Abstract
In this paper, we explore the relationship between the hybrid passivity and finite gain systems framework and the generalized Kalman-Yakubovich-Popov (GKYP) Lemma. In particular, we investigate how to optimally design finite frequency (FF) controllers which possess strictly positive real (SPR) properties over a low frequency range, and bounded real (BR) properties over a high frequency range. Such FF SPR/BR controllers will be used to control systems which have experienced a passivity violation. We first review the hybrid systems framework and how linear time-invariant hybrid systems relate to FF positive real (PR), FF SPR, and FF BR systems and the GKYP Lemma. A convex optimization problem is posed where constraints are imposed via linear matrix inequalities yielding optimal FF SPR/BR controllers. The FF SPR/BR controllers are optimal in that they approximate the traditional H2 control solution. FF SPR/BR controllers are used to control both single- and two-link flexible manipulators. Experimental results successfully demonstrate closed-loop stability via the hybrid systems framework, and implementation of the proposed controller synthesis scheme.
Published Version
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