一类离心轮系统的混沌数学模型及其线性反馈控制

A Class of Centrifugal Flywheel's Chaos Mathematical Model and Its Linear Feedback Control

通过分析一类离心轮系统的非线性特性,在其对应数学模型的基础上进行复杂动力学分析得出其Poincaré映射图、Lyapunov指数图、时域波形图和分岔图,进而证明该模型是混沌数学模型,从而将此类离心轮系统控制转化为对混沌系统的控制,用线性反馈控制方法对此类离心轮的三种运行状态进行控制,利用MATLAB仿真实现了控制离心轮系统的目的。结果表明,利用线性反馈可以很好地消除混沌,使系统达到一个稳定的状态。该控制策略能有效地改善离心轮系统的动态性能,并能增强其鲁棒性与抗干扰能力。

Through the analysis of a class of centrifugal flywheel system,this paper gave its mathematical model.By analysing its complex dynamics,such as Lyapunov exponent spectrum,bifurcation diagram,Poincaré diagram,time-domain waveform diagram and the spectrogram,a chaotic mathematical model was established to describe the dynamic process.Then,the control of the centrifugal flywheel system can be converted into chaotic system control.It controlled the chaotic systems of the centrifugal flywheel system by the adaptive control method,and it achieved the goal through the simulation of MATLAB.The results show that chaotic system can be controlled well by adaptive control,and the system can come to a steady state.The control method can greatly improved dynamic performance and anti-disturbance capacity of the system.