An H∞ power flow approach to control of uncertain structures

Abstract

A technique is described for generating guaranteed stable control laws for uncertain, modally dense structures with collocated sensors and actuators. By ignoring the reverberant response created by reflections from other parts of the structure, a dereverberated mobility model can be developed which accurately models the local dynamics of the structure. This is similar in many respects to a wave based model, but can treat more general structures, and can be determined directly from transfer function data. In order to minimize the effect of disturbances propagatimg through the structure, the power dissipated by the controller is maximized in an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. This guarantees that the controller is positive real, and thus that the system will remain stable for any uncertainty, provided that the power flow is correctly modelled. The approach is demonstrated for a beam example. The resulting controllers are much more effective than simple collocated rate feedback.