Microelectromechanical Systems Gyroscope Research Articles

A method to improve tracking ability of drive control of MEMS gyroscopes

PurposeA high-precision gyroscope is an important tool for accurate positioning, and the amplitude stability and frequency tracking ability of the drive control system are important and necessary conditions to ensure the precision of micro-electro-mechanical systems (MEMS) gyroscopes. To improve the precision of MEMS gyroscopes, this paper proposes a method to improve the amplitude stability and frequency tracking ability of a drive control system.Design/methodology/approachA frequency tracking loop and an amplitude control loop are proposed to improve the frequency tracking ability and amplitude stability of the drive control system for a MEMS gyroscopes. The frequency tracking loop mainly includes a phase detector, a frequency detector and a loop filter. And, the amplitude control loop mainly includes an amplitude detector, a low-pass filter and an amplitude control module. The simulation studies on the frequency tracking loop, amplitude control loop and drive control system composed of these two loops are implemented. The corresponding digital drive control algorithm is realized by the Verilog hardware description language, which is downloaded to the application-specific integrated circuits (ASIC) platform to verify the performances of the proposed method.FindingsThe simulation experiments in Matlab/Simulink and tests on the ASIC platform verify that the designed drive control system can keep the amplitude stable and track the driving frequency in real time with high precision.Originality/valueThis study shows a way to design and realize a drive control system for MEMS gyroscopes to improve their tracking ability. It is helpful for improving the precision of MEMS gyroscopes.

Modelling, Simulation and Dynamic Sliding Mode Control of a MEMS Gyroscope.

An adaptive dynamic sliding mode control via a backstepping approach for a microelectro mechanical system (MEMS) vibratory z-axis gyroscope is presented in this paper. The time derivative of the control input of the dynamic sliding mode controller (DSMC) is treated as a new control variable for the augmented system which is composed of the original system and the integrator. This DSMC can transfer discontinuous terms to the first-order derivative of the control input, and effectively reduce the chattering. An adaptive dynamic sliding mode controller with the method of backstepping is derived to real-time estimate the angular velocity and the damping and stiffness coefficients and asymptotical stability of the designed systems can be guaranteed. Simulation examples are investigated to demonstrate the satisfactory performance of the proposed adaptive backstepping sliding mode control.

Navigation Grade MEMS IMU for A Satellite.

This paper presents a navigation grade micro-electromechanical system (MEMS) inertial measurement unit (IMU) that was successfully applied for the first time in the Lobster-Eye X-ray Satellite in July 2020. A six-axis MEMS gyroscope redundant configuration is adopted in the unit to improve the performance through mutual calibration of a set of two-axis gyroscopes in the same direction. In the paper, a satisfactory precision of the gyroscope is achieved by customized and self-calibration gyroscopes whose parameters are adjusted at the expense of bandwidth and dynamics. According to the in-orbit measured data, the MEMS IMU provides an outstanding precision of better than 0.02 °/h (1σ) with excellent bias instability of 0.006 °/h and angle random walk (ARW) of around 0.003 °/h1/2. It is the highest precision MEMS IMU for commercial aerospace use ever publicly reported in the world to date.

A Dual-Mass Resonant MEMS Gyroscope Design with Electrostatic Tuning for Frequency Mismatch Compensation

The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic z-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis.

A quadrature compensation method to improve the performance of the butterfly vibratory gyroscope

A simple and effective method for realizing the quadrature compensation of the butterfly vibratory gyroscope by electrostatic tuning is presented. The unique symmetrical structure of the butterfly vibratory gyroscope makes it a highly sensitive micro-electromechanical systems gyroscope. However, in the actual fabrication processes, due to the limited precision of the fabrication, the fabrication imperfections result in non-ideal geometries in the butterfly gyroscope structure, which leads to the quadrature error. The quadrature error has great influence on the performance of the butterfly vibratory gyroscope, such as the zero rate output, the detection resolution and the dynamic range. The quadrature error of the butterfly vibratory gyroscope is calculated theoretically, the influence of quadrature error on the performance of the gyroscope is analyzed, and the mathematical model of quadrature compensation is established. Therefore, the electrode structure of the butterfly vibratory gyroscope is optimized, and the design of the electrode areas of the adjusting axis is determined. Then, the experiment of quadrature compensation is carried out on the butterfly vibratory gyroscope. The experimental results show that the quadrature error can be controlled to the minimum. The feasibility of quadrature compensation in butterfly vibratory gyroscope is illustrated. According to the comparative experimental tested, the performance of the butterfly vibratory gyroscope is improved. The bias instability is reduced from 1.05°/h to 0.53°/h after suppresing the quadrature error.

