A New Methodology for Rejection Non-periodic disurbances in Repetitive Control Systems

本研究提出一种新的重复控制设计方法，采用离散时间变结构（VS）控制算法和基于曲率模型的干扰估计。首先，一个扩展的系统包含一个内部模型的重复控制。在此基础上，设计了滑动模态和滑动扇区。然后设计变结构控制律，使系统状态收敛于滑模面内。它确保存在一个在状态空间中单调递减的李雅普诺夫函数。因此系统是渐近稳定的。仿真结果表明，所提出的控制系统提供了良好的性能。为了提高重复控制系统对干扰的抑制性能，提出了一种基于曲率模型的干扰估计方法。其主要特点是，当估计的干扰直接纳入重复控制律的设计重复控制系统的稳定性得到保证。仿真和实验结果表明，该方法能有效地抑制干扰。

This study presents a new design method for repetitive control that employs discrete-time variable structure (VS) control algorithm and disturbance estimation based on a curvature model. First, an extended system containing an internal model of repetitive control is derived. Based on that, a sliding mode and a sliding sector are designed. Then a variable structure control law is designed so that the state converges inside the sliding sector. It ensures that there exists a Lyapunov function that decreases monotonically in the state space. Thus the system is asymptotically stable. Simulation results show that the proposed control system provides good performance. In order to improve the rejection performance of disturbances in a repetitive control system, a disturbance estimation method based on a curvature model is proposed. The main feature is that the stability of the repetitive control system is guaranteed when the estimated disturbance is incorporated directly into the designed repetitive control law. Simulation and experimental results show that disturbances are rejected efficiently when this approach is used.