Controlling the position of satellites in PCO formation with the help of adaptive sliding model controller

This article introduces PCO formation. The PCO array is extended to three satellites, and one satellite is assumed to be the leader and two satellites to be the follower. A new controller has been introduced to control the position (distance) of the follower satellites in relation to the leader satellite and to reject environmental disturbances (atmospheric drag, gravitational perturbations, solar radiation pressure, etc.). The proposed controller is the Adaptive Sliding Mode Controller (ASMC) and somehow based on feedback linearization and the PI controller with adaptive coefficients for both stabilization and tracking. This controller is nonlinear and its stability is proved by Lyapunov method. To evaluate the performance of the proposed controller, first the method of linearization of nonlinear dynamic equations of position of satellites is presented then LQR method is used in the simulation for these equations and the results are compared with the proposed controller. The simulation results show that the proposed controller performed well in the initial formation of the PCO arrangement and also no collision occurs due to the desire relative positions of the follower satellites. The proposed controller performs better than the LQR method in keeping the PCO formation and reject environmental disturbances.