AC actuation carrier frequency optimization for cross-coupling suppression in space inertial sensor

Abstract The space inertial sensor (IS) is a critical payload in space-based gravitational wave detection missions. The test mass, serving as the gravitational reference, should be maintained at the center of its electrode housing through AC electrostatic control and drag-free attitude control. However, excessive electrostatic actuation cross-coupling between degrees of freedom can significantly deteriorate the residual acceleration performance along the sensitive axis ( x -axis). This paper investigates the influence of carrier frequency selection on the electrostatic actuation noise coupling from the ϕ -axis to the x -axis. The analysis shows that the coupling coefficient can be suppressed below 2 × 10 − 3 over the 0.1 mHz–1 Hz band by properly choosing the AC carrier frequencies. Specifically, both the sum and the difference of the carrier frequencies should be integer multiples of the desired force/torque update rate f s . Furthermore, the difference frequency should exceed 180 Hz with a deviation smaller than 0.4% to satisfy TianQin’s requirement. These conclusions are validated through a dedicated Simulink simulation platform. The proposed frequency configuration guideline offers a clear basis for AC feedback design in IS, effectively suppressing cross-coupling and enhancing low-frequency performance for future space-based gravitational wave missions.