Bandwidth Expansion for Force-to-Rebalance Measurement of MEMS Gyroscopes Based on Equivalent Unit Negative Feedback Loop

This article focuses on the bandwidth expansion of MEMS gyroscope for force-to-rebalance (FTR) rate measurement in both nondegenerate and degenerate cases. First, the composition of the MEMS gyroscope system is introduced, and the transfer functions of the operational modes are analyzed. Second, equivalent transformation and simplification of the FTR control loop without feedthrough were performed to obtain the sense modal transfer functions for the nondegenerate and degenerate cases. Third, a unit negative feedback loop characterizing the frequency characteristics of the FTR control loop is formed based on the above transfer function, and impact factors of bandwidth are analyzed by its open-loop transfer function. Based on the above open-loop transfer function and its cutoff frequency, gain margin, and phase margin, judging criteria, and design approaches for bandwidth expansion and its elements are proposed. The bandwidth expansion element is connected in series with the FTR rate control loop to increase the cutoff frequency and ensure reasonable phase and gain margins, thus accomplishing the bandwidth expansion of the phase-lead compensated FTR rate measurement. A method for obtaining the channel gain of the FTR rate control loop is finally presented. This allows for comparisons to be made without and with bandwidth expansion for the nondegenerate and degenerate cases, respectively. The results demonstrate that bandwidth expansion cannot be achieved through the sole adjustment of proportional-integrating controller parameters. Instead, the bandwidth expansion can be accomplished by incorporating additional components by the proposed judging criteria and design approaches.