GPI-repetitive control for linear systems with parameter uncertainty / variation

Abstract

Robust repetitive control problems for uncertain linear systems have been considered by different approaches. This article proposes the use of Repetitive Control and Generalized Proportional Integral (GPI) Control in a complementary fashion. The conditioning and coupling of these techniques has been done in a time discrete context. Repetitive control is a control technique, based on the internal model principle, which yields perfect asymptotic tracking and rejection of periodic signals. On the other hand, GPI control is established as a robust linear control system design technique that is able to reject structured time polynomial additive perturbation, in particular, parameter uncertainty that can be locally approximated by time polynomial signal. GPI control provides a suitable stability and robustness conditions for the proper Repetitive Control operation. A stability analysis is presented under the frequency response framework using plant samples for different parameter uncertainty conditions. We carry out some comparative stability analysis with other complementary control approaches that has been effective for this kind of task, enhancing a better robustness and an improved performance for the GPI case. Illustrative simulation examples are presented which validate the proposed approach.