Linearized J2 and Atmospheric Drag Model for Control of Inner Formation Satellite System in Elliptical Orbits

Abstract

A new set of linearized differential equations governing relative motion of innerformation satellite system (IFSS) is derived with the effects of J2 as well as atmospheric drag. The IFSS consists of the “inner satelliteâ€‌ and the “outer satellite,â€‌ this special configuration formation endows its some advantages to map the gravity field of earth. For longterm IFSS in elliptical orbit, the highfidelity set of linearized equations is more convenient than the nonlinear equations for designing formation control system or navigation algorithms. In addition, to avoid the collision between the inner satellite and the outer satellite, the minimum sliding mode error feedback control (MSMEFC) is adopted to perform a realtime control on the outer satellite in the presence of uncertain perturbations from the system and space. The robustness and steadystate error of MSMEFC are also discussed to show its theoretical advantages than traditional sliding mode control (SMC). Finally, numerical simulations are performed to check the fidelity of the proposed equations. Moreover, the efficacy of the MSMEFC is performed to control the IFSS with high precision.