Orbit and formation control for low-earth-orbit gravimetry drag-free satellites

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Orbit and formation control for low-earth-orbit gravimetry drag-free satellites

Canuto, Enrico / Colangelo, Luigi / Buonocore, Marcello / Massotti, Luca / Girouart, Benedicte

The paper outlines orbit and formation control of a long-distance (>100 km) two-satellite formation for the monitoring of the Earth gravity. Orbit control applies to a single satellite and performs altitude control. Here, formation control is formulated as a control capable of altitude and distance control at the same time. The satellites being placed in a low Earth orbit, orbit, and formation control employ the measurements of a global navigation system. Formation control is imposed by long-distance laser interferometry, which is the key instrument for gravity measurement. Orbit and formation control are low-frequency control systems in charge of canceling bias and drift of the residual drag-free accelerations. Drag-free control is the core of the orbit/formation control since it allows the formation to fly drag-free only subject to gravity. Drag-free control being required to have a bandwidth close to 1 Hz, is designed as the inner loop of the formation control. In turn, formation control must not destroy drag-free performance, in which objective demands that formation control be effective only below the 0.2 mHz orbital frequency. Control design is based on a new orbit and formation dynamics, which are compared with the classical Hill–Clohessy–Wiltshire equations. The new dynamic equations are the first step in building the embedded model, which is the core of the control unit. Embedded model derivation is explained only for the orbit control, and briefly mentioned for the formation control. Simulated results are provided. Drag-free results are compared with GOCE experimental data.