Micromachined Vibratory Gyroscopes Controlled by a High-Order Bandpass Sigma-Delta Modulator

Abstract

Abstract-This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (61M). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass 61M's.Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude-modulated signal. Therefore, a bandpass 61M is a more appropriate control strategy for a vibratory gyroscope than a low-pass 61M. Using a high-order bandpass 61M, the control system can adopt a much lower sampling frequency compared with a low-pass 61M while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass 61M is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order 61M control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level.

A Closed-Loop Digitally Controlled MEMS Gyroscope With Unconstrained Sigma-Delta Force-Feedback

“…This way, temperature effects such as drift of the resonant frequency and the quality factor of the primary mode are neutralized. For the secondary (sense) mode the readout is based on Σ∆ force feedback [1][2][3][4][5][6][7][8]. This nearly inherently "digital" solution is fully compatible with our philosophy.…”

Design and Implementation of an Optimized Double Closed-Loop Control System for MEMS Vibratory Gyroscope

“…Embedding the sense mode of a MEMS vibratory gyroscope in a high-order sigma-delta modulator () has proven to be advantageous, in terms of increased zero bias stability, linearity and direct digital output [14][15][16][17][18][19][20][21][22]. The control loop in [14,15] used a fourth-order low-pass two electronic integrators were cascaded with the micromachined sensing element.…”

“…These aforementioned architectures are all principally low-pass electromechanical , which required a relatively high sampling frequency compared to the bandwidth of the gyroscope. Therefore, as reported in [19][20][21], the sense mode of a MEMS vibratory gyroscope lends itself to being incorporated in a band-pass force feedback control loop. The electronic integrators of a low pass modulator are replaced with electronic resonators.…”

Microgyroscope control system using a high-order band-pass continuous-time sigma-delta modulator

“…Consequently, the detection mode of a micromachined vibratory gyroscope lends itself to being incorporated in a band-pass force feedback control loop. Moreover, a control system based on a high-order M has better noise-shaping, and can be operated at relatively low sampling frequencies [11][12][13][14][15]. Continuous-time (CT) circuits are easy to be prototyped using discrete components and have very low power consumption if implemented as an ASIC [14].…”

“…Most importantly, relatively mature design techniques for band-pass analogue to digital converters (ADC) can be applied to a gyroscope detection mode force feedback control system. Therefore, a high-order band-pass M [15] is a more suitable control strategy for a vibratory gyroscope than a low-pass M.…”