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This paper proposes a novel robust design method for the sense mode of a MEMS vibratory gyroscope based on fuzzy reliability and Taguchi design. The principles of fuzzy reliability and Taguchi design are both introduced and described in detail. Experimental results demonstrate that the signal to noise ratio of the robust design scheme is better than those of the other experimental schemes. Over the full temperature range from −40 to 80°C, the temperature sensitivities of phase margin, gain margin, sensitivity margin, the maximum amplitude of open loop system, bandwidth of closed loop system, and the performance function of the robust design system are all smaller than those of the original design system. Meanwhile, the temperature sensitivity of the bandwidth of the robust design system is improved to 126 from 1075 ppm/°C. Moreover, the bias drift over the full temperature range of the robust design system is improved to 61°/h from 179°/h.

This paper analyzes the influence of the electrical coupling among interconnection lines in MEMS gyroscopes and proposes strategies during designing structure to eliminate its effect. Moreover, a compensation circuit is designed to further suppress coupling signal at the readout. The results of bias drift tests under full temperature range indicate that not only the bias drift in the vacuum is much smaller than at atmospheric pressure, but also the coupling signal can be decayed efficiently after compensation. The fluctuation of the bias drift is decreased by 95.5% at atmospheric pressure while 89.1% in the vacuum.

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 highly reliable contact, to lower the contact resistance and to increase the maximum allowable current. The switch was fabricated by low-cost two-mask silicon on glass process and tested. The latching shock is 4500G and the response time is less than 0.1 ms. The contact resistance is no more than 5 Ω while the isolation resistance is more than 200 MΩ and the maximum allowable current is up to 100 mA.

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, therefore, it can work even at atmospheric pressure. 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 22 mV/°/s while the nonlinearity is 2.19% at atmosphere. The noise floor is 0.02°/s/Hz1/2.

In this paper, a micromachined differential resonant accelerometer with electrostatic stiffness tuning is presented. The ring-down measurement is used for the first time to pick-up the real-time resonant frequencies of the accelerometer, which is more robust to device parameter variations and parasitic capacitances compared with the self-sustained oscillation based read-out. The total output drift over the temperature range of 120 °C for a single resonator and differential ones are 40.9 Hz and 1.0 Hz respectively, indicating a self-calibration capability of the differential configuration.

This letter reports an acceleration latching switch with integrated normally on/off paths. The normally on path, formed by notched beams connected in series, will be broken and latched to reach the open state when the acceleration exceeds the threshold. A multicontact is adopted for the normally off path, while both paths are mechanically separated from the proof mass to prevent them from the impact of the proof mass at the latched state. Experimental results show that the latching shock is 10 000 G, and the response time is about 0.1 ms. The normally on path has an on-state resistance of 4.0 ? and an allowable current of 200 mA, whereas the normally off path has an on-state resistance of 3.8 ? and a maximum current of 140 mA.

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.

This paper presents a micromachined vibrating wheel gyroscope with folded driving beams, which can improve the linearity and temperature stability of the gyroscope. The angular comb drives on the outer frame are used for large driving displacement, while the gap-changing comb capacitors on the inner frame are used for sensing the displacement with high sensitivity. The experimental results show that the scale factor and nonlinearity are 4.2 mV/°/s and 0.08% with the measurement range of ±500 °/s. The short term bias instability is evaluated to be about 34.1 °/h.

This paper describes a control procedure for the startup of a digital MEMS gyroscope system. Unlike the normal operating mode in which the gyroscope is actuated by synthesized sinusoidal drive signal, self-resonance of the gyroscope is stimulated by feeding back the drive-sense signal and converting it to a square-wave drive signal. During this procedure the resonant frequency that is near the natural frequency of the gyroscope can be calculated, and then provides a key parameter for the sinusoidal wave synthesizer, which will generate high-quality reference signals for driving and demodulation. Experiment shows a rapid rising of the magnitude of vibration, resulting a faster startup procedure for the system.

In this paper, we present the fabrication and testing of a novel probe for micromechanical surface profiler with double-ended tuning forks (DETFs) resonator as the displacement-sensing element. The probe is fabricated through the standard silicon-on-glass process developed by Peking University. The frequency variation of the DETF caused by the induced axial stress is directly proportional to the input displacement. Two stages micro-leverage mechanisms are introduced for force amplification to increase the overall sensitivity. The experimental results indicate the device has a nominal resonant frequency of 54.5 kHz under atmosphere at room temperature and the overall sensitivity is approximately 359.7 Hz/µm, which shows a good agreement with the simulation value of 330 Hz/µm using ANSYS™. Furthermore, the testing results depict the variation of frequency is linear to the displacement load within the range of 10µm.

The device described in this paper is a threshold acceleration switch which has been designed and fabricated base on bulk micromachining technology. It mainly consists of four parts: A suspended proof mass serves as the moveable electrode, which sense the acceleration loaded; two symmetrical “L-shape” beams provide the function of latching, which is easy to latch and hard to release; the center contact, which is the latch point; the top anchor is to make the contact more reliable, what's more, the cylinder contact can help improve the bad contacting effect due to imperfect fabrication. The packaged switches were tested by the drop table system. The measured minimum response shock is 3600g and the latching shock is 4800g and the response time is about 0.1 ms. The insulation resistance is more than 200M ohms and the on-state resistance is no more than 3.5 ohms.

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.

