Modeling and compensation of cross-axis coupling in an electrostatic accelerometer for testing the equivalence principle.

Abstract

Electrostatic accelerometers have extremely high sensitivity and are ideal scientific instruments for measuring very weak acceleration. In particular, a single-sensitive-axis electrostatic accelerometer can be used for testing the equivalence principle in space. Sensitive-axis capacitances formed by axial electrodes and a cylindrical proof mass vary with the axial motion of the mass and are also affected by radial motion, which results in cross-axis coupling disturbances. A quantitative model is built to analyze the cross-axis coupling effect on the sensitive axis from the radial suspension loop, including a nonlinear model for large radial motion and a linear model for small radial motion. Frequency response simulation shows that the cross-axis coupling effect for a small signal case arises mostly in the high-frequency range. Experiments are carried out with a ground-based electrostatic accelerometer made of a single, non-rotating test cylinder, and in this case, the experimental results are utilized to verify the mathematical model. Cross-axis coupling for small signal perturbations is virtually removed if the equilibrium position of the proof mass is calibrated to the null position of the sensor cage. In addition, data post-processing can further attenuate the cross-axis coupling disturbances when dealing with large radial motion. The cross-axis coupling disturbances on both the position and the acceleration measurement signals in the sensitive axis are mostly removed in ground-based experiments. The proposed model and compensation can be extended to space equivalence principle instruments and other electrostatic accelerometers with a cylindrical proof mass.