : 胡育嘉 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 9, SEPTEMBER 2009, p.p. 3424-3431.

2. Outline Abstract Introduction Conventional Sliding-Mode Observer For Rotor Position and Speed Hybrid Terminal Sliding-Mode Observer For Rotor Position and Speed Simulations Experiments Conclusion References

3. Abstract This paper proposes a hybrid terminal sliding-mode observer based on the nonsingular terminal sliding-mode (NTSM) and the high-order sliding-mode (HOSM) for the rotor position and speed estimation in the permanent-magnet synchronous motor control system. An NTSM manifold is utilized to realize both fast convergence and better tracking precision. In addition, a derivative estimator is used to obtain the derivative of the sliding-mode function. Meanwhile, an HOSM control law is designed to guarantee the stability of the observer and eliminate the chattering, so that smooth back-electromotive-force (EMF) signals can be obtained without a low-pass filter.

4. Abstract According to the back-EMF equations, the rotor position and speed of the motor can be calculated. Simulation and experimental results arepresented to validate the proposed method.

5. Introduction In order to achieve high performance of PMSMs, a vector control strategy and a rotor position sensor are typically required. Usually, both the position and speed of the motor are measured by mechanical sensors such as encoders, resolvers, and so on. However, these high-precision mechanical sensors would increase the cost and size of thePMSM system, hence reducing the reliability and limiting the applications under certain conditions. The sensorless technique enables control of PMSM without mechanical sensors as well as estimation of the rotor position and speed by the stator voltage and current of the motor.

6. Introduction In [15], a hybrid structure integrating a flux observer and signal injection techniques was utilized for a wide-speed-range sensorless control of a surface-mounted permanent-magnet machine, including zero-speed operation. In [16], an adaptive full-order observer was augmented with the signal injection method for PMSM drives equipped with aninverter output filter. By combining the nonsingular terminal sliding mode (NTSM) with the high-order sliding-mode (HOSM) method, this paper proposes a hybrid terminal sliding-mode observer for the rotor position and speed estimation in PMSM systems.

7. Introduction The NTSM manifold is utilized to realize the convergence of the observer in finite time. In addition, a derivative estimator is used to obtain the derivative of the sliding-mode function.Meanwhile, an HOSM control law is designed to guarantee the system stability. Since the HOSM method can eliminate the chattering phenomenon by using continuous signals instead of switching signals [20]–[23], the smooth back-EMF signals can be obtained directly from the observer, and the low-pass filter can be omitted. Both the simulation and experimental results are presented to validate the method

8. Conventional Sliding-Mode Observer For Rotor Position and Speed A typical structure of a sliding-mode-observer-based PMSMvector control system is shown in Fig. 1 [11], [17]–[19]. In the system, a sliding-mode observer is utilized instead of the mechanical position sensor of the motor. The stator voltage and current measurements of the motor are used to estimate the rotor position and speed using the observer based on the PMSM model. Then, the estimated position and speed can be used for the motor position or speed control and the coordinate transformation between the stationary reference frame and the synchronous rotating frame. The position sensor in the motorsystem is replaced by a software algorithm, which can reducethe cost of hardware and improve the reliability of the motorsystem.

9. Conventional Sliding-Mode Observer For Rotor Position and Speed In the α–β stationary reference frame, the electrical dynamics of the PMSM can be described using the following equations [11], [17]–[19]: where u α and u β are stator voltages, i α and i β are stator currents, L is the α–β-axis inductance, Rs is the stator winding resistance, and e α and e β are back-EMFs which satisfy the following equations:

10. Conventional Sliding-Mode Observer For Rotor Position and Speed It can be seen from (2) that the back-EMFs contain the information of both the rotor position and speed of the motor. Therefore, the rotor position and speed can be calculated from (2) if the back-EMFs can be obtained accurately. From (1), the conventional sliding-mode observer can be designed as follows [11]:

11. Conventional Sliding-Mode Observer For Rotor Position and Speed Assume that the parameters satisfy ˆRs = Rs and ˆL = L. Then, the error equations of the stator current can be obtained by subtracting (3) from (1) where i α =ˆi α − i α and i β =ˆi β − i β are two stator current errors, respectively. The control law for the observer (4) can be designed using the method in [11]

12. Conventional Sliding-Mode Observer For Rotor Position and Speed The observer (4) with control (5) can reach two sliding modes i α = 0 and i β = 0, respectively, in finite time and then stay on it. Once on the sliding-mode, the variable states of the system (4) will be i α = ˙i α = 0, i β = ˙i β = 0. From (4), the following equations can be obtained:

13. Conventional Sliding-Mode Observer For Rotor Position and Speed which means that the back-EMFs can be estimated by using the equivalent control of the observer. However, the actual control signals (5) in the conventional sliding-mode control method are discontinuous switching signals. Therefore, a low-pass filter is needed to extract the continuous back-EMF components. The low-pass filter is designed as follows [18]:

14. Conventional Sliding-Mode Observer For Rotor Position and Speed where τ0 is the time constant of the filter. According to (2) and (7), the estimated speed and position of the motor can be calculated as

15. Conventional Sliding-Mode Observer For Rotor Position and Speed This estimation algorithm based on the conventional slidingmode observer is robust with respect to both internal parameter uncertainties and external disturbances in the motor system. However, the phase lag of the estimation is unavoidable because of applying the low-pass filter (7). Therefore, the estimated rotor position should be compensated to improve the estimation precision. Usually, the phase-lag compensation to (9) is made according to the frequency response of the low-pass filter as follows [18]:

16. Hybrid Terminal Sliding-Mode Observer For Rotor Position and Speed Here, a hybrid terminal sliding-mode observer is proposed to estimate the rotor position and speed of the motor. The chattering in the control signals can be eliminated. Thus, the low-pass filter is omitted, and the phase lag in the back-EMF signals can be avoided. The stator current error equation (4) can be rewritten as follows In order to achieve good performances, such as fast convergence and better tracking precision, an NTSM manifold [24] is designed as follows:

17. Hybrid Terminal Sliding-Mode Observer For Rotor Position and Speed The NTSM manifold s is used to realize the second-order sliding-mode control and eliminate the chattering phenomenon in the system. After s reaches zero in finite time, both is and˙is will also reach zero in finite time; then, the system will stay on the second-order sliding mode is = ˙is = 0. The HOSM control law of the observer is designed according to the following theorem.

18. Hybrid Terminal Sliding-Mode Observer For Rotor Position and Speed Fig. 3. Hybrid terminal sliding-mode observer.

19. Hybrid Terminal Sliding-Mode Observer For Rotor Position and Speed

22. Simulations

24. Experiments

26. S Experiments

27. Experiments

29. Conclusion This paper has proposed a hybrid terminal sliding-modeobserver design method for estimating the rotor position and speed to achieve sensorless drive for PMSM. The NTSM manifold has been utilized to realize the convergence of the observer in finite time and better tracking precision. Meanwhile, the HOSM control law has been designed to eliminate the chattering. The control signals of the observer are smooth enough to be used for estimating the back-EMFs directly. The phase lag caused by the low-pass filter in the back-EMF signals can be avoided, and the motor position and speed can be calculated according to the back-EMF equations. Simulation and experimental results show that the hybrid terminal sliding-mode observer can converge fast and has low sensitivity to parameter variations

30. References