Combined inverse and gradient iterative learning control: Performance, monotonicity, robustness and non-minimum-phase zeros

Abstract

Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete-time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non-minimum-phase dynamics on algorithm performance in terms of a 'plateauing' or 'flat-lining' effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti-causal inverse non-minimum-phase plant is presented and analysed in detail. Copyright © 2012 John Wiley & Sons, Ltd.