Investigation on Test Mass Capture of an Inertial Sensor via Torsion Pendulum Under Limited Electrostatic Actuation for Space-Based Gravitational Wave Detection

For space-based gravitational-wave detection, a released test mass in an inertial sensor may retain appreciable residual angular motion, while electrostatic actuation authority is finite. This work investigates single-axis test-mass capture about the suspension-wire axis using a torsion-pendulum platform integrating differential capacitive sensing, electrostatic actuation, and digital control in the same hardware loop. Capacitive-readout calibration, free-oscillation identification, and static torque-balance actuation calibration establish quantitative relations among test-mass motion, suspension dynamics, control voltage, and electrostatic torque, and characterize the nominal near-center actuation authority. At controller activation, the measured angular offset is approximately 15.6 mrad, and the estimated angular velocity is approximately 800 μrad/s. Under limited electrostatic actuation, the control output remains at or near saturation for approximately 110 s during the initial braking stage; the test mass then reverses direction, the output desaturates, and the response converges toward the housing center. The maximum angular displacement after activation is approximately 0.067 rad, with no further test-mass–electrode-housing contact observed. After approximately 550 s, the test mass enters a stable near-center region, where an out-of-loop autocollimator measures an angular RMS of 1.81 μrad. The corresponding command-equivalent electrostatic control torque has an RMS value of 2.6×10−11 N·m. These results provide a quantitative experimental characterization of single-axis test-mass capture from a large initial dynamic state under limited electrostatic actuation authority.