Robust repetitive control with saturating actuators: a LMI approach
Proceedings of the 2010 American Control Conference, 2010
This paper addresses the problem of tracking and rejection of periodic signals for uncertain line... more This paper addresses the problem of tracking and rejection of periodic signals for uncertain linear systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. From this structure, conditions in a “quasi” LMI form are proposed to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain invariant ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection. Based on these conditions, an optimization problem aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances is proposed.
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