Studies in robust control systems with application to various spacecraft attitude control schemes

Abstract

A robust control system remains stable under perturbations. In the last two decades, robust control has become one of the most important fields in testing the stability of control systems and determining the bounds of parameter perturbations within which a system would remain stable. The theory of robustness began from Kharitonov's theorem in 1978, and after that time many other theories have been given to check the stability of a system that is subjected to parameter perturbations. The aim of this thesis is to study the application of different robustness tests on various attitude control systems for spacecraft subject to parameter perturbations. The robust control theories for time domain and frequency domain with linear and non-linear parameters perturbations will be studied. The spacecraft attitude control and dynamics are discussed and complete models for different spacecraft controllers are also shown. The types of attitude control systems to be studied include; gravity gradient stabilization, three-axis control using reaction wheels or thrusters, and momentum wheel attitude control. Finally, the thesis will introduce a new method for decreasing the conservatism of the robustness bound given by Kharitonov's theorem. A "Gridding Method" will be introduced which divides the uncertainty regions of the parameter perturbations into small regions and tests the robustness inside each small region to obtain a new stable region for a given perturbed system. Also, the gridding method is used to test the linear and nonlinear parameter coefficients of the perturbed systems by using a linearization of the nonlinear system and then testing the robustness by using the ordinary Kharitonov's theorem. Then a comparison between these results and the actual results given by the robustness theories that deal with nonlinear systems will be shown to illustrate the effect of the grid size in the bounds of the uncertainties.