Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

William E. Wiesel, PhD


Low thrust propulsion systems such as electrodynamic tethers offer a fuel-efficient means to maneuver satellites to new orbits, however they can only perform such maneuvers when they are continuously operated for a long time. Such long-term maneuvers occur over many orbits often rendering short time scale trajectory optimization methods ineffective. An approach to multi-revolution, long time scale optimal control of an electrodynamic tether is investigated for a tethered satellite system in Low Earth Orbit with atmospheric drag. Control is assumed to be periodic over several orbits since under the assumptions of a nearly circular orbit, periodic control yields the only solution that significantly contributes to secular changes in the orbital parameters. The optimal control problem is constructed in such a way as to maneuver the satellite to a new orbit while minimizing a cost function subject to the constraints of the time-averaged equations of motion by controlling current in the tether. To accurately capture the tether orbital dynamics, libration is modeled and controlled over long time scales in a similar manner to the orbital states. Libration is addressed in two parts; equilibrium and stability analysis, and control. Libration equations of motion are derived and analyzed to provide equilibrium and stability criteria that define the constraints of the design. A new libration mean square state is introduced and constrained to maintain libration within an acceptable envelope throughout a given maneuver. A multiple time scale approach is used to capture the effects of the Earth’s rotating tilted magnetic field. Optimal control solutions are achieved using a pseudospectral method to maneuver an electrodynamic tether to new orbits over long time scales while managing librational motion using only the current in the tether wire.

AFIT Designator


DTIC Accession Number