Robust Station-Keeping Control of Sun-Earth/Moon Libration Point Orbits Using Electric Propulsion

A novel strategy combining an extended state observer (ESO) and a backstepping sliding mode (BSM) controller is proposed for station-keeping of unstable collinear libration point orbits (LPOs) in the Sun-Earth/Moon system. The framework of the circular restricted three-body problem is utilized. The control thrusts are assumed to be generated by electric propulsion and, thus, continuous. In the proposed method, the system dynamics and uncertainties are treated as total disturbance and estimated by an ESO using only the input and output information. The BSM controller is designed to compensate for the total disturbance and ensure the actual trajectory converge to the nominal orbit. A rigorous stability analysis of the ESO-BSM controller is presented. A pure BSM controller without an extra observer is employed for comparison. Numerical simulations and a set of Monte Carlo simulations are presented to illustrate the proposed controller's effectiveness and robustness. The results indicate that the model-free ESO-BSM controller is adequate for station-keeping of unstable LPOs, and performs better than the model-based BSM controller in the presence of orbital insertion errors, external disturbances, and random uncertainties.