Adaptive reaching law based sliding mode control for electromagnetic formation flight with input saturation

Electromagnetic formation flight utilizes electromagnetic forces to control the relative positions of satellites, and offers a promising alternative to a traditional propellant-based spacecraft formation flying due to no fuel expenditure. Since available electromagnetic forces generated on board are small, their efficient use is a challenging issue in the presence of saturation. This paper proposes a novel adaptive reaching law based sliding mode control for the trajectory tracking of electromagnetic formation flight with actuator saturation. The adaptive reaching law is characterized by a modulation function which combines a saturated term with a non-switching term. The saturated term makes the sliding variable converge as fast as possible under input saturation, while the non-switching term is used to guarantee a terminal tracking performance and remove chattering. Thus, the introduced modulation function enables a smooth transition of the reaching law between two terms and an adaptive decrease rate of sliding variable. The proposed control can achieve a fast convergence and offers the robustness against external disturbance with input saturation. Simulation results are given to demonstrate the performance of the presented method.