Sliding mode control for Lorentz-augmented spacecraft hovering around elliptic orbits

Abstract

A Lorentz spacecraft is an electrostatically charged space vehicle that could actively modulate its surface charge to generate Lorentz force as it moves through the planetary magnetic field. The induced Lorentz force provides propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft hovering that the chaser thrusts continuously to create an equilibrium state at the desired position relative to the target. Due to the fact that the direction of Lorentz force is determined by the local magnetic field and the velocity of the spacecraft with respect to the local magnetic field, which does not necessarily coincide with that of the required control acceleration for hovering, thus, in most cases, the Lorentz force works as a means of auxiliary propulsion to reduce the expenditure of fuel onboard. And that is why it is called Lorentz-augmented hovering. A dynamical model for Lorentz-augmented hovering around elliptic orbits is developed based upon the assumption that the Earth׳s magnetic field could be modeled as a tilted dipole that corotates with Earth. Fuel-optimal open-loop control laws are then derived based on the proposed dynamical model, presenting the optimal trajectories of the required specific charge of Lorentz spacecraft and the thruster-generated control acceleration. Considering the external disturbances that may drift the desired hovering position, a closed-loop integral sliding mode controller is also designed to guarantee the tracking of optimal control trajectories, ensuring the robustness of the system against perturbations. Numerical simulations are presented to analyze the characteristics of Lorentz-augmented hovering around eccentric orbits and the results substantiate the validity of the proposed open-loop and closed-loop control methods.