Add-on-type Robust Iterative Learning Controller Design Based on the Information of Feedback Control Systems

Iterative learning control (ILC) combined with a feedback control system improves tracking performance by iteratively tuning the feedforward control signal on the basis of the system information, such as control inputs and tracking errors from previous iterations. Although ILC systems have been added to the existing feedback control systems, the learning controllers have been designed without considering valuable information, such as weighting functions used to design a robust feedback controller. This paper proposes a method for the design of an add-on-type robust iterative learning controller for an uncertain feedback control system using its explicit tracking-performance and plant-uncertainty information. The proposed ILC system is composed of two learning controllers, one of which is directly obtained from the inverse of the nominal feedback control system, and the other is a low-pass filter, known as the Q-filter ensuring robustness for the convergence under uncertainty. To design the learning controllers, first, a robust convergence condition in the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{L}_{2}$$\end{document}-norm sense is formulated, which is represented as the Q-filter and other known system information. Subsequently, the sufficient conditions to ensure that the remaining error is less than the initial error are derived. From the results, the criteria for simply designing the learning controllers are presented. Finally, important properties of the proposed ILC system, such as convergence rate and robustness, are demonstrated through simulations.