A New Sliding Mode Control for Satellite Formation Flying in Elliptical Orbits Based on a Model in the True Anomaly Region

Abstract

In order to achieve precise maneuvers of formation flying satellites, an accurate and controllable relative motion model is greatly needed. However, most transformation equations only take either external disturbances or J₂ perturbation into consideration, which will affect satellites' long-term reconfiguration. Therefore, nonlinear relative motion equations of satellites in elliptic orbits with consideration of both external disturbances and J₂ perturbation are derived in this paper. To obtain accurate formations and improve the system robustness in the presence of external disturbances and J₂ perturbation, a reconfiguration and formation-keeping control law based on the nonlinear sliding mode function is proposed, where nonlinear gains of exponential growth are used to replace the constant gain of the traditional sliding mode function. The proposed control law restrains the control law saturation during big errors and improves the response rate during small errors, and effectively enhances the rate of reaching the sliding mode surface. Finally, the numerical simulation results verify the effectiveness of the proposed strategies.