In this paper, a bulk micromachined lateral-axis TFG (tuning fork gyroscope) with improved architecture and combined mechanism sensing capacitors is reported. The combined sensing capacitors make the TFG have high sensitivity and good linearity even under wide input range and fabrication imperfection. Moreover, the decoupled comb drive, together with the improved architecture, can efficiently decouple the mode coupling. At atmospheric pressure, the TFG has a sensitivity of 0.1126mV/°/s even with unity gain. The nonlinearity is 0.7% with an input range of up to 1000°/s.

An acceleration latching switch with integrated normally Open/Close paths is presented in this paper. Two arch trusses used as fracture parts of the normally-close path are connected in series to form the normally close path, which will be broken and latched by the latching mechanism to reach the open state once the input acceleration beyond threshold. Moreover, the normally-open path is consisted of multi-contact and both paths are mechanically separated from the proof mass to prevent them from the impact resulted from the vibration of the proof mass at the latched state. The switch was fabricated by a two-mask silicon-on-glass process and tested. The latching shock is 1 5000G and the response time is about 0.1ms. The normally-close path has a resistance of 4Ω and a maximum current of 100mA while the normally-open path has a contact resistance of no more than 3.7Ω and the safe applied current is up to 140mA.

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-?).

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.

This paper describes a system for digital signal processing to control vibrating gyroscopes which will allow more flexibility and increase performance through a reduction in electronics noise. A close-loop control method based on quadrature demodulation (QD) is presented. Improvements in signal demodulation, noise suppression, phase shift and direct digital frequency synthesizer (DDS) are also proposed. The whole open-loop system is implemented on a FPGA (Field Programmable Gate Array) platform and tested. The resulting scale factor and nonlinearity are 7.1mV/°/s and 0.55% respectively with the full scale of 400°/s.

A latching acceleration switch with cylindrical contacts is presented in this paper. The cylindrical contacts can make the switch immune to the fabrication imperfection and off sensitive axis shocks, as well as decrease the contact resistance. Moreover, all the contacts and their beams are separated from 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. The switch was fabricated by low-cost process and tested. The measured latching shock is 4500G and the response time is less than 0.1ms. The total on-resistance is less than 3 ohms while the insulation resistance is more than 200M ohms and the maximum allowable current is up to 130mA.

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.

In this paper, a doubly decoupled vibrating wheel gyroscope with novel torsional sensing comb capacitors is presented. The doubly decoupled design and symmetrical structure can efficiently suppress the mechanical coupling of the gyroscope. Moreover, the symmetrically distributed proof masses make it immune from the linear accelerations. Both driving and sensing modes of the gyroscope are dominated by slide film air damping, so it can work even at atmospheric environment. The process for this gyroscope is also compatible with z-axis gyroscope, which makes it potential to realize low cost monolithic MIMU (miniature inertial measurement unit) without vacuum packaging. The gyroscope was fabricated and tested at atmosphere. The sensitivity is 3.1mV/o/s while the nonlinearity is 7.68‰ with the full scale of 900o/s. The noise floor is 0.45o/s/Hz1/2.

A decoupled lateral-axis TFG (tuning fork gyroscope) with novel driving and sensing combs is presented. The EFBD (electrostatic force balanced comb driver) adopted in the TFG can efficiently suppress the mechanical coupling in a simple manner. The structure of the gyroscope is also optimized to suppress the coupling further. Moreover, torsional sensing combs are adopted to detect the out-of-plane movement, so it can work at atmospheric pressure. The TFG was fabricated and tested at atmosphere. The measured CFDTS (coupling from driving mode to sensing mode) and CFSTD (coupling from sensing mode to driving mode) are −45dB and −51dB respectively. The sensitivity is 2.9mV/°/s while the nonlinearity is 0.9% with the full scale of 800°/s. The noise floor is 0.035°/s/Hz.

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

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.

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.

This paper proposed an effective method to test some key parameters of the micro-machined gyroscope at low ambient pressure condition including quality factor, amplitude of the drive signal, bandwidth and scale factor. The results demonstrated that the best working pressure must confine some pressure range.

A single-crystal silicon probe for micromechanical surface profilers is presented, which uses a double-ended tuning fork (DETF) resonator as the displacement-sensing element. In addition, a two-stage micro-leverage mechanism for force amplification is introduced to increase the overall sensitivity. The frequency shift of the DETF caused by the induced axial stress is directly proportional to the displacement input. The probe was fabricated through a standard silicon-on-glass process, which can realise high aspect ratio single-crystal silicon structures. The experimental results indicated that the probe had a nominal resonant frequency of 54.5 kHz under atmosphere at room temperature. The scale factor and linearity of the probe with the input range of 0–10 µm were evaluated to be 359.7 Hz/µm and 6.3%, respectively. The measured scale factor shows good agreement with the simulated value of 330 Hz/µm using ANSYSTM.

A microelectromechanical systems acceleration latching switch with cylindrical contacts and an easy-latching/difficult-releasing (ELDR) latching mechanism is presented in this paper. The cylindrical contacts can make the switch immune to fabrication imperfections and off-axis shocks and can decrease the contact resistance as well. The ELDR latching mechanism can latch the switch reliably. Moreover, all the contacts and their support beams are separated from the proof mass so as to prevent the contacts from opening due to the impact resulting from the rebound or vibration of the proof mass once the switch is latched. The switch has been fabricated by a two-mask silicon-on-glass process and tested. The measured latching shock is over 4600 g and the response time is less than 0.2 ms. The total on-resistance is less than 3 Ω while the insulation resistance is more than 100 GΩ and the maximum allowable current is up to 130 mA.

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.

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.