基于二维混合模型的重复控制系统设计新方法

A New Design Method for Repetitive Control Systems Based on Two-dimensional Hybrid Model

现有重复控制方法是在一维空间上同时处理控制与学习过程,这不利于重复控制系统的分析与设计.本文针对一类线性不确定系统,提出一种基于连续/离散二维混合模型的重复控制系统设计方法.首先,通过分析重复控制系统中独立存在的控制行为与学习行为,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;然后应用二维连续/离散系统方法,获得重复控制系统的稳定性条件,根据稳定性条件并利用线性矩阵不等式(Linear matrix inequality,LMI)方法,求得重复控制器参数.与现有方法相比,所提出的重复控制设计方法更加符合其本质特征,具有简单实用、直观明了的特点,克服了现有重复控制方法所存在的局限性.最后,数值仿真实例验证了本文所提方法的有效性.

Existing design methods for repetitive control systems cannot effectively synthesize such a system because the control and learning processes are carried out simultaneously in a one-dimensional space. This paper presents a method of designing a repetitive control system for a class of linear uncertain systems that are based on a two-dimensional （2D） continuousdiscrete hybrid model. First, a 2D continuous-discrete hybrid model is established to describe two independent types of actions in repetitive control： control and learning. The problem of designing a repetitive controller is then converted to a statefeedback design problem for the model. Next, a stability condition for the model is obtained from the 2D system theory. The parameters of the repetitive controller are then obtained from the stability condition in combination with linear matrix inequalities. This method is simpler, more intuitive, and more practical than existing methods, and does not suffer from their limitations. Finally, the validity of the method is verified by a numerical example.