电磁轴承支承转子系统的运动稳定性

Motion stability of the rotor system supported by electromagnetic bearings

结合定参数PID控制器方程和具有陀螺效应的不对称转子运动方程形成了电磁轴承支承的转子系统的机电耦合动力学方程.将Poincaré映射与Newton打靶法相结合求解了系统非线性不平衡周期响应.结合Floquet分岔理论分析了系统周期运动的稳定性边界和分岔行为.对电磁轴承支承的转子系统设计了变参数PID控制规律,运用所设计的PID控制算法对系统进行计算,发现变参数PID控制算法使得系统非线性周期响应的稳定性有所提高,保证了系统稳定的谐波运动.

The Electromechanical coupling dynamic equations of the rotor system supported by electromagnetic bearings are obtained by combining the equations of the PID controllers with invariable parameters and the motion equations of the un-symmetric rotor with gyro effect.The nonlinear unbalance periodic responses of the system are solved by Poincaré mapping together with Newton shooting method.The stability margins of the nonlinear periodic motions and their bifurcation types are obtained according to Floquet bifurcation theory. The variable parameter PID control algorithm is designed for the system.The motion simulation of the system is implemented by using the designed PID algorithm.The numerical examples show that the designed PID algorithm greatly increases the stability of the nonlinear periodic motions and ensures the stable harmonic motions of the system.