Nonlinear Control of Interior PMSM Using Control Lyapunov Functions


In this paper, we introduce a non-linear torque control for an interior permanent-magnet synchronous motor (IPMSM). The nonlinear control is based on a Control Lyapunov Function (CLF) technique. The proposed stabilizing feedback law for the IPMSM drive is a damping control method and is shown to be globally asymptotically stable. The CLF method takes the system nonlinearities into account in the control system design stage. Such nonlinearities are due to the cross coupling between the q and the q currents in addition to the system parameters like the inductances and the flux linkages. The complete IPMSM drive incorporating the proposed CLF has been successfully simulated in a plant model for both motor and inverter. The performance of the proposed drive is investigated in simulation at different operating conditions. It is found that the proposed control technique provides a good torque control performance for the IPMSM drive ensuring the global stability. In later work, we are planning to investigate other phenomena such as magnetic saturation, nonlinear loads, mechanical friction and flexibilities.

Share and Cite:

Sabra, M. , Khasawneh, B. and Zohdy, M. (2014) Nonlinear Control of Interior PMSM Using Control Lyapunov Functions. Journal of Power and Energy Engineering, 2, 17-26. doi: 10.4236/jpee.2014.21003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. A. Rahman, D. M. Vilathgamuwa, M. N. Uddin and K.-J. Tseng, “Nonlinear Control of Interior PermanentMagnet Synchronous Motor,” IEEE Transactions on Industry Applications, Vol. 39, No. 2, 2003, pp. 408-416.
[2] J. Solsona, M. I. Valla and C. Muravchik, “Nonlinear Control of a Permanent Magnet Synchronous Motor with Disturbance Torque Estimation,” IEEE Transactions on Energy Conversion, Vol. 15, No. 2, 2000, pp. 163-168.
[3] G. S. Lakshmi, S. Kamakshaiah and T. R. Das, “Closed Loop PI Control of PMSM for Hybrid Electric Vehicle Using Three Level Diode Clamped Inverter for Optimal Efficiency,” International Conference on Energy Efficient Technologies for Sustainability (ICEETS), Nagercoil, 10-12 April 2013, pp. 754-759.
[4] J. Espina, A. Arias, J. Balcells and C. Ortega, “Speed Anti-Windup PI Strategies Review for Field Oriented Control of Permanent Magnet Synchronous Machines,” Compatibility and Power Electronics, Badajoz, 20-22 May 2009, pp. 279-285.
[5] P. March and M. C. Turner, “Anti-Windup Compensator Designs for Nonsalient Permanent-Magnet Synchronous Motor Speed Regulators,” IEEE Transactions on Industry Applications, Vol. 45, No. 5, 2009, pp. 1598-1609.
[6] J. L. Gao and Y. F. Zhang, “Research on Parameter Identification and PI Self-Tuning of PMSM,” 2nd International Conference on Information Science and Engineering (ICISE), Hangzhou, 4-6 December 2010, pp. 5251-5254.
[7] R. G. Kanojiya and P. M. Meshram, “Optimal Tuning of PI Controller for Speed Control of DC Motor Drive Using Particle Swarm Optimization,” International Conference on Advances in Power Conversion and Energy Technologies (APCET), Mylavaram, 2-4 August 2012, pp. 1-6.
[8] P. Pillay and R. Krishnan, “Modeling, Simulation, and Analysis of Permanent-Magnet Motor Drives. II. The Brushless DC Motor Drive,” IEEE Transactions on Industry Applications, Vol. 25, No. 2, 1989, pp. 274-279.
[9] A. Bacciotti and L. Rosier, “Liapunov Functions and Stability in Control Theory,” Springer-Verlag, London, 2001, pp. 119-154.
[10] H. K. Khalil, “Nonlinear Systems,” Prentice Hall, Upper Saddle River, 2002, pp. 111-161.
[11] E. Sontag, “A Lyapunov-Like Characterization of Asymptotic Controllability,” SIAM Journal on Control and Optimization, Vol. 21, No. 3, 1983, pp. 462-471.
[12] F. H. Clarke, Y. S. Ledyaev, E. D. Sontag and A. I. Subbotin, “Asymptotic Controllability Implies Feedback Stabilization,” IEEE Transactions on Automatic Control, Vol. 42, No. 10, 1997, pp. 1394-1407.
[13] F. A. Alazabi and M. A. Zohdy, “Nonlinear Uncertain HIV-1 Model Controller by Using Control Lyapunov Function,” International Journal of Modern Nonlinear Theory and Application, Vol. 1, No. 2, 2012, pp. 33-39.
[14] M. Pahlevaninezhad, P. Das, J. Drobnik, G. Moschopoulos, P. K. Jain and A. Bakhshai, “A Nonlinear Optimal Control Approach Based on the Control-Lyapunov Function for an AC/DC Converter Used in Electric Vehicles,” IEEE Transactions on Industrial Informatics, Vol. 8, No. 3, 2012, pp. 596-614.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.