Document Type : Original Research Paper


Malek Ashtar University of Technology, Tehran, Iran


This paper deals with the modeling, analysis, design and simulation of a robust control method for a permanent magnet synchronous machine (PMSM) supplied with a PWM inverter based on a LPV (Linear Parameter Variation)  standard controller. Under the influence of uncertainties and external disturbances, by a variation of ±150% of motor parameters from the nominal values, the robust performance control problem is formulated as a LPV  standard scheme and solved by a suboptimal LMI (Linear Inequality Matrices) iterative  strategy. This new design method is able to ensure the stabilization of the augmented system formed of the perturbed system with improved performance in face of parameter variation and external disturbances. A Simulation study was carried out to illustrate the effectiveness of the proposed method. The results obtained are compared with a simple conventional PI controller.


[1] K. Qing, X. Xi, S. Kai ,X. Jie, and Z. Jingmei, “A design of active damper for the deployment of solar arrays using PMSM,” in Proc. 2014 ITEC Asia. Pacific conf., Beijing, China, DOI: 10.1109/ITEC-AP.2014.6940779.
[2] P.C. Sen, “Electric motor drives and control-past, present and future,” IEEE Trans. Industrial Electronics, vol. 37, pp. 562- 575, 1990.
[3] P.M. Pelecezewski, W. Oberschelp, and U.K. Kunz, “Optimal model following control of a positioning drive system with a permanent magnet synchronous motor,” IEEE Proceeding Control Theory and Applications, Part-D, vol. 138, pp. 267-273, 1991.
[4] N. Matsui and H. Ohashi, “DSP-based adaptive control of a brushless motor,” IEEE Trans. Industry Applications, vol. 28, pp. 448-454, 1992.
[5] E. Cerruto, A. Consoli, A. Racitti, and A. Testa, “A robust adaptive controller of PM motor drives in robotic applications,” IEEE Trans. Power Electronics, vol. 10, pp. 62-71, 1992.
[6] N. Hemati, J.S. Thorp, and M.C. Leu, “Robust nonlinear control of brushless DC motors for direct-drive robotic applications,” IEEE Trans. Industrial Electronics, vol. 37, pp. 460-468, 1990.
[7] T.H. Liu and C.P.Cheng, “Controller design for a sensorless permanent magnet synchronous drives system,” IEEE. Proceedings Electrical Power Applications Part B, vol. 140, pp. 368-378.
[8] W. Xu, “Permanent Magnet Synchronous Motor with Linear Quadratic Speed Controller,” 2nd International Conference on Advances in Energy Engineering (ICAEE 2011), Bangkok, Thailand, 2011.
[9] V.F. Montagner, R.C.L.F. Oliveira, V.J.S. Leite, and P.L.D. Peres, “LMI approach for linear parameter-varying state feedback control,” in Proc. Control Theory Appl., 2005, pp. 195–201, DOI: 10.1049/ip-cta:20045117.
[10] P. Gahinet, A. Nemirovski, A.J. Laub, and M. Chilali, “LMI control toolbox for use with MATLAB,” The MathWorks, Inc., 1995.
[11] LO¨ fberg J., “YALMIP: A toolbox for modeling and optimization in MATLAB,” Proc. CACSD Conf. 2004, available at
[12] J. Bernussou, P.L.D. Peres, and J. Geromel, “A linear programming oriented procedure for quadratic stabilization of uncertain systems,” Syst. Control Lett., vol. 13, pp. 65–72, 1989.
[13] S. Boyd, L. EL Ghaoui, E. Feron , and V. Balakrishnan “Linear matrix inequalities in system and control theory,” vol. 15, SIAM, 1994
[14] E.S, Pyatnitskii and V.I. Skorodinskii “Numerical methods of Lyapunov function construction and their application to the absolute stability problem,” Syst. Control Lett., vol. 2, pp. 130– 135, 1982.
[15] S. Skogestad and I. Postlethwaite, “Multivariable feedback control: analysis and design,” John Wiley and Sons, 1996. [16] P. Gahinet and p. Apkarian “A linear matrix inequality approach to control,” Int. J. Robust Nonlinear Control, vol. 4, pp. 421–448, 1994.
[17] M. Chilali and P. Gahinet, “ design with pole placement constraints: an LMI approach,” IEEE Trans. Autom. Control, vol. 41, pp. 358–367, 1996
[18] W.M. Haddad and D.S. Bernstein, “Controller design with regional pole constraints,” IEEE Trans. Autom. Control, vol. 37, pp. 54–69, 1992.
[19] G. Garcia, J. Daafouz, and J. Bernussou “Output feedback disk pole assignment for systems with positive real uncertainty,” IEEE Trans. Autom. Control, vol. 41, pp. 1385–1391, 1996


Journal of Electrical and Computer Engineering Innovations (JECEI) welcomes letters to the editor for the post-publication discussions and corrections which allows debate post publication on its site, through the Letters to Editor. Letters pertaining to manuscript published in JECEI should be sent to the editorial office of JECEI within three months of either online publication or before printed publication, except for critiques of original research. Following points are to be considering before sending the letters (comments) to the editor.

[1] Letters that include statements of statistics, facts, research, or theories should include appropriate references, although more than three are discouraged.

[2] Letters that are personal attacks on an author rather than thoughtful criticism of the author’s ideas will not be considered for publication.

[3] Letters can be no more than 300 words in length.

[4] Letter writers should include a statement at the beginning of the letter stating that it is being submitted either for publication or not.

[5] Anonymous letters will not be considered.

[6] Letter writers must include their city and state of residence or work.

[7] Letters will be edited for clarity and length.