Optimal sliding mode control for spacecraft formation flying in eccentric orbits

Abstract

In order to control the relative motion for spacecraft formation flying in eccentric orbits, an optimal sliding mode controller is presented. This controller is designed based on the linearized two-body relative motion dynamics and is applied to the nonlinear system that includes the effects of external disturbances. The optimal control design is based on a linear quadratic method that is supplemented by an integral sliding mode control technique to robustify the controller. It is assumed that the leader and follower spacecraft are in a low Earth orbit and subject to the perturbing effects of J₂ and atmospheric drag. Using the Lyapunov second method, the stability of the closed-loop system is guaranteed. The performance of the proposed controller in tracking the desired reference trajectory is compared to a sliding mode controller, and simulation results show the effectiveness of the proposed controller.