Attitude stabilization of electrodynamic tethers in elliptic orbits by time-delay feedback control

• We apply 2 feedback methods to control the attitude motion of electrodynamic tethers.
• We use a dumbbell model in a non-tilted geomagnetic field and constant tether current.
• The goal is to stabilize the basic unstable periodic attitude motions of the tether.
• We have computed the stability domains of both methods for different elliptic orbits.
• Comparative study of the stabilization effectiveness of both control methods.

It is well known that libration motion of electrodynamic tethers operating in inclined orbits is affected by dynamic instability due to the electromagnetic interaction between the tether and the geomagnetic field. We study the application of two feedback control methods in order to stabilize the periodic attitude motions of electrodynamic tethers in elliptic inclined orbits. Both control schemes are based on the time-delayed autosynchronization of the system. Numerical simulations of the controlled libration motion show that both control techniques are able to transform the uncontrolled unstable periodic motions into asymptotically stable ones. Such stabilized periodic attitude motions can be taken as starting points for the operation of the tether. The control domains of both methods have been computed for different values of the system parameters, as functions of the two control parameters shared by both control schemes. The relative effectiveness of the two techniques in the stabilization of the periodic attitude motion has also been studied.