Nonlinear Dynamic Surface Control of Chaos in Permanent Magnet Synchronous Motor Based on the Minimum Weights of RBF Neural Network

Shaohua Luo

doi:10.1155/2014/609340

Abstract

This paper is concerned with the problem of the nonlinear dynamic surface control (DSC) of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM) wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results.

Highlights

The permanent magnet synchronous motor is widely used in the industrial applications [1, 2]
It is well known that the PMSM is applied widely in the motor drives, servo systems, and household appliances owing to advantages, for instance, simple structure, high efficiency, high power density, and low manufacturing cost [20]
The PMSM is experiencing chaotic behavior when the system parameters are falling into a special area, which can lead to the enormous destruction

Summary

Introduction

The permanent magnet synchronous motor is widely used in the industrial applications [1, 2]. Parameter id ω ud TL Ld ψr J iq t uq R Lq B np Denotation The direct-axis currents (A) The velocity of the rotor (rad/s) The direct-axis voltage (V) The load torque (Nm) The direct-axis winding inductance (H) The permanent magnet flux (Wb) The polar moment of inertia (kgm2) The quadrature-axis currents (A) The time (s) The quadrature-axis voltage (V) The stator winding resistance (Ω) The quadrature-axis winding inductance (H) The viscous damping coefficient (N/rad/s) The number of pole pairs perturbed uncertainties using neural networks [12], Na et al in 2011 [13] presented adaptive neural dynamic surface control for servo systems with unknown dead zone, Li et al in 2013 presented an adaptive fuzzy DSC output feedback approach for a single-link robotic manipulator coupled to a brushed direct current motor with a nonrigid joint [14], and Tong et al in 2013 presented an adaptive fuzzy decentralized backstepping output feedback control approach for a class of uncertain large-scale stochastic nonlinear systems without the measurements of the states [15] In their works, it is assumed that there exists positive constant which satisfies specified constraint condition. This makes our design controller more suitable for practical applications

Mathematic Model

Controller Design

Stability Analysis

Conclusion

Performance Evaluation