Analysis, Measurement, and Optimization for Displacement Degree-of-Freedom Coupling of Inertial Reference Sensor Applying to Spaceborne Gravitational Wave Detection

The mechanical sensitive probe (SP) and the multiple degree-of-freedom (DOF) displacement sensing unit are two critical components of the inertial reference sensor for spaceborne gravitational wave (GW) detection. Due to the complex distribution capacitance in the SP and concurrent cross-coupling among sensing-circuit channels, the displacement DOF coupling phenomenon must happen which the test mass (TM) drifting along one DOF direction excites nonzero sensing outputs along other DOF directions. In this article, all distribution capacitances of the SP are extracted by the electrostatic field energy method, then representing the SP as an indefinite admittance matrix (IAM) network and finally modeling the multiple DOF displacement sensor as an equivalent lumped parameter circuit. A novel time–frequency dual-domain fast transient response analysis method is then proposed to quantitatively evaluate the inherent displacement DOF coupling of the displacement sensor. Through comprehensive analysis about the origin of sensing channel zero offset and field-circuit coupling, a new digital zero-offset compensation method and a cross-coupling matrix model are established. Furthermore, a hybrid network cascaded analysis technique is proposed to simultaneously solve the aforementioned inherent DOF coupling and field-circuit coupling. Finally, the experimental results from the six-DOF displacement sensor prototype demonstrate the following: for high-precision/wide-range sensing modes, sensing channel X1 exhibits $0.0107~\pm ~0.002$ V/ $0.3972~\pm ~0.009$ V zero offsets with $84.35~\pm ~0.02$ V/pF/ $1.40~\pm ~0.06$ V/pF capacitive sensing coefficients, respectively; the TM drifting along the X-axis direction causes coupling output on the $\phi $ -rotation DOF to be approximately $- 27.67~\pm ~0.4$ dB, and the carrier injection efficiency of SP is 1.65% $\pm ~0.01$ %. Additionally, a simplified SP equivalent circuit model is developed with efficiency enhancement techniques proposed.