半主动控制拉索的稳定性分析

Stability Analysis of a Semi-active Controlled Stay Cable

研究拉索在支座运动激励下参激振动不稳定性的半主动最优控制问题。建立斜拉索的多自由度参激振动方程,根据动态规划原理确定最优控制律,再按照MR阻尼器的B ingham模型得到半主动最优控制力及其相应的实施条件,分析控制力有界性、控制时滞、系统观测误差等主要因素对于索参激不稳定性控制的影响。数值结果表明,半主动最优控制可较大程度地提高索参激稳定性,控制时滞超过一定阀值将导致索完全不稳定。

The semi-active optimal control for the parametrically excited instability of a stay cable subjected to a support motion excitation was investigated. The multi-degree-of-freedom parameter-excitation vibration equations of the cable are established. An optimal control law is determined according to the dynamical programming principle. Then the semi-active optimal control force and its implementing condition are obtained in terms of the Bingham model of MR dampers. The influences of the control force bound, control time-delay and system observation error on controlling the cable instability are analyzed. Numerical results show that the semi-active optimal control can enhance the stability of the parametrically excited cable very much. The time-delay in control beyond a critical value will cause the cable completely unstable.