The Development of high fidelity linearized J2 models for satellite formation flying control

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.