Open-closed-loop PID-type iterative learning control for linear systems with initial state error

Abstract

An open-closed-loop proportional-integral-derivative (PID) type iterative learning control (ILC) strategy is studied for linear time-invariant systems with initial state errors. Two cases of initial state errors are considered. The first case is that the initial states are the same but different from the desired initial states, and another is subject to random initial states. For both cases, the sufficient and necessary conditions guaranteeing the convergence and robustness of proposed open-closed-loop ILC system are presented. It will be shown that the proposed ILC scheme is robust when initial state errors are bounded, and furthermore, we will also show that the open-closed-loop PID-type learning algorithm can speed up the convergence of the tracking error and the controller parameters in comparison with the open-loop PID-type learning algorithm. In order to show the validity and advantage of our schemes, two numerical examples are given.