Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope

This paper presents microfabrication process-driven design of a multi-degree of freedom (multi-DoF) non-resonant electrostatic microelectromechanical systems (MEMS) gyroscope by considering the design constraints of commercially available low-cost and widely-used silicon-on-insulator multi-user MEMS processes (SOIMUMPs), with silicon as a structural material. The proposed design consists of a 3-DoF drive mode oscillator with the concept of addition of a collider mass which transmits energy from the drive mass to the passive sense mass. In the sense direction, 2-DoF sense mode oscillator is used to achieve dynamically-amplified displacement in the sense mass. A detailed analytical model for the dynamic response of MEMS gyroscope is presented and performance characteristics are validated through finite element method (FEM)-based simulations. The effect of operating air pressure and temperature variations on the air damping and resulting dynamic response is analyzed. The thermal stability of the design and corresponding effect on the mechanical and capacitive sensitivity, for an operating temperature range of −40 °C to 100 °C, is presented. The results showed that the proposed design is thermally stable, robust to environmental variations, and process tolerances with a wide operational bandwidth and high sensitivity. Moreover, a system-level model of the proposed gyroscope and its integration with the sensor electronics is presented to estimate the voltage sensitivity under the constraints of the readout electronic circuit.

Design of Readout Circuit with Quadrature Error and Auxiliary PLL for MEMS Vibratory Gyroscope

Traditional MEMS gyroscope readout eliminates quadrature error and relies on the phase relationship between the drive displacement and the Coriolis position to accomplish a coherent demodulation. This scheme shows some risk, especially for a mode-matching gyro. If only a slight resonant frequency deviation between the drive and sense mode occurs, a dramatic change in the phase relationship follows, which leads to a wrong demodulation. To solve this, this paper proposes a new readout based on the quadrature error and an auxiliary phase-locked loop (PLL). By tuning the phase shifter in the sense-mode circuit, letting the quadrature error and the carrier of the mixer be in 90° phase alignment, the Coriolis was simultaneously in phase with the carrier. Hence, the demodulation was accomplished. The carrier comes from the PLL output of the drive-mode circuit due to its low jitter and independence of the work mode of the gyro. Moreover, an auxiliary PLL is used to filter the quadrature error to enhance the phase alignment accuracy. Through an elaborate design, a printed circuit board was used to verify the proposed idea. The experimental results show the readout circuit functioned well. The scale factor of the gyro was 6.8 mV/°/s, and the bias instability was 204°/h.

A Design Methodology of Digital Control System for MEMS Gyroscope Based on Multi-Objective Parameter Optimization

This paper presents a novel multi-objective parameter optimization method based on the genetic algorithm (GA) and adaptive moment estimation (Adam) algorithm for the design of a closed-loop control system for the sense mode of a Microelectromechanical systems (MEMS) gyroscope. The proposed method can improve the immunity of the control system to fabrication tolerances and external noise. The design procedure starts by deriving a parameterized model of the closed-loop of the sense mode. The loop parameters are then optimized by the GA. Finally, the ensemble of optimized loop parameters is tested by Monte Carlo analysis to obtain a robust optimal solution. Simultaneously, the Adam-least mean square (LMS) demodulator, which is appropriate for the demodulation of very noisy signals, is also presented. Compared with the traditional method, the time consumption of the design process is reduced significantly. The digital control system is implemented by the print circuit board based on embedded Field Programmable Gate Array (FPGA). The experimental results show that the optimized control loop has achieved a better performance, the system bandwidth in open-loop and optimal closed-loop control system is about 23 Hz and 101 Hz, respectively. Compared to a non-optimized closed-loop system, the bias instability reduced from 0.0015°/s to 7.52 × 10−4°/s, the scale factor increased from 17.7 mV/(°/s) to 23 mV/(°/s) and the non-linearity of the scale factor reduced from 0.008452% to 0.006156%.

Design and Mechanical Sensitivity Analysis of a MEMS Tuning Fork Gyroscope with an Anchored Leverage Mechanism

This paper presents the design and analysis of a new micro-electro-mechanical system (MEMS) tuning fork gyroscope (TFG), which can effectively improve the mechanical sensitivity of the gyroscope sense-mode by the designed leverage mechanism. A micromachined TFG with an anchored leverage mechanism is designed. The dynamics and mechanical sensitivity of the design are theoretically analyzed. The improvement rate of mechanical sensitivity (IRMS) is introduced to represent the optimization effect of the new structure compared with the conventional one. The analytical solutions illustrate that the IRMS monotonically increases with increased stiffness ratio of the power arm (SRPA) but decreases with increased stiffness ratio of the resistance arm (SRRA). Therefore, three types of gyro structures with different stiffness ratios are designed. The mechanical sensitivities increased by 79.10%, 81.33% and 68.06% by theoretical calculation. Additionally, FEM simulation demonstrates that the mechanical sensitivity of the design is in accord with theoretical results. The linearity of design is analyzed, too. Consequently, the proposed new anchored leverage mechanism TFG offers a higher displacement output of sense mode to improve the mechanical sensitivity.

