基于二维混合模型的保成本重复控制

Guaranteed-cost repetitive control based on 2D hybrid model

中文关键词  线性不确定系统  保成本重复控制  二维系统  线性矩阵不等式

英文关键词  uncertain linear systems  guaranteed cost repetitive control  two dimensinoal (2D) systems  linear matrix inequality(LMI)

中文摘要

      针对一类线性不确定系统, 提出一种基于二维混合模型的重复控制设计新方法, 研究具有反馈作用的保成本重复控制设计与优化问题. 首先, 为了提高系统稳定性, 将反馈控制器引入到重复控制系统中, 设计一种具有反馈作用的重复控制系统结构; 然后通过建立重复控制系统的连续/离散二维混合模型, 将重复控制器设计问题转化为一类连续/离散二维系统的状态反馈控制问题. 在此基础上, 对给定的线性二次型性能指标, 给出闭环系统的保成本重复控制律参数设计及其优化方法. 对所有容许的不确定性, 保成本重复控制使稳态跟踪误差渐近稳定的同时, 线性二次型性能指标值小于某个常数. 所得结果以线性矩阵不等式的形式给出, 可利用MATLAB工具箱方便地求解.最后, 数值仿真验证了本文所提方法的有效性.

英文摘要

      For a class of linear systems with parametric uncertainties, we propose a new method for designing a guaranteed-cost repetitive control system based on two-dimensional (2D) hybrid model. First, a feedback controller is incorporated with the repetitive control system to improve the stability, resulting in a feedback repetitive control (FRC) system; then a hybrid continuous-discrete 2D model for the FRC system is developed. Thus, the FRC design problem is converted to a state feedback design problem for this continuous-discrete 2D system. A guaranteed-cost repetitive control algorithm and its optimization are then developed for a given quadratic performance function. In the FRC such designed, the tracking error is asymptotically stable and the quadratic performance function value is less than a specified upper bound for all admissible uncertainties. The results are derived based on the linear matrix inequalities (LMI) which can be realized easily by using Matlab Toolbox．Finally, the validity of the method is verified by a numerical example.