Tether tension control law design during orbital transfer via small-gain theorem

Issues of controller design via small gain theorem for tethered satellite system (TSS) during orbit maneuvering under transversal thrust are considered. First, dynamic equations of tethered satellite system in orbital maneuvering are established based on a dumbbell model. It is proved that the in-plane system is weak minimum phase by selecting a proper Lyapunov candidate function, and there are some difficulties for controller designing based on nonlinear model directly. Next, a controller is designed by utilizing Small-gain Theorem based on a control oriented model. An input-to-state stable (ISS) based tether rate control law is derived as the reference signal for the tether length system. A tether tension control law is proposed such that the uncertainties caused by linearization will be suppressed by properly selected control parameters and the closed loop system will be forced to a small neighborhood of origin as time approaches infinity. Finally, numerical simulation results demonstrate the validity of the proposed algorithm.