一类振荡电路的混沌及其控制

Study and Control of Chaos in Resonant Circuit

研究了一个振荡电路的混沌形成过程,并利用分岔图、Lyapunov指数图以及相图分析了该系统的混沌行为.利用分岔控制和x|x|控制等两种方法实现了系统的混沌控制,将系统的混沌行为有效地控制到稳定的周期轨道.其中,在分岔控制方法下,对受控系统做出了控制参数的系统分岔图,由分岔图可以得到控制到np的周期轨道的取值范围,在这范围内适当选择数值,将电路系统控制到p-1,p-2,p-4,p-8等周期轨道.x|x|控制是对混沌动力系统增加一个具有分段二次函数x|x|形式的非线性反馈控制器.仿真结果表明,这两种方法对控制电路系统的可行性.

Chaos motion of the resonant circuit is studied and the chaotic motion area is obtained by numerical calculation. The behaviors of the resonant circuit are fully analyzed by using bifurcation exponent diagram, Lyapunov diagram and phase diagram. Two methods are applied to realizing the chaos controlling, which efficiently control the chaos motion of system into different steady periodic orbits, such as bifurcation control,controller of x｜x｜. The bifurcation diagram is plotted for the controlled system with parameter. The range of parameter to stabilize a certain np periodic orbit in circuit can be obtained through the bifurcation diagram. The periodic orbit such as p-1, p-2, p-3, p-4 can be stabilized with parameter controller of x｜x｜. A method of controlling chaos employing a dynamical nonlinear feedback controller is developed to guide chaotic motions towards regular motions,and it is piecewise-quadratic function in the form of x｜x｜. The result shows that the methods can successfullv control the chaotic motion of the circuit.