Active stabilization of a two-satellite tether in elliptic orbits using Coulomb forces

This paper investigates the dynamics and control of a charged two-craft tether formation in elliptical orbit. Due to the fact that the inter-spacecraft Coulomb forces are not sufficient to stabilize the tether, a method of hybrid control is proposed which uses conventional thrusts and Coulomb forces. A feedback control law is developed which could asymptotically stabilize the tether size and attitude while mitigating plume impingement issues. The equations governing this system are periodic in time, thus a feedback control using constant gains can not work. A periodic control law is suggested basing on Floquet theory. The control law consists of two main parts. First Floquet transformation is utilized to transform the system into a new linear system with a constant state matrix but a periodic control matrix. Then a feedback control is used to stabilize the new system. Numerical examples are provided to demonstrate the performance of the control law.