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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 3690240, 14 pages
Research Article

Adaptive Robust Backstepping Control of Permanent Magnet Synchronous Motor Chaotic System with Fully Unknown Parameters and External Disturbances

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding 071003, China

Received 15 December 2015; Revised 16 March 2016; Accepted 30 March 2016

Academic Editor: Shengjun Wen

Copyright © 2016 Yang Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The chaotic behavior of permanent magnet synchronous motor is directly related to the parameters of chaotic system. The parameters of permanent magnet synchronous motor chaotic system are frequently unknown. Hence, chaotic control of permanent magnet synchronous motor with unknown parameters is of great significance. In order to make the subject more general and feasible, an adaptive robust backstepping control algorithm is proposed to address the issues of fully unknown parameters estimation and external disturbances inhibition on the basis of associating backstepping control with adaptive control. Firstly, the mathematical model of permanent magnet synchronous motor chaotic system with fully unknown parameters is constructed, and the external disturbances are introduced into the model. Secondly, an adaptive robust backstepping control technology is employed to design controller. In contrast with traditional backstepping control, the proposed controller is more concise in structure and avoids many restricted problems. The stability of the control approach is proved by Lyapunov stability theory. Finally, the effectiveness and correctness of the presented algorithm are verified through multiple simulation experiments, and the results show that the proposed scheme enables making permanent magnet synchronous motor operate away from chaotic state rapidly and ensures the tracking errors to converge to a small neighborhood within the origin rapidly under the full parameters uncertainties and external disturbances.