Current Analysis and Optimal Control of a Spinning Bare Electrodynamic Tether System during its Spin-up Process

This paper mainly studies the electrical current control of the spinning bare electrodynamic tether system (SBEDT) during its spin-up process. The SBEDT combines the high electrical absorption efficiency of bare tethers and the centrifugal stability of spinning tethers, which provides a propellant-free solution to missions including space debris removal, artificial gravity, and payload transportation. However, the nonlinear current distribution of bare tethers poses serious challenges to its dynamic and control. To deal with this problem, this paper focuses on the current analysis and optimal control of tether motions. First, a dynamic model is established for analyzing the varying currents in different positions, and the analytical expressions of the electrodynamic force are given. Second, the minimum tether length for spin-up is calculated by the maximum equilibrium position, providing a theoretical basis for system design. Third, an optimal tether deploying/retrieving controller is proposed to adjust electrodynamic force. The control law is designed according to the Bellman optimality principle, which tracks the angular velocity and controls the tether length within a certain range. Under the proposed analyzing method and the corresponding control strategy, spinning stability can be maintained during the spin-up process and the system successfully reaches the desired spinning state.