Modal control of an unstable periodic orbit.
Abstract
Floquet theory is applied to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a timeperiodic linear system, which is augmented by a timeperiodic control term. It is shown that this can be done such that (1) the application of control produces only inertial accelerations, (2) positive real Poincareexponents are shifted into the left halfplane, and (3) the shift of the exponent is linear with control gain. These developments are applied to an unstable orbit near the earthmoon L(3) point pertubed by the sun. Finally, it is shown that the control theory can be extended to include first order perturbations about the periodic orbit without increase in control cost.
 Publication:

Journal of the Astronautical Sciences
 Pub Date:
 March 1983
 Bibcode:
 1983JAnSc..31...63W
 Keywords:

 Floquet Theorem;
 Satellite Control;
 Satellite Orbits;
 Satellite Perturbation;
 Stationkeeping;
 Control Theory;
 Equations Of Motion;
 Periodic Functions;
 Perturbation Theory;
 Poincare Problem;
 Astrodynamics;
 Artificial Satellites:Periodic Orbits;
 Periodic Orbits:Artificial Satellites