μ Control for Satellites Formation Flying

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 800km 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 7,978km 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 (43.86m∕s∕year) as used in the nominal mission (39.65m∕s∕year) . For comparison, linear quadratic regulator (LQR) and sliding mode controllers (SMC) are developed and extensively tuned to get the same ΔV consumption as that of the designed μ controller for the nominal mission. However, as shown in the simulation, the designed linear robust controller (LQR) and nonlinear robust controller (SMC) have a serious ΔV consumption penalty ( 1.72km∕s∕year for SMC) or are unstable (for LQR) in the nonnominal mission.