Effects of both the drive- and sense-mode circuit phase delay on MEMS gyroscope performance and real-time suppression of the residual fluctuation phase error

Abstract

This work analyses circuit phase delay for carrier-modulation MEMS capacitive gyroscopes. The temperature-dependent circuit phase delay is a major source of gyroscope output drift, which deteriorates the gyroscope bias instability (BI) and angle random walk (ARW). Effects of both drive-mode and sense-mode circuit phase delay on gyroscope performance when using different signal extraction architectures are analyzed in detail. The online suppression method which combines the so-called modified double sideband (MDSB) extraction architecture in the gyroscope drive mode and closed-loop force-rebalance loop in the sense mode can eliminate the impact of residual fluctuation error of circuit phase delay in real time. When drive-mode circuit phase delay equivalently varies from −20° to 20°, using MDSB decreases the fluctuation of the open-loop zero-rate output (ZRO) by 70% compared to using double sideband (DSB) and by 99.7% with respect to using single sideband (SSB). Meanwhile, improvement for the closed-loop ZRO using MDSB is 92.48% and 94% compared to cases using DSB and SSB, respectively. Furthermore, when the equivalent circuit phase delay of the sense-mode alters from −20° to 20°, ZRO variation for the gyroscope with force rebalanced sense loop and quadrature stiffness nulling loop decreases by 80% in contrast to the case with open loop, which demonstrates the effectiveness of online suppression for circuit phase delay of both the drive-mode and sense-mode. Using the online suppression method, the gyroscope has achieved a BI of 0.16° h−1 and ARW of 0.011° (√h)−1. Furthermore, using the MDSB in the drive mode obtains the best stability compared to using the DSB and SSB as the temperature changes.

Online Compensation of Phase Delay Error Based on P-F Characteristic for MEMS Vibratory Gyroscopes

“…Sources of phase delay in the control system were demonstrated in detail in previous research [ 15 , 20 , 23 ]. Similarly, the complete loop phase delay in the control system mentioned above can be divided into , , , , , which represent the phase delay of the DAC, the analog amplifier, CV convert circuit, OPA circuit, and the digital algorithm, respectively, that is, .…”

“…A two-stage capacitor amplifier circuit as a front-end amplifier [ 22 ] was conducted in an MEMS Quadruple Mass Gyroscope to reduce the overall phase shift of the loop, which also validated that the demodulation phase has a dominant impact in zero bias drift. A modified double sideband extraction algorithm was presented based on the symmetry of double sideband modulation [ 23 ] to eliminate the disturbance of circuit phase delay in the drive mode and sense mode. Moreover, a BP Neural Network was applied to establish an accurate compensation model [ 24 ] of a demodulation phase angle by training samples of resonant frequency and quality factor, which requires a higher arithmetic capability.…”