基于二维混合模型的重复控制系统稳定性分析与控制器设计

Stability Analysis and Controller Design for Repetitive Control Systems Based on 2D Hybrid Model

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新方法,首先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/离散二维系统的稳定性问题;然后应用二维连续/离散系统方法,给出了重复控制系统新的稳定性条件,进一步,利用线性矩阵不等式方法,获得了重复控制系统稳定边界和重复控制器参数的计算方法,与现有方法不同的是,本文以二维混合模型来描述重复控制系统,更加符合其本质特征,实现了对重复控制过程中两种不同行为的独立调节,最后,数值仿真实例验证了本文所提方法的有效性。

This paper concerns stability analysis and controller design for repetitive control. First, a two-dimensional （2D） continuous-discrete hybrid model is derived to describe a repetitive control system. The problem of designing a repetitive controller is then converted to a stabilization problem for the model. Next, new criteria for the asymptotic stability of the system are presented based on the 2D system theory. Furthermore, these criteria are extended to calculate lower bounds on stability margins and design an appropriate controller. Unlike existing methods, this method describes a repetitive control system in terms of a 2D hybrid model so as to independently handle two completely different actions within the system. Finally, a numerical example demonstrates that this approach can provide good performance.