Xiaozhu Chi

Transient response and stability of the AGC-PI closed-loop controlled MEMS vibratory gyroscopes

This paper presents a detailed study on the transient response and stability of the automatic gain control (AGC) with a proportion-integral (PI) controller for a MEMS vibratory gyroscope, which constructs a closed-loop control system to make the gyroscope achieve a constant amplitude vibration at its resonant frequency. The nonlinear mathematical model for the control system is established by applying the averaging and linearization method, which is evaluated through numerical simulations. The stability and convergence characteristics of the whole loop are investigated by using the phase plane method and Routh?Hurwitz criterion. The analysis provides a quantitative methodology for selecting the system parameters to approach stability and an optimal transient response. The negative impact induced by drift of the resonant frequency and Q-factor is also discussed. Simulation results predicted by the model are shown to be in close agreement with the experimental results carried out on a doubly decoupled bulk micromachined gyroscope. By optimizing the control parameters, the measured rising time is less than 100 ms without obvious overshoot. The setting time of the whole loop is less than 200 ms with the relative fluctuation of velocity amplitude within approximately 16 ppm for an hour. The resulting overall performance of the gyroscope is tested under atmospheric pressure. The resonant frequencies and the Q-factor of the drive mode and sense mode are 2.986 kHz, 213 and 3.199 kHz, 233, respectively. The gyroscope achieves a scale factor of 27.6 mV/deg/s with nonlinearity less than 120 ppm in the full-scale range of 800? s?1. The threshold of sensitivity is measured to be about 0.005? s?1 with noise equivalent angular rate evaluated to be 0.001?/s/Hz1/2.

A High-Resolution Silicon-on-Glass

This paper describes a high-resolution silicon-on-glass z axis gyroscope operating at atmospheric pressure. The mechanical structure is designed in such a way that it exhibits low cross coupling between drive and sense mode of less than 0.5% simulated using finite-element method and 1.35% verified by experimental measurements. Due to a symmetrically designed structure, the specified bandwidth can be maintained despite of fabrication imperfections. The fabrication process flow is based on a combination of silicon on glass bonding and deep reactive ion etching which results in a large proof mass and capacitances. A closed loop self-oscillation drive interface is used to resonate the gyroscope in the drive mode, which reaches steady-state after 150 ms. Using area-varying capacitors, large quality factors of 217 and 97 for drive and sense mode, respectively, were achieved operating at atmospheric pressure. A low drive voltage, with a 1 Vpeak-peak AC drive amplitude and 10 V DC bias was used to excite the drive mode. The measured scale factor was 10.7 mV/°/s in a range of ±300°/s with a R 2-nonlinearity of 0.12%. The noise equivalent angular rate is 0.0015°/s/Hz1/2 (=5.4°/h/Hz1/2) in a 50 Hz bandwidth. The measured SNR was 34 dB at an angular rate input signal with an amplitude of 12.5°/s and a frequency of 10 Hz. Without any active temperature control, zero bias stability of 1°/s was achieved for long-term measurements over six hours and 0.3°/s for short-term measurements over 120 seconds (1-¿).

Z

In this paper, a doubly decoupled x-axis gyroscope with novel torsional sensing comb capacitors is presented. The doubly decoupled design is more efficient to suppress mechanical coupling of gyroscope. Both driving and sensing modes of the gyroscope are dominated by slide film air damping, then it can work even at atmosphere. Moreover, the sensing capacitors adopt asymmetrical comb fingers so that they can differentially detect out-of-plane torsional movements. The fabrication process of the gyroscope is compatible with z-axis gyroscope process, which makes it potential to realize low cost monolithic MIMU (miniature inertial measurement unit) without vacuum packaging. The gyroscope was fabricated and tested. The sensitivity is 3mV/deg/s while the nonlinearity is 1.1% at atmosphere. The noise floor is 0. 1deg/s/Hz1/2.

Axis Gyroscope Operating at Atmospheric Pressure

In recent years, MEMS gyroscope which is a kind of angular-rate-sensor has been improved greatly. In this paper, the effect of temperature changing on MEMS gyroscope is analysed. An evaluation and compensation platform based on the MCU and PC software has been fabricated. The temperature tests were done and some novel compensation algorithms were presented to fit the temperature curve. The thermal bias drift of the gyroscope compensated by the platform was reduced to 0.0667deg/s/degC compared with 0.618deg/s/degC before compensation.

