μ Control for Satellites Formation Flying

Abstract

In this paper, a μ controller is designed for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position equation. In this model, nonzero eccentricity and varying semimajor axis are included as parametric uncertainties. J2 perturbation, atmospheric drag, and actuation and sensor noise are bounded by functional uncertainties. The μ controller design based on the nominal mission (an 800 km altitude circular reference orbit) is capable of achieving desired performance, is robust to uncertainties, and satisfies fuel consumption requirements even in a challenge nonnominal mission (a 0.1 eccentricity and 7,978 km semimajor axis elliptic reference orbit) with the same control gain. In this nonnominal mission, the designed μ controller is able to keep formation with almost the same level of the ΔV budget (43.86 m∕s∕year) as used in the nominal mission (39.65 m∕s∕year) . For comparison, linear quadratic regulator (LQR) and sliding mode controllers ...