Tether Deformation of Spinning Electrodynamic Tether System and Its Suppression with Optimal Controller

Spinning electrodynamic tether systems are considered ideal platforms for payload transportation, removal of space debris, artificial gravity, and so on, for they provide a propellantless solution to orbital maneuver and good centrifugal stability. However, all spinning electrodynamic tether systems have to transition into a spinning state from the equilibrium state, during which tethers are likely to become deformed because of Lorentz forces. This paper studies tether deformation during such a transition process. Two open-loop programs are proposed in the Lagrangian model as the reference trajectories of acceleration under different mission backgrounds. The dynamic characteristic of tether is studied in a more accurate model with distributed parameters (bead model). Considering the significant tether deformation in the case of high electrical current, an optimal controller is proposed based on Bellman dynamic programming. Numerical results indicate that the proposed control laws can ensure a safe transition of the proposed tether system into a spin and limit tether deformation to a reasonable level.