Towards the objective of direct angle measurement using a rate integrating gyroscope (RIG) without a minimum rate threshold and with performance limited only by electrical and mechanical thermal noise, in this paper we present the implementation of a generalized electronic feedback method for the compensation of MEMS gyroscope damping asymmetry (anisodamping) and stiffness asymmetry (anisoelasticity) on a stand-alone digital signal processing (DSP) platform. Using the new method, the precession angle-dependent bias error and minimum rate threshold, two issues identified by Lynch for a MEMS RIG [1] due to anisodamping are overcome. To minimize angle-dependent bias, we augment the electronic feedback force of the amplitude regulator with a non-unity gain output distribution matrix selected to correct for anisodamping. Using this method, we have decreased the angle-dependent bias error by a factor of 12, resulting in a minimum rate threshold of ~3 °/s. To further improve RIG performance, an electronically-induced self-precession rate is incorporated and successfully demonstrated to lower the rate threshold.

We present a demonstration of a whole-angle mode operation of a 0.6 mm single-crystal silicon disk resonator gyroscope (DRG). This device has a Q factor of ~80,000 and a resonant frequency of ~250 kHz and is fabricated in the epi-seal process. Discrete-time control algorithms for rate-integrating gyro operation were implemented based on Lynch's algorithm. Despite the fact that this DRG is over 5 orders of magnitude smaller than the 58 mm HRG, the device's error sources are shown to be accurately modeled by the basic error models developed by Lynch.

We present a 2-mm diameter, 35- $\mu $ m-thick disk resonator gyro (DRG) fabricated in silicon with integrated 0.35- $\mu $ m CMOS analog front-end circuits. The device is fabricated in the commercial InvenSense Fabrication MEMS-CMOS integrated platform, which incorporates a wafer-level vacuum seal, yielding a quality factor ( $Q$ ) of 2800 at the DRGs 78-kHz resonant frequency. After performing electrostatic tuning to enable mode-matched operation, this DRG achieves a $55~\mu $ V/°/s sensitivity. Resonator vibration in the sense and drive axes is sensed using capacitive transduction, and amplified using a low-noise, on-chip integrated circuit. This allows the DRG to achieve Brownian noise-limited performance. The angle random walk is measured to be 0.008°/s/ $\surd $ Hz and the bias instability is 20°/h.

This letter presents a micromachined silicon three-axis gyroscope based on a triple tuning-fork structure utilizing a single vibrating element. The mechanical approach proposed in this letter uses a secondary “auxiliary” mass rather than a major “proof” mass to induce motion in the proof mass frame for Coriolis force coupling to the sense mode. These auxiliary masses reduce the unwanted mechanical coupling of force and motion from the drive mode to the three sense modes. The experimental data show that the bias error due to coupling is reduced by a factor up to 10, and the bias instability of each sense axis is reduced by a factor of up to 3 when the gyroscope is actuated using the auxiliary masses rather than the major masses. The gyroscope exhibits a bias instability of 0.016°/s, 0.004°/s, and 0.043°/s for the x-, y-, and z-sense modes, respectively. Furthermore, initial temperature characterization results show that the gyroscope actuated by the auxiliary masses ensures a better bias instability performance in each sense axis over a temperature range from 10 °C to 50 °C in comparison with the gyroscope actuated by the major masses.

This paper addresses the impact of cubic nonlinearity on the operation of a rate-integrating gyroscope (RIG). It is demonstrated that below the bifurcation threshold, cubic nonlinearity results in angle-dependent frequency split between the two resonant modes of the gyroscope, which impacts angle-dependent bias, quadrature error, and controller efficacy in addition to distorting the scale factor due to off-resonant excitation. These errors are experimentally demonstrated using a high-Q disk resonator gyroscope, which are shown to be in close agreement with theory. A method of compensating for angle-dependent frequency error is proposed and experimentally validated. It is demonstrated that mode mismatch can be experimentally reduced to the level of thermal noise, effectively cancelling the effects of nonlinearity and eliminating the distortion of readout angle.