On Nonlinear Station-Keeping Control of Tethered Satellites

This work extends the results of [1] on stabilization of tethered satellite systems during the station-keeping mode using tension feedback. In [1], it was observed that the linearization of a rigid tether dynamic model in the station-keeping mode possesses two pairs of pure imaginary eigenvalues, and that one of these pairs is uncontrollable. The design proposed in [1] begins with a linear feedback which stabilizes the controllable imaginary eigenvalue pair. Next, nonlinear terms are added to the feedback control law to ensure stability of the resulting nonlinear critical system. This latter step employs a stability calculation from Hopf bifurcation analysis. Here, we consider the stabilization of the tethered satellite system using a tension control feedback which does not modify either pair of pure imaginary eigenvalues. The transient responses obtained using this approach are compared with those reported in [1]. The stability calculations are based on new results for stability of critical nonlinear systems with multiple critical eigenvalues [2], which generalize results of [3].