Robust Nonlinear Control of Underactuated Satellite Formation

In this thesis, the control of the underactuated satellite formation system is examined. The underactuated satellite formation consists of a leader-follower configuration where there is no control force available in the radial direction relative to the orbit of the leader satellite. Two new relay sliding mode controllers are proposed as a method of controlling the formation system. The first controller is developed using the Hill's equation of motion of the satellite formation and the sliding manifold is designed based on linear quadratic regulation and the algebraic Riccati equation. The second controller uses a 2nd order state dependent time varying approximation of the satellite formation and the sliding manifold is chosen in real-time through the evaluation of the causal approximation of the differential Riccati equation. The incorporation of the nonlinearity and time varying properties of the system into the control law expands the operational range of application. The theoretical stability bounds of the two control laws are determined guaranteeing the robust nature of the closed loop system against both matched and unmatched disturbances. A series of numerical simulations are used to validate the stability and robustness of the proposed control laws. Finally, some simulations are provided to determine the effect of controller and system parameters on the control laws' performance.