Robust iterative learning control for uncertain linear systems and convergence properties in the frequency domain

Abstract

This dissertation deals with an iterative learning control (ILC) with current feedback for uncertain linear systems and investigates properties of ILC, convergence in particular, in the frequency domain. n addition, to show a practical benefit of ILC, the ILC scheme proposed in the dissertation is applied to the track-following servo system of an optical disk drive. A study on ILC for uncertain plants has not been performed sufficiently. In case that the plant uncertainty is represented as an additive noise or disturbance, unexpected results often occur in practical situations because of its conservativeness. Moreover, in designing iterative learning controllers, it is generally assumed that a feedback controller is already given. However, the feedback controller should be dealt with in the viewpoint of ILC because it has effects on the performance of the ILC system as well as iterative learning controllers. For the reasons, the ILC scheme with current feedback is considered. Given uncertain linear plant, it is divided a known part and an uncertain part using linear fractional transformation (LFT). Using the structured singular value ($\mu$) and LFT, a sufficient condition is derived, which ensures not only robust ${\cal L}_2$ convergence and robust stability of the ILC system in the presence of the uncertainty. On a basis of the proposed condition, the iterative learning controllers and feedback controller are designed by $\mu$-synthesis at the same time. A weighting function is introduced to improve the learning performance. Convergence is the most significant concept in ILC as stability in general feedback control theories. Nevertheless, little notice has been taken of its importance. In the frequency domain, the ${\cal H}_\infty$ norm of the transfer function between consecutive errors has been used to test convergence of a learning system. It is shown that the conventional convergence condition is sufficient for ${\cal L}_2$ convergence and sufficient and ...