Passivity Motivated Controller Design for Flexible Structures

Inherent passivity in fully actuated mechanical systems has long been recognized and exploited for their stabilitzation.  Even for underactuated systems, such as flexible robots, passivity remains a useful property.  It has been shown that under an observability condition strict passive feedback between these passive pairs can render the closed-loop system asymptotically stable, even for an open-loop undamped system.  When the input/output relationship is not passive, e.g., in the case of noncollocated actuator and sensor pairs, strictly passive feedback no longer guarantees stability. The purpose of this note is to present some extesnion of the passvity approach to nonpassive input/ouptut pairs through suitable incorporation of a nominal dynamical model of the system.