A systematic approach for precision electrostatic mode tuning of a MEMS gyroscope

Abstract

In this paper a systematic approach to precision electrostatic frequency tuning of the operational modes of a MEMS ring vibratory gyroscope is presented. In both rate and rate integrating gyroscopes the frequency split between the two modes of vibration which detect the Coriolis acceleration is one of the principal factors in determining the sensitivity and noise floor of the sensor. In high precision applications in the defence/aerospace sector a frequency split of the order of 10 mHz or less is highly desirable. In the ground-breaking Hemispherical Resonator Gyroscope (HRG) electrostatic tuning has been employed as a tuning mechanism. However, a description of the procedure is not available in the literature. The tuning scheme described here involves assessing mode mistuning by the ratio of the in-phase and quadrature components of the response to an external force that has similar properties to the gyroscopic force resulting from Coriolis action, and choosing the tuning voltages so that independent modification of the elements of the system stiffness matrix can be achieved. Experiments on a commercially available gyroscope with a natural frequency of 14 kHz show that the frequency split can be reduced from 1.5 Hz to 6 mHz. This represents a frequency precision of better than 1 part in a million.

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force

“…Neglecting the influence of centrifugal force and angular acceleration, a simplified equation of motion for the plane bending vibration of n = 2 operating mode can be established as a generalized two-dimensional oscillator with mass, damping and stiffness defects. The motion Equation of the non-ideal DRG is described as [19,20,40,41] [M]P + (…”

“…Anti-angle term (coupling term) of frequency matrix can be eliminated by using γ 12 alone in Equation (16), which means that the voltage difference applied to the quadrature control electrodes can electrostatically correct the quadrature coupling so that the two modal principal axes of the working mode are aligned with each corresponding excitation electrode. Besides, it can also be seen from Equations (20) and (21) that in order to achieve mode-matching, the quadrature error of the DRG must be restrained first. Otherwise, the frequency split cannot be eliminated.…”

“…Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 • /h to 2.8331 • /h, and the Angle Random Walk (ARW) decreases from 1.0208 • / √ h to 0.0524 • / √ h. Compared with the mode mismatch condition, the ARW is improved by 19.48 times.Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed.…”

“…Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed.…”

A mode-matched force-rebalance control for a MEMS vibratory gyroscope

“…Mode alignment and frequency matching are often implemented and verified open loop. Using this approach results in mode matching to the order of mHz [5] [6] [7]. A disadvantage of this open loop approach is that the mode matched state is not independent of the external rate.…”