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A. Steindl:
"Stabilization of the Radial Position of a Tethered Satellite System";
Talk: ICOVP-2013, Lissabon; 2013-09-09 - 2013-09-12; in: "ICOVP-2013 International Conference on Vibration Problems", Z. Dimitrovová (ed.); (2013), 8 pages.

We investigate the stabilization of the radial position of a tethered satellite by tension
control with respect to in-plane and out-of-plane perturbations.
In previous investigations
we considered the deployment and retrieval of a satellite
from the main station, assuming that the motion of the satellite is restricted to the orbital plane.
Now we ask, whether it is possible to stabilize the stationary radial position for small deviations
from this configuration in arbitrary directions by applying a tension force on the tether.
Due to the rotation of the system around the central mass the dynamics in the plane and
transversally to it are significantly different: For the in-plane motion the variation of the tethers´s
length acts like an external force, and the motion can be extinguished in finite time. For
the pure out-of-plane perturbation the length change rate acts as parametrical excitation. By
pulling the tether periodically with the proper phase, this motion can only be controlled to
decay algebraically. Even for this rather simple sub-problem we need to apply nonlinear bifurcation
theory to obtain the center and stable manifolds, because due to the parametrical input,
the linearization at the stationary solution fails to describe the dynamics properly. In a first
attempt to find a control law to diminish both types of oscillations we use the length change rate
as control parameter and apply Optimal Control theory to obtain the feedback law. Since the
length change rate might not be a valid control variable, because it is impossible to push the
tether and also the tension in the tether could be too large, in an improved model we use the
tension as control variable with proper constraints and regard the length and its change rate as
additional state variables. The expected solutions are obtained numerically by solving a
boundary value problem for the Hamiltonian differential equations with intermediate switching
conditions, derived by Pontryagin´s Maximum Principle.

Optimal Control, Invariant manifolds, Deployment, out-of-plane perturbations, Hamiltonian Hopf bifurcation

http://publik.tuwien.ac.at/files/PubDat_223540.pdf