Resonant Control of Satellite Orbits

What is it about?

Resonant control, where the period of the control accelerations matches the period of the corresponding Gauss equation's coefficients, is a promising method for satellite orbit control. The benefits of creating resonance artificially for saving fuel are considerable. A candidate resonant control law consisting of nine elements is capable of changing all orbital elements. The nine components can be divided into three groups: the accelerations $u_{s0}$, $u_{sc}\cos M$, $u_{rs}\sin M$, changing the mean semimajor axis and mean eccentricity; $u_{w0}$, $u_{wc}\cos M$, $u_{ws} \sin M$, changing the mean inclination, mean right ascension of the ascending node, and mean argument of perigee; and $u_{r0}$, $u_{rc} \cos M$, $u_{ss} \sin M$, controlling the mean argument of perigee and mean anomaly. The periodic acceleration $u_{wc}\cos M$ is more efficient in changing $i$ and $\Omega$ than a constant acceleration $u_{w0}$ when $e<0.4404$ and the constant acceleration $u_{w0}$ is better when $e>0.4404$; a constant acceleration $u_{s0}$ should be the best choice for controlling the semimajor axis and $u_{sc}\cos M$ is better than $u_{rs}\sin M$ in changing the eccentricity. Based on these findings, the candidates for resonant control can be further optimized and decoupling control laws can be developed. Applying these proposed decoupling control laws to a formation-keeping mission, it is found that the tracking errors of differential mean semimajor axis and differential mean inclination decrease near linearly with respect to time. The fuel consumption is only 51.84\% that of the fuel cost of a fixed-thrust-magnitude feedback controller.

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