Extended time-delay autosynchronization method for libration control of electrodynamic tether using Lorentz force

It is well known that the libration motion of the electrodynamic tether is unstable. Libration control of the electrodynamic tether system using the Lorentz force produced by current in the tether is studied. In the libration dynamic equation, the Lorentz force is virtually divided into two parts. One part takes the role of keeping the essential function of the electrodynamic tether system. The other part takes the role of controlling the libration motion. The control scheme of the Lorentz force is based on the extended time-delay autosynchronization method. In this scheme, the control current which is the control parameter is determined by real-time states of libration and angular velocities for delay time of previous periods. The validity of the control scheme proposed in this study is confirmed by numerical simulations in the case of circular orbit, elliptical orbit, orbit in the equatorial plane and noises existing in measuring the states of libration. The results show that the perturbed libration motions converge to the periodic solution with time growing in examples of circular orbit, elliptical orbit, and noises existing. The perturbed libration motion converges to an approximate periodic orbit in the example of equatorial orbit. The control current is in a reasonable range during the process of control, and converges to zero in the end. The curve of the current in the tether is continuous and smooth which can be easily achieved in an actual system.