Abstract:

A drag-free satellite is an important platform for space-borne gravitational wave (GW) observation. To achieve the high-precision control of a drag-free satellite in practical engineering, an accurate dynamic model is essential. This paper presents a nonlinear model of the electrostatic effect between a satellite and a test mass (TM), and designs a model predictive controller based on the drag-free satellite model with the nonlinear electrostatic effect. To determine the analytical form of the electrostatic effect, a comprehensive theoretical analysis is performed for gravitational reference sensors (GRSs). An electrostatic force and a torque are simulated with the displacement as a varying parameter through a commercial software. Then, the results are fitted to derive the nonlinear expressions of the electrostatic effect. The model predictive controllers based on the models with the nonlinear and linear electrostatic effects are designed in the capture mode. Finally, the control results are given to show the advantages of the nonlinear electrostatic effect.

Key words: drag-free satellite, nonlinear electrostatic effect, capture mode, model predictive control (MPC)