Capacitive Sensing and Electrostatic Control System Design and Analysis With a Torsion Pendulum

The micro capacitive sensing and electrostatic drive control system (front-end electronics, FEE) is the core component of inertial sensor in space gravitational wave detection. The FEE requires high-precision displacement detection, high-stability electrostatic drive, and stable system control to achieve an acceleration resolution of 10⁻¹⁵ m/s²/Hz^1/2 in the low-frequency range of 0.1 mHz-1 Hz. Based on the requirements of the future Chinese space gravitational wave detection task (Taiji Program), this paper conducted key technical research of the FEE using differential capacitance detections and electrostatic drives. The structure and working principle of the FEE were also introduced. The structural parameters of the entire system, working parameters, and electrostatic control system model were provided, and the performance of the PID controller was analyzed. Finally, using the torsion pendulum to overcome the influence of gravity on the earth, the FEE multi-degree of freedom control function was verified on the vibration isolation marble platform, the measurement range and power conversion coefficient were calibrated, and the noise level under current conditions was measured. Experimental results show that the FEE developed in this paper can achieve stable control in multiple degrees of freedom, the acceleration range is larger than 10⁻³ m/s², the electric force conversion factor is <inline-formula> <tex-math notation="LaTeX">$4.8 \times 10^{-3}$ </tex-math></inline-formula> m/s²/V, and the measured acceleration resolution is <inline-formula> <tex-math notation="LaTeX">$9.6 \times 10^{-6}$ </tex-math></inline-formula> m/s²/Hz^1/2. After optimizing the sensitive structure parameters, the acceleration resolution can be estimated at <inline-formula> <tex-math notation="LaTeX">$3.3 \times 10^{-15}$ </tex-math></inline-formula> m/s²/Hz^1/2. These results satisfy the Taiji Program requirements. This paper provides a solid foundation for the future exploration of space gravitational waves in China and clears the optimization direction for the next step.