Longtao Lin

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

A single-crystal silicon-based lateral-axis tuning-fork gyroscope (TFG) with electrostatic force-balanced (EFB) driving and torsional z-sensing is presented. The EFB comb drive used in this TFG can efficiently suppress the mechanical coupling in a simple manner. The TFG structure is also optimized to further reduce the coupling. Moreover, the Coriolis acceleration-induced out-of-plane rotation of the sensing mode is detected by using bending springs and differential comb fingers. This z-sensing design has relatively high Q, so this gyroscope can work at atmospheric pressure. This TFG design has been fabricated and tested. Measured in air, the device demonstrates a sensitivity of 2.9 mV/°/s, a full range of 800° s−1 with a 0.9% nonlinearity and the noise floor of 0.035°/s/Hz1/2. This TFG design also has very low coupling, where the measured drive-to-sense coupling and sense-to-drive coupling are −45 dB and −51 dB, respectively.

Axis Gyroscope Operating at Atmospheric Pressure

This paper describes the design of a digital closed drive loop for a MEMS vibratory, vacuum packaged gyroscope. The displacement of the gyroscope is demodulated by the adaptive filter-least mean square (LMS) though which the amplitude and phase of the displacement are separated for respective control. The amplitude is kept constant by the automatic gain control (AGC) method with a proportion-integral (PI) controller while the phase is controlled by phase locked loop (PLL). Results of experiments carried out on field-programmed-gate-array (FPGA) with a doubly decoupled bulk gyroscope are shown to be in close agreement with simulation results. The amplitude variance of the detect signal of drive mode is 28ppm in half an hour while the phase variance is 770ppm.

A lateral-axis micromachined tuning fork gyroscope with torsional Z-sensing and electrostatic force-balanced driving

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.

Digital closed-loop control based on adaptive filter for drive mode of a MEMS gyroscope

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

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.

An Electrically Decoupled Lateral-Axis Tuning Fork 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

The electrostatic negative-stiffness behavior of vertical structures under out-of-plane motion decreases the resonant frequency and deteriorates the linearity of a lateral-axis tuning-fork gyroscope (TFG). An electrostatically isolated silicon island is proposed to suppress this behavior. The negative-stiffness behavior is observed and the effectiveness of the electrostatic isolation is experimentally verified. The nonlinearity of the TFG is reduced to 0.34% with a full range of 1,000°/s. This is a 5× improvement.

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

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.