Stability and robustness analysis of boundary control of a flexible space structure

Abstract

We consider the question of the robustness of boundary control for a simplified SCOLE (spacecraft control laboratory experiment) model. A continuum model consisting of a long flexible mast joining two rigid bodies, one of which represents the space shuttle orbiter, the other an antenna reflector, is developed. The dynamics of the system are represented by a coupled set of ordinary and partial differential equations, and formulated as a wave equation in a Hilbert space by using a semigroup approach. For a continuum, distributed controls have often been proposed to stabilize the perturbed system. However, distributed controls for the continuous system are not practical to implement. Hence, for easy implementation we employ the boundary controls, as a special class of localized controls, that are control forces or torques applied only at the boundary. In this paper it is shown that the flexible system subject to a certain class of perturbations remains stabilizable by the same boundary feedback control as that for the nominal system. The results of numerical simulations for the simplified model are also presented to demonstrate the effective strong stabilization and robustness of the boundary controller with respect to the various perturbations.