时变周期系统鲁棒重复控制设计  

Robust repetitive control design of periodically time-varying plants

作　　者：周兰[1] 吴敏[2] 佘锦华[3] 

机构地区：[1]湖南科技大学信息与电气工程学院,湖南湘潭411201 [2]中南大学信息科学与工程学院,长沙410083 [3]日本东京工科大学计算机学部

出　　处：《控制与决策》2013年第1期61-66,共6页Control and Decision

基　　金：国家自然科学基金项目(60974045;61203010);湖南省自然科学基金青年基金项目(11JJ4059;09JJ3117)

摘　　要：针对一类具有周期不确定性的线性系统,提出基于二维模型的鲁棒改进型重复控制系统设计方法.在改进型重复控制系统中,低通滤波器的嵌入将控制和学习耦合在一起.通过运用"连续提升"方法,建立连续-离散二维模型,获得能够分别优先调节控制和学习的二维反馈控制律.运用Lyapunov稳定性理论,推导出系统鲁棒稳定的线性矩阵不等式(LMI)条件,包含在LMI中的两个可调参数可以实现对控制和学习的分别优先调节.数值仿真实例验证了所提出方法的有效性.A method of designing a robust modified repetitive-control system based on a continuous-discrete two- dimensional（2D） model is proposed for a class of strictly proper plants with time-varying periodic uncertainties. In the modified repetitive-control system, the insertion of a low-pass filter makes control and learning coupled together. Employing acontinuous lifting technique, a continuous-discrete 2D model is established, where the 2D control law is in the form of direct sum of control and learning effects. Then, the Lyapunov stability theory is used to derive a linear-matrix-inequality（LMI） based sufficient robust stability condition. Two tuning parameters in the LMI enable the preferential adjustment of the control and learning actions. Finally, a numerical example shows the effectiveness of the proposed method.

关 键 词：重复控制 低通滤波器 连续 离散二维系统 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]