Libration Control of Electrodynamic Tethers Using Predictive Control with Time-Delayed Feedback

One of the key problems for electrodynamic tethers is stabilization of the librational motion. In the case of a constant current in a circular orbit, an electrodynamic tether exhibits periodic solutions that are unstable, with the instability growing with the level of applied current. This paper proposes a new feedback control scheme that is capable of stabilizing the librational dynamics of electrodynamic tethers using only modulations in the electric current. The feedback does not require knowledge of the reference periodic solution, and as such, stabilizes the tether during orbital transfers. The feedback controller is based on a time-delayed predictive control law, which chooses the electric current at the current sampling time to minimize the predicted librations of the tether from the librations that were measured during the previous orbit. The control law is fully nonlinear and demonstrates convergence from large disturbances from the known periodic solution. Numerical results are presented that demonstrate its applicability when the orbit of the tether system is changing over time. In particular, the control law is able to handle both circular and elliptical orbits, as well as deorbit in the presence of a tilted, rotating magnetic field.