### LMI-based Sliding Mode Speed Tracking Control Design for Surface-mounted Permanent Magnet Synchronous Motors

Leu, Viet Quoc;Choi, Han-Ho;Jung, Jin-Woo

• 투고 : 2011.04.15
• 심사 : 2012.04.29
• 발행 : 2012.07.01
• 37 12

#### 초록

For precisely regulating the speed of a permanent magnet synchronous motor system with unknown load torque disturbance and disturbance inputs, an LMI-based sliding mode control scheme is proposed in this paper. After a brief review of the PMSM mathematical model, the sliding mode control law is designed in terms of linear matrix inequalities (LMIs). By adding an extended observer which estimates the unknown load torque, the proposed speed tracking controller can guarantee a good control performance. The stability of the proposed control system is proven through the reachability condition and an approximate method to implement the chattering reduction is also presented. The proposed control algorithm is implemented by using a digital signal processor (DSP) TMS320F28335. The simulation and experimental results verify that the proposed methodology achieves a more robust performance and a faster dynamic response than the conventional linear PI control method in the presence of PMSM parameter uncertainties and unknown external noises.

#### 키워드

Permanent magnet synchronous motor (PMSM);Sliding mode control;Robust control;Speed control;Load torque observer;Linear matrix inequality (LMI)

#### 참고문헌

1. G. Zhou and J. W. Ahn, "A novel efficiency optimization strategy of IPMSM for pump applications," Journal of Electrical Engineering & Technology, Vol. 4, No. 4, pp. 515-520, Dec. 2009. https://doi.org/10.5370/JEET.2009.4.4.515
2. H. S. Kang, C. K. Kim, and Y. S. Kim, "Position control for interior permanent magnet synchronous motors using an adaptive integral binary observer," Journal of Electrical Engineering & Technology, Vol. 4, No. 2, pp. 240-248, Jun. 2009. https://doi.org/10.5370/JEET.2009.4.2.240
3. J. G. Lee, K. H. Nam, S. H. Lee, S. H. Choi, and S. W. Kwon, "A lookup table based loss minimizing control for FCEV permanent magnet synchronous motors," Journal of Electrical Engineering & Technology, Vol. 4, No. 2, pp. 201-210, Jun. 2009. https://doi.org/10.5370/JEET.2009.4.2.201
4. Y. Yan, J. G. Zhu, and Y. G. Guo, "Initial rotor position estimation and sensorless direct torque control of surface-mounted permanent magnet synchronous motors considering saturation saliency," IET Electr. Power Appl., Vol. 2, No. 1, pp. 42-48, Jan. 2008. https://doi.org/10.1049/iet-epa:20070083
5. T. L. Hsien, Y. Y. Sun, and M. C. Tsai, "$H_{{\infty}}$ control for a sensorless permanent-magnet synchronous drive," Proc. Inst. Elect. Eng.-Electr. Power Appl., Vol. 144, No. 3, pp. 173-181, May 1997. https://doi.org/10.1049/ip-epa:19970988
6. K. Y. Lian, C. H. Chiang, and H. W. Tu, "LMI-based sensorless control of permanent-magnet synchronous motors," IEEE Trans. Ind. Electron., Vol. 54, No. 5, pp. 2769-2778, Oct. 2007. https://doi.org/10.1109/TIE.2007.899829
7. F. J. Lin and P. H. Chou, "Adaptive control of twoaxis motion control system using interval type-2 fuzzy neural network," IEEE Trans. Ind. Electron., Vol. 56, No. 1, pp. 178-193, Jan. 2009. https://doi.org/10.1109/TIE.2008.927225
8. Y. A. R. I. Mohamed, "Adaptive self-tuning speed control for permanent-magnet synchronous motor drive with dead time," IEEE Trans. Energy Conversion, Vol. 21, No. 4, pp. 855-862, Dec. 2006. https://doi.org/10.1109/TEC.2005.853739
9. I. C. Baik, K. H. Kim, and M. J. Youn, "Robust nonlinear speed control of PM synchronous motor using boundary layer integral sliding mode control technique," IEEE Tran. Cont. Syst. Tech., Vol. 8, No. 1, pp. 47-54, Jan. 2000. https://doi.org/10.1109/87.817691
10. D. Q. Zhang and S. K. Panda, "Chattering-free and fast-response sliding mode controller," IEE Proc.- Control Theory Appl., Vol. 146, No. 2, pp.171-177, Mar. 1999. https://doi.org/10.1049/ip-cta:19990518
11. J. F. Camino, J. W. Helton, and R. E. Skelton, "Solving matrix inequalities whose unknowns are matrices," IEEE CDC, Vol. 3, pp. 3160-3166, Dec. 2004.
12. C. K. Lin, T. H. Liu, and S. H. Yang, "Nonlinear position controller design with input-output linearisation technique for an interior permanent magnet synchronous motor control system," IET Power Electron., Vol. 1, No. 1, pp. 14-26, Mar. 2008. https://doi.org/10.1049/iet-pel:20070177
13. V. I. Utkin, "Variable structure systems with sliding modes", IEEE Trans. Autom. Control, Vol. 22, No. 2, pp. 212-222, Apr 1977. https://doi.org/10.1109/TAC.1977.1101446
14. J. W Jung, Y. S. Choi, V. Q. Leu, and H. H. Choi, "Fuzzy PI-type current controllers for permanent magnet synchronous motors," IET Electr. Power Appl., Vol. 5, No. 1, pp. 143-152, Jan. 2011. https://doi.org/10.1049/iet-epa.2010.0036
15. H. Z. Jin and J. M. Lee, "An RMRAC current regulator for permanent magnet synchronous motor based on statistical model interpretation," IEEE Trans. Ind. Electron., Vol. 56, No. 1, pp. 169-177, Jan. 2009. https://doi.org/10.1109/TIE.2008.928554
16. P. Kshirsagar, R. P. Burgos, A. Lidozzit, J. Jang, F. Wang, D. Boroyevich, and S. K. Sul, "Implementation and sensorless vector-control design and tuning strategy for SMPM machines in fan-type applications," IEEE Industry Appl. Conf., Vol. 4, pp. 2062-2069, Oct. 2006.

