Minimum sliding mode error feedback control for inner-formation satellite system with J 2 and small eccentricity

Abstract

With the recent flurry of the research on Inner-Formation satellite system, there has been apparent need for a set of linearized equations to describe the relative motion of satellites under the effect of the J 2 geopotential disturbance, which is the important perturbed-factor for low-orbit Inner-Formation system. Hence, on the assumption of small eccentricity, a new set of linearized equations of motion is proposed that accounts for J 2 perturbations in an elliptical orbit. To avoid the collision between the inner satellite and the outer satellite, the Minimum Sliding Mode Error Feedback Control (MSMEFC) is developed to perform a real-time control on the outer satellite with the uncertain perturbations from the space. The highlight of MSMEFC is to introduce the concept of equivalent control error, which is the key utilization of MSMEFC. It is shown that the proposed MSMEFC can compensate any kinds of uncertain perturbations. Besides, in this paper, the relationship between the equivalent control error and uncertain perturbations is discussed. The robustness and steady-state error of MSMEFC are also analyzed to show its theoretical advantages compared with traditional SMC. Numerical simulations are employed to check the fidelity of the linearized equations. In addition, the efficacy of MSMEFC is verified by the utilization of Inner-Formation system with high control precision.