SPR Condition Establishment by Filter Design of Feedback Error Learning Control

Abstract

Feedback error learning (FEL) control attains accurate response to a target signal by tuning parameters in the feedforward (FF) controller, provided that feedback (FB) control stabilizes closed-loop in two-degree-of-freedom structure. The authors proposed an FEL tuning law by which the output error converges to zero for any target signals, under a strictly positive real (SPR) condition of the closed-loop. However, this condition is not always satisfied even if the plant is biproper or has a relative degree one. In this paper, we propose to satisfy the SPR condition by designing a filter in the FF controller by solving i) a linear matrix inequality (LMI) for a nominal plant; and ii) a finite set of LMIs for the uncertain plant in a polytope representation. We verify the effectiveness of these methods via a numerical example.