The force-balanced accelerometer (FBA), unlike other types of sensors, incorporates a closed-loop control. The efficacy of the system is contingent not solely on the hardware, but more critically on the formulation of the control algorithm. Conventional control strategies are usually designed for the purpose of response minimization of the sensitive elements, which limits the measurement accuracy and applicable frequency bandwidth of FBAs. In this paper, based on the model predictive control (MPC), a control algorithm of a force-balance accelerometer considering time delay is designed. The variable augmentation method is proposed to convert the force-balance control into an easy-handed measurement error minimization control problem. The discretization method is applied to deal with the time delay problem in the closed loop. The control algorithm is integrated into a practical FBA. The effectiveness of the proposed control is demonstrated through experiments conducted in an ultra-quiet chamber, as well as simulations. The results show that the closed loop in the FBA has a time delay 10 times of the control period, and, utilizing the proposed control, the acceleration signals can be accurately measured with a frequency range larger than 500 Hz. Meanwhile, the vibration response of the sensitive element of the controlled FBA is maintained at the level of microns, which guarantees a large measurement range of the FBA.
Keywords: force-balance sensing; optimal control; time delay; vibration response.