分数阶同步磁阻电机的混沌与控制

利用分数阶Caputo微分及其理论,讨论了分数阶同步磁阻电机的混沌及其控制问题.首先利用分岔图、最大Lyapunov指数以及相图和时序图,分析了分数阶同步磁阻电机的混沌特性,研究了阶次对混沌行为的影响,得出同量分数阶系统出现混沌运动的最低阶次约为2.94.其次基于分数阶系统的稳定性理论,构造Lyapunov函数,设计合理的控制器,使其达到全局渐进稳定.最后通过数值仿真验证了该方法的有效性.

Chaos in the Fractional Order Synchronous Reluctance Motor and its Control

In this paper we propose a fractional Synchronous Reluctance Motor(SynRM)by using the Caputo fractional differential and its theory.We also investigate the chaotic behaviors of the fractional SynRM.Firstly,we discuss chaotic characteristic of the fractional SynRM by analyzing the bifurcation diagram,Lyapunov exponent,phase portraits and time responses.Then we study the influnce of system's order to the chaos.In the case of commensurate fractional order SynRM system,the lowest order at which chaos exists is turned out to be about 2.94.Based on the stability theory of fractional order system,Lyapunov function is constructed,a reasonable controller is designed to achieve global asymptotic stability.Finally,numerical investigations demonstrate the validity and feasibility of the presented control method.