针对一类正则线性系统, 提出一种基于状态观测器和二维混合模型的重复控制系统设计方法. 首先, 通过构造一个状态观测器来重构系统的状态, 建立基于重构状态的线性控制律. 然后, 通过独立地考虑重复控制系统的连续控制过程与离散学习行为, 给出基于状态观测器和重构状态反馈的连续/离散二维混合模型. 针对这个混合模型, 运用二维Lyapunov泛函方法, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出重复控制系统存在重复控制器和状态观测器的充分条件, 所给条件可用Matlab工具箱方便地求解. 数值仿真验证了本文所提方法的有效性.
This paper presents a method of designing a repetitive control system for a class of regular linear systems. The method is based on a state observer and a two-dimensional (2D) hybrid model. First, a state observer is constructed to reconstruct system states and a linear control law is established based on the reconstructed states. Next, by describing the continuous control and discrete learning actions of repetitive control system independently, a continuous-discrete 2D hybrid model is established based on the state observer and the reconstructed state feedback. In the light of the 2D Lyapunov function, a sufficient condition is given in the form of linear matrix inequality (LMI) for the existence of the state observer and the repetitive controller for the repetitive control system. The condition can be resolved conveniently by using the Matlab toolbox. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.