风激拉索张弛振荡的最优控制分析

摘要

研究斜拉索在横向风力作用下多模态张弛振荡的最优控制.建立索受控和风力作用的非线性运动方程,导出索横向运动的偏微分振动方程,运用Galerkin法转化为常微分方程组,以描述受控索的多模态张弛振荡；根据最优控制的动态规划原理确定非线性控制力,应用平均法解得该系统自激振动及其稳定性的分析解,通过分析和数值模拟说明该最优控制能够有效地抑制索的张弛振荡.%The optimal control of self-excited oscillation of an inclined taut cable with multi-modes under wind loading is studied. The nonlinear equations of motion are derived for the cable with control and wind forces. The partial differential equation for transverse cable vibration is obtained and converted into ordinary differential equations by using the Galerkin method, that describe the self-excited oscillation of the multi-mode system. Then based on the dynamical programming principle, the HJB equation is established and the optimal nonlinear control force is determined. The analytical solutions of the controlled system in self-excited oscillation are obtained by using the averaging method. The analytical and numerical results show that the proposed control can effectively suppress the self-excited oscillation of the cable.