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Research Papers

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, China

Baoli Ma

The Seventh Research Division,
Beijing University of Aeronautics
and Astronautics,
Beijing 100191, China
e-mail: mabaoli@buaa.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 14, 2017; final manuscript received August 25, 2017; published online November 1, 2017. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 13(2), 021003 (Nov 01, 2017) (8 pages) Paper No: CND-17-1166; 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 (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.

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Figures

Grahic Jump Location
Fig. 1

Equivalent circuit of the PMSM [45]

Grahic Jump Location
Fig. 2

The chaotic behavior of the system when fractional order α=0.98 and initial-value (5, 1, −1)

Grahic Jump Location
Fig. 3

The chaotic behavior of the system when fractional order α=1.05 and initial-values (−1, −2, 4) and (5, 1, −1)

Grahic Jump Location
Fig. 4

Evolution of the states id, iq and w of the system when fractional order α=0.98 and initial-value (5, 1, −1)

Grahic Jump Location
Fig. 5

Evolution of the states id, iq and w of the system when fractional order α=1.05 and initial-values (−1, −2, 4) and (5, 1, −1)

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