Robust Control of Spacecraft Formation Flying Using Optimal Sliding Mode

In this paper, in order to control the relative motion for spacecraft formation flying, an optimal sliding mode controller is presented. This controller is designed based on the linearized equations of relative motion in circular orbit and applied to nonlinear system that is subjected to external disturbance. Firstly optimal controller is designed based on linear quadratic (LQ) method, and then integral sliding mode control technique is used to robustify the controller. It is assumed that spacecrafts move in low-earth orbits and J2 perturbation is considered as external disturbance. Using Lyapunov second method, the stability of the closed-loop system is guaranteed. The performance of the proposed controller in tracking the desired trajectory is compared to sliding mode controller and simulation results show the effective performance of the proposed controller.