Long term dynamics and control of a bare electrodynamic tethers under multi-environment perturbations

This paper studies the long term libration dynamics and control of deorbiting nano-satellites by a short and bare electrodynamic tether (EDT). It is well known that the EDT libration is unstable if it is not properly controlled due to the periodic excitations of electrodynamic force induced by the current across the tether. In the present work, we firstly analysed the orbital and librational dynamics of a bare EDT without control in orbit with high inclination angles. Then in order to avoid the tether tumbling, a simple current on-off control law is designed and applied to the deorbit process. A single index derived from the libration energy is used to determine the maximum allowed out-of- plane libration amplitude and an on-off switching current regulation is used to ensure the negative work done by the electrodynamic force when the out-plane libration amplitude exceeds the determined threshold. The long-term behaviour of the EDT both in the orbital motion and tether libration under the simple control is examined and the effectiveness of the proposed control law is evaluated. Multiple time-varying space environmental perturbations including atmospheric drag, the Earth's oblateness effect, solar radiation pressure, lunisolar gravitational attraction are considered. These perturbations, much smaller than electrodynamic force in long tether cases, are proved to have important effect on EDT dynamics, especially during long period. Copyright