磁力轴承转子系统的Hopf分叉

研究ＰＤ控制器作用下的分散控制型磁力轴承转子系统，结果表明：磁力的非线性是引起系统自激振动的原因之一。通过研究两种非共振情况下的Ｈｏｐｆ分叉，分析了系统参数对自激振动的影响，给出条件稳定准则，还得到了共振情况下的系统响应方程。

RESEARCH ON HOPF BIFURCATION OF MAGNETIC BEARING-ROTOR SYSTEM

The influence of nonlinear factors on the active magnetic bearing-rotor system(AMBRS)with closed loop controller can't be derived from the classical linear control theories. It was analysed for the first time by the modern analytical methods used in nonlinear vibrahon. The Hopf bifurcations of AMBRS in autonomous and nonautonomous cases were researched by the normal form theorem and the improved averaging method respectively. Results show that the nonlinear factor of magnetism is one of the important factors causing the self-excited vibration of AMBRS.