Resonant Control of Satellite Orbits

Low-thrust orbit control has been widely studied, mostly by using direct or indirect optimization to detect time-optimal and fuel-optimal orbit transfers. This paper proposes an alternative approach for designing efficient low-thrust orbit transfers. The main idea is to create an artificial resonance between the period of the control accelerations and a characteristic period of the orbital dynamics. To that end, Gauss's variational equations are written using a Fourier series expansion in the mean anomaly. The secular changes of the orbital elements are determined based on averaging theory. It is shown that an artificially created low-thrust resonance can save fuel compared with piecewise-constant thrust. A general resonant-control candidate for changing all mean orbital elements efficiently is proposed. Four simple decoupling control laws are designed for changing the semimajor axis, eccentricity, inclination, and right ascension of the ascending node separately. In addition, periodic corrections transforming between mean elements and osculating elements are derived. The proposed decoupling control laws are applied to a formation-keeping problem, illustrating the potential merit of the new control law compared with a fixed-thrust-magnitude feedback control.