Dynamics and Control of a Tethered Satellite System Based on the SDRE Method

This paper presents the nonlinear dynamic modeling and control of a tethered satellite system (TSS), and the control strategy is based on the state-dependent Riccati equation (SDRE). The TSS is modeled by a two-piece dumbbell model, which leads to a set of five nonlinear coupled ordinary differential equations. Two sets of equations of motion are proposed, which are based on the first satellite and the mass center of the TSS. There are two reasons to formulate the two sets of equations. One is to facilitate their mutual comparison due to the complex formulations. The other is to provide them for different application situations. Based on the proposed models, the nonlinear dynamic analysis is performed by numerical simulations. Besides, to reduce the convergence time of the librations of the TSS, the SDRE control with a prescribed degree of stability is developed, and the illustrative examples validate the proposed approach.