Fig. 5: The experimental results of the frequency tracking system for dynamic low-frequency acceleration.

a The output response of the sensing oscillator for modulated low-frequency acceleration (Ω = 0.01 Hz, ∆a = 82 mg). b The tracking response of the readout oscillator under the control of FATS. The amplitude of the readout oscillator is three times that of the sensing oscillator, which means that the sensitivity of the synchronized resonant accelerometer has been enhanced threefold. The readout oscillator can perfectly track and measure the dynamic environmental acceleration. c The frequency ratio between the sensing oscillator and readout oscillator. The ratio is constant at 3 in the synchronization state. Once the sensing oscillator’s frequency exceeds the synchronization range, the control system will execute immediately and quickly reach the synchronization state again. This process will lead to ‘glitches’. d The recorded compensation voltage of the DAC in the automatic control system. The overall trend lags behind the modulated acceleration signal. e, f The detailed expression of the sensing oscillator and readout oscillator corresponding to the gray rectangular plane. g The statistical distribution of the frequency difference between the sensing oscillator and readout oscillator of dynamic testing. The mean frequency difference δf is 25.02 μHz, and the NRMSE is 18.66 ppm, which means that the automatic control system can effectively track the dynamic modulation signal with great accuracy