不确定性线性系统的H_∞输出反馈鲁棒重复控制

H-infinity output feedback robust repetitive control for uncertain linear systems

为了抑制乘性不确定性线性系统中的外部扰动,提出了一种重复控制器与输出反馈控制器参数同时优化的方法.引入一个假想摄动将系统的扰动抑制问题归结为具有结构型摄动的系统鲁棒稳定性问题.根据小增益定理得到该结构型摄动系统鲁棒稳定性的充分条件.引入一个稳定的定标阵,得到该结构型摄动系统低保守性的鲁棒稳定性充分条件.基于该充分条件和线性矩阵不等式方法(LMI)、锥补线性化方法(CCL),提出的迭代算法可以同时计算出重复控制器中低通滤波器剪切频率的最大值及其对应的输出反馈控制器的参数.最后,低频线振动台系统验证了该方法的有效性。

A new design method for linear system with model uncertainty is presented to restrain the external disturbance,which can design the repetitive controller and the output feedback controller simultaneously.The disturbance rejection problem of the linear system is reformulated as a robust stability problem of the system with structured uncertainties through introducing a fictitious uncertainty.Using small gain theorem,a sufficient condition is derived,which ensures robust stability of the system with structured uncertainties.A stable matrix is introduced to get a sufficient condition with less conservativeness for the system with structured uncertainties.Basing on the resulting sufficient condition,by using linear matrix inequality（LMI） and cone complementarity linearization（CCL）,an iterative algorithm is presented to calculate the largest cut-off frequency of the low-pass filter in the repetitive controller and the parameters of the output feedback controller simultaneously.Finally,the validity of this method is verified by a low-frequency linear vibration table system.