柔性结构振动主动控制器的μ综合设计方法

Robust active vibration control of the flexible structure via μ synthesis

在设计柔性结构振动主动控制器时,考虑了受控子系统参数摄动的一种典型情况:模态频率和模态阻尼的建模误差,并用线性分式变换的形式在状态方程描述的框架里,用一个对角块结构表达出这种参数不确定性;同时,把残余子系统视作对受控子系统的一种摄动,将溢出稳定性问题转化为同时含有参数不确定性与未建模动态的系统鲁棒稳定性问题;利用μ理论中的鲁棒性能定理,引入虚拟不确定块,把抑制外部扰动的鲁棒性能问题,统一到上述鲁棒稳定性问题中.最后通过最小化一个结构奇异值μ得到的控制器,以保证具有上述混合不确定性的闭环系统稳定并满足鲁棒性能要求.该方法在控制器设计时计入了混合不确定性块的结构特征,避免了常规H∞鲁棒控制器在处理此类问题时的保守性.仿真算例表明该方法是有效的.

The parameter uncertainty in the controlled subsystem and the spillover problem were taken into consideration when designing the active vibration controller. Then the uncertainty of modal frequency and modal damping in the controlled subsystem was expressed as a diagonal structure in the form of linear fraction transform （LFT）. At the same time, by treating the residual subsystem as a kind of uncertainty of the controlled subsystem, the spillover problem was converted to a mixed uncertainty robust stability problem. According to the robust performance theorem in the μ theory, the robust performance requirement of restraining external disturbance was unified with the robust stability problem by importing virtual uncertainty. Finally, by minimizing the structure singular value （SSV）μ, a robust controller is obtained, which doesn＇t ignore the structural character of the mixed uncertainty, so that it can guarantee the stability of the system and meet the robust performance requirement without conservation that is unavoidable in the conventional （）∞ controller.