G.Z. Yan

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 Lateral-Axis Microelectromechanical Tuning-Fork Gyroscope With Decoupled Comb Drive Operating at Atmospheric Pressure

In this paper, a silicon bulk micromachined lateral-axis tuning-fork gyroscope (TFG) with a decoupled comb drive and torsional sensing comb capacitors is presented. The novel driving comb capacitors are used to suppress the parasitic out-of-plane electrostatic force and, hence, can decouple the mechanical crosstalk from the sensing mode to the driving mode in a simple manner. The torsional sensing combs are designed to differentially sense the out-of-plane rotational moment and are arranged centroidally to be immune to fabrication imperfections for good linearity and electrostatic force balancing. The torsional sensing combs adopted in the TFG help to lower the air damping of the sensing mode while the driving mode of the gyroscope is dominated by slide-film air damping; hence, it can work even at atmospheric pressure. The process for this lateral-axis gyroscope can also be used to fabricate z-axis gyroscopes; therefore, low-cost miniature monolithic inertial measurement units can be realized without vacuum packaging. The TFG is tested at atmospheric pressure with a sensitivity of 17.8 mV/°/s and a nonlinearity of 0.6% in a full-scale range of 1000°/s. The bias stability is measured to be 0.05°/s (1 ¿) in 30 min with an equivalent noise angular rate of 0.02°/s/Hz1/2.

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

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.

An x-axis micromachined gyroscope with doubly decoupled oscillation modes

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.

Electrical coupling suppression and transient response improvement for a microgyroscope using ascending frequency drive with a 2-DOF PID controller

In this paper, we demonstrate a novel control strategy for the drive mode of a microgyroscope using ascending frequency drive (AFD) with an AGC-2DOF PID controller, which drives a resonator with a modulation signal not at the resonant frequency and senses the vibration signal at the resonant frequency, thus realizing the isolation between the actual mechanical response and electrical coupling signal. This approach holds the following three advantages: (1) it employs the AFD signal instead of the resonant frequency drive signal to excite the gyroscope in the drive direction, suppressing the electrical coupling from the drive electrode to the sense electrode; (2) it can reduce the noise at low frequency and resonant frequency by shifting flicker noise to the high-frequency part; (3) it can effectively improve the performance of the transient response of the closed-loop control with a 2-DOF (degree of freedom) PID controller compared with the conventional 1-DOF PID. The stability condition of the whole loop is investigated by utilizing the averaging and linearization method. The control approach is applied to drive a lateral tuning fork microgyroscope. Test results show good agreement with the theoretical and simulation results. The non-ideal electrical antiresonance peak is removed and the resonant peak height increases by approximately 10 dB over a 400 Hz span with a flicker noise reduction of 30 dB within 100 Hz using AFD. The percent overshoot is reduced from 36.2% (1DOF PID) to 8.95% (2DOF PID, about 75.3% overshoot suppression) with 15.3% improvement in setting time.

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

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

Decoupled Comb Capacitors for Microelectromechanical Tuning-Fork Gyroscopes

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

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.

Electrical coupling suppressing for a microgyroscope using ascending frequency drive with 2-DOF PID controller

This work demonstrates a novel control strategy for the drive mode of a MEMS gyroscope using ascending frequency drive with AGC-2DOF PID controller instead of resonant frequency drive. It can suppress the electrical coupling from the drive electrodes to the sense electrodes, reduce the low frequency noise and improve the transient response by using 2DOF PID controller. Test results indicate the electrical antiresonance peak is eliminated and the resonant peak height increases approximate 10dB over 400Hz span with a flicker noise reduction of 30dB within 100Hz. The percent overshoot is reduced from 36.2% (1DOF PID) to 8.95% (2DOF PID) with 15.3% improved in setting time. The scale factor is measured to be 5.6mv/deg/s with nonlinearity about 0.95% in the full range of 800deg/s.

Wafer-level vacuum packaging with lateral interconnections and vertical feedthroughs for microelectromechanical system gyroscopes

A wafer-level vacuum packaging based on anodic bonded glass-silicon-glass triple stack with both lateral interconnections and vertical feedthroughs is presented. A z -axis gyroscope is packaged and tested to verify the packaging process. The packaged gyroscope achieved a Q factor of 26000, increased by a factor of 30 when compared to the same gyroscope without vacuum packaging. The pressure in the packaged cavity is ∼100 Pa, and the stability of the Q factor in three months is ∼3%. Experiment results indicate that the proposed wafer-level vacuum packaging is feasible and suitable for high-performance wafer-level packaged gyroscopes.