Nonlinear control of librational motion of tethered satellites in elliptic orbits

A method to control the librational motion of a tethered satellite system in an elliptic orbit is presented. To simplify the analysis, gravity is treated as the only external force affecting the tethered satellite system, only in-plane motion is considered, and the flexibility and mass of tethers are neglected. The tethered satellite system treated in this paper consists of two subsatellites and a mother satellite, such as the space shuttle, connected together in series via massless tethers. This type of tethered satellite system has very important applications in Earth observation, space observation, communications, and satellite constellations. The librational motion of the tethered satellite system in an elliptic orbit is known to be chaotic and can be stabilized to undergo periodic motion by the delayed feedback control method. The, periodic motion of a tethered satellite in a circular orbit is employed as the reference trajectory for tracking by the actual tethered satellite, which is in an elliptic orbit. The decoupling and model tracking control methods, based on differential geometric control theory are combined with the delayed feedback control method in a new approach to controlling the librational motion of the tethered satellite system in elliptic orbits. The results of numerical simulations show that the proposed control scheme has good performance in controlling the librational motion of a tethered satellite system in an elliptic orbit.