A Novel Design of High Resolution MEMS Gyroscope Using Mode-Localization in Weakly Coupled Resonators

This paper presents a novel design for a high resolution microelectromechanical systems (MEMS) technology based resonant gyroscope using the mode-localization effect in weekly coupled resonators (WCRs) as a mechanism for sensing the input angular rate. The design consists of a single proof mass with two three degree-of-freedom (3-DoF) WCRs systems attached on either side. The MEMS gyroscope is designed according to the microfabrication constraints of the foundry process, silicon-on-insulator multi-user MEMS process (SOIMUMPs). The shift in the resonance frequency values, amplitude ratios of the WCRs, and amplitude ratios difference of two sets due to electrostatic stiffness perturbation, corresponding to the input angular rotation, are discussed as an output metric for the measurement of angular rate. The results show that the amplitude ratio difference as an output metric allows to achieve a linear output response and large dynamic range in comparison to the shift in the amplitude ratio and resonance frequency in 3-DoF WCRs in a single set. The dynamic range and resolution of the MEMS gyroscope in terms of maximum allowed resonators amplitude and noise floor is discussed. The proposed MEMS gyroscope design has a sensitivity of 62830 ppm/°/s based on a difference in the amplitude ratios of resonators in two 3-DoF WCRs systems and a dynamic range of ±100 °/s. The resolution of the MEMS gyroscope is 31.09 × 10-6 °/s which is significantly higher than existing MEMS gyroscopes and is comparable to traditional bulky ring laser gyroscopes. This high resolution makes the proposed MEMS gyroscope design suitable for use in applications such as earth rotation rate measurement for gyrocompassing and high precision robotics.

Improving Accuracy of Low-Cost Vehicle Attitude Estimation by Denoising MIMU Based on SSA and ICA

In this article, we develop a novel method to improve the accuracy of the low-cost vehicle attitude estimation using singular spectrum analysis (SSA) and independent component analysis (ICA). The microelectromechanical system (MEMS) accelerometers and the MEMS gyros are fused by the Kalman filtering algorithm to provide a low-cost attitude estimation. The low-frequency vibration noise and the maneuvering acceleration disturbance in the measurements of the MEMS accelerometers introduce large errors to the attitude estimation. To mitigate the low-frequency vibration noise, we propose a method based on SSA to separate the quasi-periodic components in accelerometer measurements and keep the trend remained as the true attitude measurement. SSA is effective in decomposing original signal into trend, periodic or quasi-periodic components, and thus, the low-frequency vibration noise that behaves as a quasi-periodic signal can be well separated. However, the acceleration disturbance still exists in the trend. Thus, a method based on ICA is then proposed to remove the acceleration disturbance by the aid of the turning rate measurement. The proposed method is verified with driving tests under city road and off-road conditions, showing a significant improvement of the attitude accuracy.

Vibration Characteristic Measurement Method of MEMS Gyroscopes in Vacuum, High and Low Temperature Environment and Verification of Excitation Method