#### 피인용 문헌

1. Suboptimal Control Scheme Design for Interior Permanent-Magnet Synchronous Motors: An SDRE-Based Approach vol.29, pp.6, 2014, https://doi.org/10.5370/JEET.2012.7.4.513
2. θ-D Approximation Technique for Nonlinear Optimal Speed Control Design of Surface-Mounted PMSM Drives vol.20, pp.4, 2015, https://doi.org/10.5370/JEET.2012.7.4.513
3. T–S Fuzzy-Model-Based Sliding-Mode Control for Surface-Mounted Permanent-Magnet Synchronous Motors Considering Uncertainties vol.60, pp.10, 2013, https://doi.org/10.5370/JEET.2012.7.4.513
4. Speed control system design and experimentation for interior PMSM drives vol.102, pp.5, 2015, https://doi.org/10.5370/JEET.2012.7.4.513
5. Sliding Mode Control of SPMSM Drivers: An Online Gain Tuning Approach with Unknown System Parameters vol.14, pp.5, 2014, https://doi.org/10.5370/JEET.2012.7.4.513
6. Uncertain Saturated Discrete-Time Sliding Mode Control for A Wind Turbine Using A Two-Mass Model 2017, https://doi.org/10.5370/JEET.2012.7.4.513
7. Second-order integral sliding-mode control with experimental application vol.53, pp.5, 2014, https://doi.org/10.5370/JEET.2012.7.4.513
8. Finite Set Model Predictive Control of Interior PM Synchronous Motor Drives With an External Disturbance Rejection Technique vol.22, pp.2, 2017, https://doi.org/10.5370/JEET.2012.7.4.513
9. Finite-Time Chaos Control of a Complex Permanent Magnet Synchronous Motor System vol.2014, 2014, https://doi.org/10.5370/JEET.2012.7.4.513
10. Speed tracking and nonlinear disturbance rejection of PM synchronous motor by internal model design vol.15, pp.4, 2017, https://doi.org/10.5370/JEET.2012.7.4.513
11. Intelligent voltage control strategy for three-phase UPS inverters with outputLCfilter vol.102, pp.8, 2015, https://doi.org/10.5370/JEET.2012.7.4.513
12. Novel Adaptive Sliding Mode Control with Nonlinear Disturbance Observer for SMT Assembly Machine vol.2016, 2016, https://doi.org/10.5370/JEET.2012.7.4.513
13. Improved nonlinear sliding mode control based on load disturbance observer for permanent magnet synchronous motor servo system vol.8, pp.4, 2016, https://doi.org/10.5370/JEET.2012.7.4.513
14. Neuro-Fuzzy Control of Interior Permanent Magnet Synchronous Motors: Stability Analysis and Implementation vol.8, pp.6, 2013, https://doi.org/10.5370/JEET.2012.7.4.513

#### 과제정보

연구 과제 주관 기관 : Korea Institute of Energy Technology Evaluation and Planning (KETEP)