Control of uncertain structures using an H(infinity) power flow approach

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 that 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, not only those that can be represented as a collection of waveguides. This model can be determined directly from transfer function data using an analysis technique based on the complex cepstrum. In order to minimize the effect of disturbances propagating through the structure, the power dissipated by the controller is maximized in an //<» 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 modeled. The approach is demonstrated for two examples. The resulting controllers are much more effective than simple collocated rate feedback.