A method for measuring vibration characteristics of MEMS (Micro Electro Mechanical System) is presented. This method aims to simulate a real environment where MEMS operates. At first, the method of applying high and low temperature in a vacuum environment is studied. And the excitation method applying to movable microstructures of MEMS in this environment is found. Based on the above environmental conditions, the vibration characteristics of MEMS movable microstructure are measured by micro-laser vibration measurement. The base excitation method is used to measure the vibration characteristics of MEMS movable microstructures outside the plane. ANSYS 14.0 was used for finite element simulation to verify this method. The electrostatic excitation method is used to measure the inside of the plane. The stroboscopic method is used to verify the electrostatic excitation by fitting the displacement signal of the movable microstructure and the excitation output signal. The results show that the out-of-plane first-order frequency is 11.926 kHz, and the error is 0.30% compared with the experimental results. The amplitude is 44.218 nm, and the error is 0.59%. The in-plane first-order frequency is 5715.7Hz, which achieves the requirement of design precision. Both the numerical simulation and the stroboscopic method verify the excitation method well. The effect of temperature on the natural frequency of the structure is negatively correlated. And as the temperature drops, the motion of the structure becomes increasingly violent. The findings of this study provide important guidance for maintenance, reliable operation and optimal design of MEMS.

Crow Search Algorithm for MEMS Gyroscope Temperature Drift Signal and Processing for Denoising

To solve the problem of micro‐electro‐mechanical system (MEMS) gyroscope noise, this paper presents a variational mode decomposition (VMD) method based on crow search algorithm. First, the signal was decomposed by variational mode decomposition for optimization of crow search algorithm (CSA‐VMD) method. The parameters required by the VMD method (penalty parameter α and decomposition number K) are given by the crow search algorithm, and then the signal is decomposed into the superposition of multiple subsignals, called intrinsic mode functions (IMFs). The sample entropy (SE) corresponding to each IMF is then obtained. By calculating the sample entropy, the noise signal can be divided into pure noise part, mixing part, and temperature drift part. Second, Savitzky–Golay smoothing denoising (SG) is used to filter the mixed noise signal to eliminate the influence of noise. Third, for the filtering of the drift part, the least square support vector machine optimized by the crow search algorithm (CSA‐LSSVM) was used to filter, so as to reduce the effect of temperature drift. Finally, the processed signal is reconstructed to achieve the goal of denoising. Through the results, it can be found that the optimized VMD and LSSVM using CSA algorithm can achieve more effective denoising. After using the method proposed in this paper, the angular random walk value is 1.1175 ∗ 10−4°/h/√Hz, and the bias stability is 0.0017°/h. Compared with the original signal, the two signals are optimized by 98.1% and 98.2%, respectively. It can be seen from the experimental results that the proposed CSA‐VMD method, SG method, and CSA‐LSSVM method can effectively eliminate noise effects.

Robust Observer Based on Fixed-Time Sliding Mode Control of Position/Velocity for a T-S Fuzzy MEMS Gyroscope

This study focused on a control system of the nonlinear micro-electro-mechanical systems (MEMS) gyroscope. First, sector nonlinearity was used to model a MEMS gyroscope in the Takagi-Sugeno (T-S) fuzzy system. Second, a state observer was designed based on linear matrix inequality (LMI) to identify the optimal eigenvalues of the state tracking error function. Then, full-state fixed-time sliding mode control (FTSMC) was constructed to control the system. Third, a case study of a harmonic disturbance observer was used to address the unknown disturbance of the system. A disturbance observer (DOB) was simply designed based on the error signals of the system outputs and observer outputs. The output signals precisely converged to the predefined trajectories in a very short time, with no overshoots and small of steady-state errors. Moreover, the estimated output states were precisely tracked by the system outputs. These important factors were used to confirm that the control of the T-S fuzzy MEMS was effective and easy to achieve. The study used MATLAB simulation to archive the verification. The maximum of tracking error was ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ∈ [-4.657:5.565]×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-11</sup> , and the maximum settling time was T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e3</sub> ~ 0.144 for the error of the ẏ- axis and the settling time of the ẋ- axis, respectively.