A Decoupling Design with T-Shape Structure for the Aluminum Nitride Gyroscope

This paper reports a novel design for the decoupling of microelectromechanical systems (MEMS) gyroscopes. The MEMS gyroscope is based on piezoelectric aluminum nitride (AlN) film, and the main structure is a mass hung by T-shape beams. A pair of parallel drive electrodes are symmetrically placed on the surface of the vertical bar for driving the oscillating mass. A serpentine sense electrode is placed on the lateral bar. When the gyroscope is oscillating in drive mode, charges with equal quantity and opposite sign will be polarized and distributed symmetrically along the lateral bar. These charges neutralize each other at the sense electrode. Therefore, no coupling signals can be detected from the sense electrode. This design can realize the decoupling between the drive mode and sense mode. In this work, the T-shape decoupled structure was designed as the key component of an AlN piezoelectric gyroscope and the whole structure was simulated by COMSOL Multiphysics 5.2a. The working principle of the decoupling is described in detail. Electrical properties were characterized by the dynamic signal analyzer. According to the test results, the drive mode and the sense mode are decoupled. The coefficient of orthogonal coupling is 1.55%.

A Digital Mode-Matching Control System Based on Feedback Calibration for a MEMS Gyroscope

A digital mode-matching control system based on feedback calibration, where two pilot tones are applied to actuate the sense mode by the robust feedback controller, is presented for a MEMS gyroscope in this paper. A dual-mass decoupled MEMS gyroscope with the integrated electrostatic frequency tuning mechanisms, the quadrature correction electrode, and the feedback electrode is adopted to implement mode-matching control. Compared with the previous mode-matching method of forward excitation calibration, the proposed mode-matching scheme based on feedback calibration has better adaptability to the variation in the frequency of calibration pilot tones and the quality factor of the sense mode. The influences of calibration pilot tone frequency and the amplitude ratio on tuning performance are studied in theory and simulation. The simulation results demonstrate that the tuning error due to the amplitude asymmetry of the sense mode increases with a frequency split between pilot tones and the drive mode and is significantly reduced by the amplitude correction technology of pilot tones. In addition, the influence of key parameters on the stability of the mode-matching system is deduced by using the average analysis method. The MATLAB simulation of the mode-matching control system illustrates that simulation results have a good consistency with theoretical analysis, which verifies the effectiveness of the closed-loop mode-matching control system. The entire mode-matching control system based on a FPGA device is implemented combined with a closed-loop self-excitation drive, closed-loop force feedback control, and quadrature error correction control. Experimental results demonstrate that the mode-matching prototype has a bias instability of 0.63°/h and ARW of 0.0056°/h1/2. Compared with the mode-mismatched MEMS gyroscope, the performances of bias instability and ARW are improved by 3.81 times and 4.20 times, respectively.

Design and Analysis of a High-Gain and Robust Multi-DOF Electro-thermally Actuated MEMS Gyroscope

This paper presents the design and analysis of a multi degree of freedom (DOF) electro-thermally actuated non-resonant MEMS gyroscope with a 3-DOF drive mode and 1-DOF sense mode system. The 3-DOF drive mode system consists of three masses coupled together using suspension beams. The 1-DOF system consists of a single mass whose motion is decoupled from the drive mode using a decoupling frame. The gyroscope is designed to be operated in the flat region between the first two resonant peaks in drive mode, thus minimizing the effect of environmental and fabrication process variations on device performance. The high gain in the flat operational region is achieved by tuning the suspension beams stiffness. A detailed analytical model, considering the dynamics of both the electro-thermal actuator and multi-mass system, is developed. A parametric optimization is carried out, considering the microfabrication process constraints of the Metal Multi-User MEMS Processes (MetalMUMPs), to achieve high gain. The stiffness of suspension beams is optimized such that the sense mode resonant frequency lies in the flat region between the first two resonant peaks in the drive mode. The results acquired through the developed analytical model are verified with the help of 3D finite element method (FEM)-based simulations. The first three resonant frequencies in the drive mode are designed to be 2.51 kHz, 3.68 kHz, and 5.77 kHz, respectively. The sense mode resonant frequency is designed to be 3.13 kHz. At an actuation voltage of 0.2 V, the dynamically amplified drive mode gain in the sense mass is obtained to be 18.6 µm. With this gain, a capacitive change of 28.11 f F and 862.13 f F is achieved corresponding to the sense mode amplitude of 0.15 μ m and 4.5 μ m at atmospheric air pressure and in a vacuum, respectively.