非线性磁悬浮控制系统的周期运动稳定性研究

THE PERIODIC MOTION STABILITY ANALYSIS OF THE NONLINEAR MAGLEV CONTROL SYSTEM

通过分析基于串级 PID 控制器的非线性磁悬浮系统的 hopf 分岔现象，从控制参数与系统周期解稳定 性的关系角度阐述磁悬浮系统产生振动的原因之一．给出了串级 PID 控制算法，建立了四阶磁悬浮系统动 力学模型，并得出了控制参数的渐近稳定范围和 hopf 分岔条件．采用中心流形定理方法得到二阶降维模型， 通过计算其 PB 规范形得到 hopf 分岔的稳定性以及对应极限环的振动频率．分析结果表明基于串级 PID 控 制的磁悬浮系统具有一个不稳定的 hopf 分岔点，在该点附近系统将会产生频率约为5～7赫兹、持续但最终 发散的振动．

Based on the research of nonlinear Maglev system＇ s Hopf bifurcation, one factor which leads to the system vibrations, was studied by analyzing the connection between the cascade PID parameters and the periodic motion. The cascade PID control arithmetic was given, the four rank system dynamic model was constructed,the stability range of the control parameters was deduced, and the condition of the Hopf bifurcation was proved. We got the reduced two rank model using the center manifold theorem, and obtained the stability of the Hopf point and the corresponding vibration frequency of the limit circle with PB normal form. The result shows that the Maglev system based on the cascade PID controller has one unstable Hopf bifurcation point, and the system vibrates in 5～7Hz, which will emanate eventually.