Motions And Their Controls Of Tethered Satellite Systems During Station-Keeping

As a new type of spacecraft, tethered satellite systems have been paid much attention for the past decades. In order to have a good control design, it is essential to understand the attitude dynamics of tethered satellite systems. This paper focuses on motions and their controls of tethers satellite systems during state-kepping phase, with consideration of rigid attitudes of the mother satellite. The contents are as follows.(1) The chaotic motion and its control of an in-plane tethered satellite system are studied, to which the dissipative damping is introduced to eliminate the chaotic motion. With the help of Elliptic functions, the pitch motions of two-degree-of-freedom systems of the tether are reduced to a single-degree-of-freedom system that relates to the attitude of the mother satellite alone. As results, the chaotic motion of the mother satellite is analyzed by using Melnikov’s method. The domain of chaotic motion a tethered satellite system with dissipative damping may occur is also determined in terms of the Melnikov’s functions.(2) The periodic and chaotic motion of a tethered satellite system in elliptic orbits and its control are studied. The periodic solution of the tethered satellite system with small eccentricity is obtained by Perturbation Method and stability of the solution is analyzed. A linearly velocity feedback control is appliyed to bring the unstable periodic motion of systems to a periodic motion. The chaotic motion of a tethered satellite system in elliptic orbits is studied by using Melnikov’s method. By using time-delay feedback control, the chaotic motion of an underactuated tethered satellite system in elliptical orbits is stabilized to a periodic motion.(3) The resonance motion of tethered satellite system is studied via the method of multiple scales, including nonlinear normal modes and their stabilities.(4) The results above are verified through reliance on the ground-based experimental facility aimed to thetered satellite syetems. First, dynamic equivalences for both circular and elliptical orbits are proposed, according to the dynamic similarity principles between the space and the ground. The chaotic motions of the two-body tethered satellite system are validated experimentally. The experimental results show that the damping torque can effectively eliminate the chaotic motion. Moreover, the delay feedback approach is available for controlling chaotic motion of the underactuated tethered satellite system in elliptical orbits.