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research-article

Asymptotic stabilization of fractional permanent magnet synchronous motor

[+] Author and Article Information
Yuxiang Guo

The Seventh Research Division, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China
gyx1207@126.com

Baoli Ma

The Seventh Research Division, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China
mabaoli@buaa.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037929 History: Received April 14, 2017; Revised August 25, 2017

Abstract

This paper is mainly concerned with asymptotic stability for a class of fractional-order nonlinear system with application to stabilization a fractional permanent magnet synchronous motor. First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall-Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag-Leffler functions, when the fractional-order belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann-Liouville's definition is presented. Then, it is generalized to stabilize a fractional-order nonlinear permanent magnet synchronous motor system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann-Liouville type fractional-order linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.

Copyright (c) 2017 by ASME
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