Stability analysis and motion control of spinning electrodynamic tether system during transition into spin

Spinning electrodynamic tether systems are considered one of the most promising potential applications of tethered satellite systems, which require little fuel and avoid the equilibrium limit of conventional vertical electrodynamic tether systems. Therefore, spinning electrodynamic tether systems have good prospects in debris removal, orbit reboost, payload transportation, and so on. It has been found that, if not carefully controlled, tethers easily become slack or sagging during the transition process from equilibrium state into spin. In this regard, this paper mainly focuses on the transition process of spinning electrodynamic tether systems from the initial equilibrium state into the final spinning state with expected angular velocities. Conditions of dynamic equilibrium position and minimum current for acceleration (critical current) are firstly derived in this paper, which provide references for future space tether experiments. The motion of spinning electrodynamic tether systems is described by the Lagrangian model, which takes orbital motion into consideration. By considering power limits of electrodynamic tether systems, this paper proposes two open-loop control methods for the safe transition into spinning state as nominal control algorithms with different mission objectives. The first method (direct transition) provides a near time-minimum solution, and the second method (swinging transition) provides a minimum current-energy solution for acceleration into spin. Considering perturbations in space, including inhomogeneous distribution of magnetic induction, varying mass distribution of the system and so on, an adaptive sliding mode controller is proposed to regulate the system and to track nominal trajectories of acceleration. The effectiveness of the proposed control methods is validated by numerical results.