Nonlinear optimal control of tethered satellite systems using tether offset in the presence of tether failure

A nonlinear optimal control design using inverse optimal technique is derived to control the attitude of a satellite using tether offset variations. This paper examines cases when tether deployment suddenly stops and tether breakage occurs. The system consists of two identical tethers of equal length connecting the downward-deployed-auxiliary mass to two distinct points symmetrically offset from the satellite mass center. The nonlinear dynamics describing the system are used to develop two optimal control algorithms based on inverse optimal theory and Sontag's formula, respectively. The performance of the control laws is tested by numerical simulations, which confirm that the high amplitude oscillations present in the in-plane motion of the main spacecraft due to tether severance are effectively damped within a quarter of an orbit. The fault tolerant inverse optimal controller demonstrates excellent system performance and robustness against variations in system parameters using less control effort in the order of a fraction of a centimeter and faster convergence. The numerical results clearly establish the robustness of the proposed inverse optimal offset control schemes in regulating the satellite dynamics of a two-tether system in the event of breakage of one of the tethers.