随机激励条件下转子系统的主动振动控制

Active Vibration Control for A Rotor System Subjected to Random Excitation

针对随机激励下线性转子系统的振动主动控制,给出了随机激励下受控柔性转子系统的状态空间模型,基于线性二次型高斯控制理论,提出了转子系统在白噪声和有色噪声激励下振动的最优控制策略。以一个柔性转子轴承系统为例,用数值方法研究了El.Centro地震激励作用下随机最优策略对转子-轴承系统的振动主动控制,并讨论了性能指标中不同权函数对控制效果的影响。结果表明:文中所提出的随机最优控制策略能有效地抑制转子系统的振动,控制效果随着与转子系统位移和速度相关的权矩阵的增大而变好,随着与控制相关的权矩阵的增大而变差。这对于旋转机械系统随机最优控制中权矩阵的选择具有一定的参考价值。

In order to study the active vibration control of a linear rotor system subjected to random excitation, a state space model of a controlled flexible rotor system subjected to random excitation was presented. Based on the Linear Quadratic Gaussian（LQG） control theory, optimal vibration control strategies of the rotor system under the white noise and the coloured noise excitation were obtained. A numerical example was presented for a rotor-bearing system subjected to nonstationary E1.Centro earthquake excitation. The influence of the performance index＇s weighting function on the control effectiveness was discussed. It is shown that the stochastic optimal control strategies presented can effectively attenuate the vibration of the rotor system. The control effectiveness becomes better with the increase of the weighting matrix corresponding to the displacement and velocity of the rotor system and becomes weaker with the increase of the weighting matrix corresponding to the control. This will provid some references for choosing weighting matrix in stochastic optimal control for rotating machinery.