Constrained fuel-free control for spacecraft electromagnetic docking in elliptical orbits

Abstract

This paper addresses the control problem of spacecraft electromagnetic docking in the presence of external disturbances, fault signals, elliptical eccentricity, and input magnitude and rate constraints (MRCs). More specifically, the dynamic model of translational motion in an elliptical orbit is derived first; by analyzing the influence of external disturbances, fault signals and elliptical eccentricity, a lumped disturbance is reconstructed to facilitate the controller design. Then, a state feedback control strategy based on disturbance observer, i.e. a disturbance observer-based controller (DOBC), is proposed, where the compensation of the lumped disturbance is considered. This controller thus has the nature of fault tolerance and robustness, and it requires no mass information on chaser or target spacecraft, no information on external disturbances, fault signals or even orbital elements except for semi-major axis. By choosing new state variables using the information on relative motion and estimation errors, an augmented plant is established. Using Lyapunov stability analysis, which shows that all states are uniformly ultimately bounded, sufficient conditions for the existence of the disturbance observer and controller subject to input MRCs are given based on linear matrix inequalities (LMIs). Numerical simulations are performed to demonstrate the validity and performance of the proposed strategy.