Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor

作者：Guo, Yuxiang; Ma, Baoli^*

来源：Journal of Computational and Nonlinear Dynamics, 2018, 13(2): 021003.

DOI：10.1115/1.4037929

• fractional calculus
• fractional time-varying systems
• permanent magnet synchronous motor
• stability

This paper is mainly concerned with asymptotic stability for a class of fractional-order (FO) nonlinear system with application to stabilization of a fractional permanent magnet synchronous motor (PMSM). 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 (ML) functions, when the FO 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 FO nonlinear PMSM system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann-Liouville type FO 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.

• 出版日期2018-2
• 单位北京航空航天大学