Stabilization of a fractional-order chaotic brushless DC motor via a single input

A fractional-order brushless DC motor (BLDCM) system is proposed in this paper. By computer simulations, we find that the fractional-order BLDCM system exhibits a chaotic attractor for fractional order 0.96<q≤1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.96 < q \le 1$$\end{document}, and that the largest Lyapunov exponent varies depending on fractional-order q. Furthermore, in order to stabilize the fractional-order chaotic BLDCM system, two control strategies are presented via single input, based on the generalized Gronwall inequality and the Mittag–Leffler function. Numerical simulations are presented to verify the validity and feasibility of the proposed control schemes.