Eigenvalue optimization algorithms for structure/controller design iterations

Abstract

An eigenspace optimization approach is proposed and demonstrated for the design of feedback controllers for the maneuvers/vibration arrests of flexible structures. The algorithm developed is shown to be equally useful in sequential or simultaneous design iterations that modify the structural parameters, sensor/actuator locations, and control feedback gains. The approach is demonstrated using a differential equation model for the Draper/RPL configuration. This model corresponds to the hardware used for experimental verification of large flexible spacecraft maneuver controls. A number of sensor/actuat or configuration s are studied vis-a-vis the degree of controllabili ty. Linear output feedback gains are determined using a novel optimization strategy. The feasibility of the approach is established, but more research and numerical studies are required to extend these ideas to truly high-dimensioned systems. Parameterization of the Controlled System's Eigenvalues and Eigenvectors C ONSIDER a linear structure (modeled by a finite element or similar discretization scheme) in which the configuration vector jc is governed by the system of differential equations