Han Ho Choi, Member, IEEE, Nga Thi-Tuy Vu, and Jin-Woo Jung

1. Design and Implementation of a Takagi–Sugeno Fuzzy Speed Regulator for a Permanent Magnet Synchronous Motor Han Ho Choi, Member, IEEE, Nga Thi-Tuy Vu, and Jin-Woo Jung IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 8, AUGUST 2012,pp.3069-3077 Student: 高永發

2. Outline • ABSTRACT • MODEL DESCRIPTION • FUZZY SPEED REGULATOR DESIGN • SPEED REGULATOR PERFORMANCE DESIGN • LOAD TORQUE OBSERVER DESIGN • DESIGN ALGORITHM • SIMULATION AND EXPERIMENT • CONCLUSION

3. ABSTRACT In this paper, a fuzzy speed regulator, as well as a fuzzy load torque observer, for a permanent magnet synchronous motor (PMSM) is designed based on the Takagi–Sugeno fuzzy approach. In terms of linear matrix inequalities (LMIs), sufficient conditions for the existence of the regulator and the observer are derived. LMI parameterizations of the gain matrices are given. LMI conditions for the existence of the fuzzy speed regulator and the fuzzy load torque observer guaranteeing various performance criteria are also derived. The proposed load-torque-observerbased fuzzy speed regulator system is implemented by using a TMS320F28335 floating-point digital signal processor, and simulation and experimental results are given to verify that the proposed method can be successfully used to control a PMSM under model parameter and load torque variations.

4. MODEL DESCRIPTION A surface-mounted PMSM can be represented by the following nonlinear equation: where TL represents the load torque, ω is the electrical-rotor angular speed, iqs is the q-axis current, Vqs is the q-axis voltage,ids is the d-axis current, Vds is the d-axis voltage, and ki > 0,i = 1, . . . , 6, are the parameter values depending on the stator resistance, the stator inductance, the rotor inertia, the viscous friction coefficient, and the magnetic flux.

5. The ith rule of the T–S fuzzy model is of the following form: where Fi(i = 1, . . . , r) values denote the fuzzy sets, r is the number of fuzzy rule, (Iqi, Idi) is the ith operating point, and is = [iqs, ids]T . Each fuzzy set Fi is characterized by a membership function mi(is) and the ith operating point (iqs, ids) =(Iqi, Idi).

6. By using a standard fuzzy inference method, the following global nonlinear model can be obtained:

7. FUZZY SPEED REGULATOR DESIGN • Fuzzy model can be transformed into:

8. Let the local speed regulator be given by the following linear controller: • where x = [˜ω,˜iqs, ids]T , uqdf = [uqf, udf ]T , and Ki ∈ R2×3 are gain matrices.

9. The final fuzzy speed regulator inferred as the weighted average of the each local controller is given by

10. The closed-loop control system is given by

11. SPEED REGULATOR PERFORMANCE DESIGN • α-Stability • Quadratic Performance • Generalized H2 Performance • Generalized H∞ Performance

12. LOAD TORQUE OBSERVER PERFORMANCE DESIGN • α-Stability • Quadratic Performance • Generalized H2 Performance • Generalized H∞ Performance

13. DESIGN ALGORITHM

14. SIMULATION AND EXPERIMENT

18. CONCLUSION Based on the T–S fuzzy approach, a load-torque-observerbased control design method has been proposed for a PMSM under model parameter and load torque variations. LMI existence conditions guaranteeing α-stability, quadratic performance,and H2/H∞ performance bound have been derived for designing the fuzzy speed regulator and the load torque observer. The proposed fuzzy control system has been implemented by using a TMS320F28335 floating-point DSP. Finally,some simulation and experimental results have been given to show the effectiveness of the proposed design method.