Dynamical analysis of the permanent-magnet synchronous motor chaotic system

Fuchen Zhang,Xiaofeng Liao,Chunlai Mu

doi:10.1186/s13662-017-1118-1

Abstract

This paper is concerned with some dynamics of the permanent-magnet synchronous motor chaotic system based on Lyapunov stability theory and optimization theory. The innovation of the paper lies in that we derive a family of mathematical expressions of globally exponentially attractive sets for this chaotic system with respect to system parameters. Numerical simulations confirm that theoretical analysis results are correct.

Highlights

Since Lorenz et al were the first to investigate the Lorenz equations in, chaotic systems have played an important role in a variety of industrial fields [ – ]
This paper mainly focuses on the chaotic system model from a permanent-magnet synchronous motor (PMSM) which is a nonlinear, multivariable, and strong coupling system
The meaning of the contribution of this article is that do we derive a family of mathematical expressions of global exponential attractive sets for permanent-magnet synchronous motor systems in [, ] with respect to the parameters of the system, but we get the rate of the trajectories of the system going from the exterior of the trapping set to the interior of the trapping set

Summary

Introduction

Since Lorenz et al were the first to investigate the Lorenz equations in , chaotic systems have played an important role in a variety of industrial fields [ – ]. Lyapunov-like functions used in [ , , , ] cannot be used to study the global attractive sets for the permanent-magnet synchronous motor system. A new Lyapunov-like function is constructed to investigate the global attractive sets of the permanent-magnet synchronous motor system. The meaning of the contribution of this article is that do we derive a family of mathematical expressions of global exponential attractive sets for permanent-magnet synchronous motor systems in [ , ] with respect to the parameters of the system, but we get the rate of the trajectories of the system going from the exterior of the trapping set to the interior of the trapping set. In Section , we prove that there exist global exponential attractive sets for the chaotic PMSM system.

Permanent-magnet synchronous motor model

Conclusions