Adaptive nonlinear feedback control of chaos in permanent-magnet synchronous motor system with parametric uncertainty

Abstract

The permanent-magnet synchronous motor (PMSM) system, which is a nonlinear dynamic system, will exhibit a variety of chaotic or limit-cycle phenomenon under some choices in system parameters and external disturbances and its chaotic characteristics will become obvious. Based on the mathematical model of the PMSM system, the property of equilibrium points is analyzed and the relationship between Hopf bifurcation and the system parameters associated with control parameters is illustrated. In addition, bifurcation diagram, Lyapunov exponent map, and phase plane diagram are also presented in this paper. An adaptive nonlinear feedback controller, which could estimate the system parameters online, is then designed to eliminate the chaos and drive the speed of PMSM to a desired value in presence of system parametric uncertainty. Numerical simulation proves that the proposed control method has a better controlling effect than the general nonlinear feedback controller.