Abstract:
The inclusion of the linearized J2 effect in the Hill equations of relative
motion gives greater insight into satellite formation flying dynamics, and the
opportunity to investigate alternative feedback control strategies for the
station keeping task. The work of Schweighart and Sedwick is verified and
extended as time varying and analytical models are developed to incorporate the
J2 perturbation and its effects on the relative motion of two or more satellites
in LEO. Analysis is performed in detail to determine the best modelling strategy
for satellite formation keeping in the J2 perturbed environment. The analytical
J2 model is found to capture relative motion the most accurately, but only given
specific initial conditions. The time varying model captures leader-follower
motion better than the Hill equation and analytical J2 models. LQR control laws
are designed and performance evaluated for the basic Hill equations and the time
varying and analytical J2 models using Matlab/Simulink and the Satellite Tool
Kit.
