一类电机系统的分岔分析与Hopf分岔控制

Bifurcation Analysis and Hopf Bifurcation Control of a Motor System

针对无刷直流电机系统等效非线性动力系统,运用中心流形理论和Hopf分岔理论研究了系统存在的分岔行为,并设计状态反馈控制器对系统进行Hopf分岔控制,分析了控制参数对Hopf分岔点位置、分岔类型以及分岔周期解振幅的影响。研究结果表明:控制器中的线性控制部分能改变原系统的Hopf分岔点位置,甚至使Hopf分岔点消失;控制器中的非线性控制部分则可改变原系统的分岔类型及分岔周期解振幅的大小。数值仿真证明控制器设计的有效性。

For the equivalent nonlinear dynamic system of brushless DC motor,the center manifold theory and Hopf bifurcation theory are used to discuss the Hopf bifurcation behaviors of original system,the Hopf bifurcation control problem of original system is investigated using a state feedback controller,and the effects of control parameters on the position of bifurcation point,bifurcation type and amplitude of periodic solution are analyzed.The research results show that the positions of Hopf bifurcation points can be changed and even the Hopf bifurcation points are eliminated by the linear control,and the bifurcation type and the bifurcation amplitude of periodic solution can be changed by the nonlinear control.Finally,the numerical simulations show the effectiveness of the proposed controllers.