An x-axis micromachined gyroscope with doubly decoupled oscillation modes

In this paper, a bulk micromachined lateral axis TFG (tuning fork gyroscope) with torsional sensing comb capacitors is presented. Both driving and sensing modes of the gyroscope are dominated by slide film air damping, then it can work even at atmosphere. Novel driving comb capacitors are used to electrically decouple the mechanical coupling from sensing mode to driving mode. The process for this gyroscope is also compatible with z-axis gyroscope, which makes it potentially to realize low coast monolithic MIMU (miniature inertial measurement unit) without vacuum packaging. The TFG was fabricated and tested at atmosphere. The sensitivity is 17.8mV/°/s while the nonlinearity is 0.6%. The bias stability is 0.05°/s (1¿) and the noise floor is 0.02°/s/Hz1/2

Research on temperature dependent characteristics and compensation methods for digital gyroscope

In this paper, a highly double-decoupled selfoscillation gyroscope is presented. Deliberate frame demonstrates small cross talk between drive mode and sense mode of less than 0.5% simulated by FEM tool and 1.35% verified by experimental measurements. Tested results exhibit that the bandwidth of the structure has a good immunity to fabrication imperfections. With the deployment of area-varied capacitors and high aspect-ratio structures, large quality factors and low drive voltage are achieved operating at atmospheric pressure, which are 217 and 97 for drive mode and sense mode, respectively, with a 1Vpeak-peak AC drive voltage and 10 V DC bias. Measured scale factor is 10.7 mv/deg/s with a R2-nonlinearity of 0.12% in the range of plusmn300deg/s. The noise equivalent rate is 0.0013deg/s/Hz1/2 (=4.68deg/h/Hz1/2) over 100 Hz bandwidth. The bias stability can achieve 1deg/s for a 6-hour measurement and 0.3deg/s for 120 seconds without any temperature control method employed (1-sigma).

An Electrically Decoupled Lateral-Axis Tuning Fork Gyroscope Operating at Atmospheric Pressure

This letter presents a novel comb capacitor which can decouple the mechanical crosstalk between the sensing and driving modes of gyroscopes. The capacitance and electrostatic force of the comb capacitor are simulated and analyzed to verify the decoupling principle. A lateral-axis tuning-fork gyroscope is used successfully to demonstrate the decoupling capability of the comb capacitor, resulting in a nonlinearity of 0.6% with full scale of 1000 °/s and a bias stability of 0.05 °/s (1¿) for 30 min.

A highly double-decoupled self-oscillation gyroscope operating at atmospheric pressure

An acceleration latching switch with independent multi-contacts is presented in this paper. All the contacts and their beams are independent to the proof-mass so as to prevent the contacts from the impact resulting from the rebound or vibration of the proof mass once the switch is latched. Moreover, multiple contacts are used in order to get high reliable contact, to lower the contact resistance and to increase the maximum allowable current. The switch was fabricated by low-cost process and tested. The latching shock is 4500G and the response time is less than 0.1ms. The contact resistance is no more than 5 ohms while the isolation resistance is more than 200M ohms and the maximum allowable current is up to 100mA.

Decoupled Comb Capacitors for Microelectromechanical Tuning-Fork Gyroscopes

This paper makes an investigation on the decoupling performance for a novel lateral axis gyroscope with varying environmental parameters. The testing results show that the decoupling performance of the gyroscope depends on the environment pressure and temperature. The coupling varies from 0.05% to 0.25% with the pressure range of 150Pa to 100kPa. The characteristic of coupling with temperature is measured from 20 °C to 100 °C, which varies from 0.35% to 0.41%. With the high quality factor and small coupling, the device can worked well even at atmospheric pressure. The sensitivity and nonlinearity are 6.7mV/°/s and 0.51% with full scale of 800 °/s, respectively.

A Latching Acceleration Switch with Multi-Contacts Independent to the Proof-Mass

In this paper, a bulk micromachined z-axis single crystal silicon gyroscope is presented. The symmetrical and double decoupled structures can greatly suppress the mechanical coupling and easily realize the match of resonant frequencies between the driving mode and sensing mode. Finite element method (FEM) simulation shows that the mechanical intercoupling is less than 0.6% in orthogonal direction and 0.1% in parallel direction. Silicon on glass (SOG) process is utilized to fabricate the gyroscope, therefore large proof mass and capacitance can be achieved with an aspect ratio about 20. The resonant frequencies of driving mode and sensing mode are 4,027 Hz and 4,111 Hz, respectively, which are in good agreement with calculated values. The deviation of bandwidth from design caused by fabrication imperfection is less than 1%. Large quality factors of the working modes are obtained which are 216 and 85 at atmosphere environment, respectively, because large gap between proof mass and substrate is fabricated, and slide film air damping is designed to dominate the operation. Test results show that the scale factor of the gyroscope is 0.9 mv/deg/s in the range of plusmn250deg/s. The signal-to-noise ratio (SNR) is more than 100 at a 10 Hz angular vibration input with a 0.4deg amplitude. The noise equivalent angular rate is 0.008deg/s/Hz1/2.