Stability robustness of linear feedback controlled flexible mechanical systems

Abstract

We consider linear mechanical systems containing flexible components and subject to linear memoryless feedback controllers. In general, if a stabilizing controller is designed based on a rigidified model, i.e., a model in which some of the flexible components are assumed rigid, it is not true that this controller also stabilizes the ‘real’ flexible system. We present a condition which guarantees that a stabilizing controller whose design is based on a rigidified model also stabilizes the flexible system, provided that the components, whose flexibilities are neglected in the rigidified model, are sufficiently stiff. This condition involves the location of the rate sensors and is independent of the location of the displacement sensors. For a natural class of systems and controllers, the condition is automatically satisfied when the rate sensors are collocated with the actuators.