Libration control of electrodynamic tethers using the extended time-delayed autosynchronization method

Abstract

Any electrodynamic tether working in an inclined orbit is affected by a dynamic instability generated by the continuous pumping of energy from electromagnetic forces into the tether attitude motion. In order to overcome the difficulties associated with this instability, a new control scheme has been analyzed in this paper. The background strategy is as follows: we add appropriate forces to the system with the aim of converting an unstable periodic orbit of the governing equations into an asymptotically stable one. The idea is to take such a stabilized periodic orbit as the starting point for the operation of the electrodynamic tether. We use an extended delay feedback control scheme which has been used successfully in problems with one degree of freedom. In order to obtain results with broad validity, some simplifying assumptions have been introduced in the analysis. Thus, we assume a rigid tether with two end masses orbiting along a circular, inclined orbit. We also assume a constant tether current which does not depend on the attitude and orbital position of the tether. The Earth’s magnetic field is modeled as a dipole aligned with the Earth’s rotation axis.