Pseudo-Inverse Based Iterative Learning Control for Linear Nonminimum Phase Plants with Unmodeled Dynamics*

Abstract

Learning control is a very effective approach for tracking repetitive processes. In this paper, the stable-inversion based learning controller as presented in (Ghosh, J. and Paden, B., 1999, “Iterative Learning Control for Nonlinear Nonminimum Phase Plants with Input Disturbances,” in Proc. of American Control Conference; Ghosh, J. and Paden, B., 1999, “A pseudo-inverse based Iterative Learning Control for Nonlinear Plants with Disturbances,” in Proc. of 38th Conference on Decision and Control.) is modified to accommodate linear nonminimum phase plants with uncertainties. The design of the learning controller is based on the computation of an approximate inverse of the nominal model of the linear plant, rather than its exact inverse. The advantages of this approach are that the output of the plant need not be differentiated and also the plant model need not be exact. A low pass zero-phase filter is used in the iteration loop to achieve robustness to plant uncertainty. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components.