Modeling and controller design of inner-formation flying system with two proof-masses

The inner-formation flying system with two proof-masses (IFFS-II) in the same cavity of a big satellite is an innovative satellite formation flying system which can be used in the Earth gravity measurement. In IFFS-II, two proof-masses freely fly in the nearly pure gravitational orbit since the satellite shields them from the outer environmental disturbances. In IFFS-II, the self-gravitational attraction among proof-masses and outer satellite is a special disturbance and modeled for the first time. In addition, other disturbances like J2 non-spherical shape perturbation and atmospheric drag, etc. also influence the formation flying of IFFS-II. In regard to these problems, a relative translational controller combined with a disturbance feedback and a coordinate controller defined by the hyperbolic tangent function is designed. The global stability of the system with the proposed controller is proved by the Barbalat lemma in theory. Then a simulation is performed and the corresponding control effects are tested. The simulation results demonstrate that the controller stabilizes the system.