Optimal control of the deployment (and retrieval) of a tethered satellite under small initial disturbances

摘要

The deployment and retrieval processes of satellites from a space station are demanding tasks during the operations of tethered satellite systems. The satellite should be steered into its working state within a reasonable amount of time and without too much control efforts. For the pure in-plane oscillation we have found time-optimal solutions with bang-bang control strategy for the deployment and retrieval process. In our working group we have also investigated different stabilization methods of the vertical equilibrium configuration, for example parametric swing control and chaotic control. In this article we concentrate on the final stage of the operation, when the oscillations around the vertical configuration should be brought to halt. While this task is quite simple for a motion of the satellite in the orbital plane, it is considerably more difficult, if the satellite has been perturbed out of that plane. We first analyze the control for a purely out-of-plane oscillation, which is governed by a Hamiltonian Hopf bifurcation, and then investigate the combined control for the spatial dynamics. Using a center manifold ansatz for the inplane oscillations, we can show, that it is possible to diminish the oscillations of the tethered satellite in both directions, but the decay is extremely slow.