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

Baoli Ma

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

1Corresponding author.

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


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.

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