0.015 Degree-Per-Hour Honeycomb Disk Resonator Gyroscope

High performance Microelectromechanical system (MEMS) gyroscopes are in great demand in the fields of precise navigation, automatic driving and precise attitude measurement. Honeycomb disk resonator gyroscope(HDRG) which works on wineglass-modes has many advantages including higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement, showing excellent potentials to be the next-generation MEMS gyroscope with high performance and good robustness. In this paper, a new HDRG prototype is designed based on the comprehensive optimizations of resonant structure and electrode configuration. The main structure parameters and the lumped-mass configuration are optimized systematically through the finite element simulation, while the configuration and arrangement of the inner electrodes are optimized based on the vibration amplification effect, offering systematic reference for the optimizations of other MEMS gyroscopes. The new HDRG is fabricated through a SOI fabrication technique and tested with a close-loop digital circuit. Quality factor of the optimized HDRG prototype reaches 650k, proving to be a record in silicon disk resonator gyroscopes. The bias instability of the optimized gyroscope reaches 0.015°/h under room temperature without any compensation, approaching the accuracy of navigation grade. Scale factor nonlinearity reached around 120ppm in the range of ±300°/s without compensation. The comprehensive performance is at the forefront of MEMS resonant gyroscopes.

A Filtering Algorithm of MEMS Gyroscope to Resist Acoustic Interference.

To reduce the impact of acoustic interference in a microelectromechanical system (MEMS) gyroscope and to improve the reliability of output data, a filtering algorithm based on orthogonal demodulation is proposed. According to the working principle and failure mechanism of a MEMS gyroscope, the sound and angular velocity frequencies are not identical, which lead to a different frequency signal output of the original single-channel demodulation scheme. Therefore, a Q channel demodulation filtering process was added to the origin single-channel demodulation scheme. For the Q channel demodulated signal, a Hilbert transform was used to compensate for the 90 degree phase shift. The IQ dual-channel difference can remove the acoustic interference signal. The simulation results indicate that the scheme can effectively suppress the acoustic interference signal and it can eliminate more than 95% of the impact of sound waves. We assembled the acoustic interference experimental platform, collected the driving and sensing data, and verified the denoising performance with our algorithm, which eliminated more than 70% of the noise signal. The simulation and experimental results demonstrate that the scheme can eliminate acoustic interference signal without destroying angular velocity signal.

A MEMS gyroscope high-order calibration method for highly dynamic environments

In a highly dynamic environment, a Micro Electro Mechanical Systems (MEMS) gyroscope becomes inaccurate after being calibrated using the traditional calibration methods. In this paper, a high-order calibration method for MEMS gyroscopes is proposed. The effects of a highly dynamic environment on gyroscope outputs are analyzed, and a high-order calibration model of the gyroscope is established according to a nonlinear relationship between the measured value and the real value of the gyroscope. An improved generalized recursive least squares (IGRLSs) algorithm is developed to solve the high-order calibration model, and an adaptive forgetting factor is introduced to correct the algorithm update capability. Compared with traditional gyroscope calibration methods, the proposed method solves the problem of data saturation and colored noise, and provides an unbiased and consistent parameter estimation. The results of calibration experiments show that the gyroscope calibration precision of the x-axis (roll axis) and the z-axis (yaw axis) are effectively increased by more than 58.30% and 19.14%, respectively.

In-Run Scale Factor Compensation for MEMS Gyroscope Without Calibration and Fitting

This paper presents an in-run scale factor error compensation for the micro-electro-mechanical system (MEMS) gyroscope without system calibration and data fitting. The causes of three scale factor errors (instability, nonlinearity, and asymmetry) are analyzed. Next, the instability and nonlinearity by open-loop detection (Mode I), and closed-loop detection (Mode II) are discussed according to the specific comb capacitance and the front-end detection circuit. The closed-loop detection transfer function is studied, and a series of equivalent conversions are performed to obtain a method (Mode III) for improving the temperature stability of scale factor. The results of the experiment indicated that the nonlinearity and asymmetry of the Mode II and Mode III are increased by 1.8 times and 3.5 times than that of Mode I. Furthermore, the instability of Mode II and Mode III is reduced by 10 times and 19 times over -20°C to 40°C. Besides, the mode III does not affect the static and dynamic performance of gyroscope according to the test results of bias and bandwidth.

Denoising Method of MEMS Gyroscope Based on Interval Empirical Mode Decomposition

The microelectromechanical system (MEMS) gyroscope has low measurement accuracy and large output noise; the useful signal is often submerged in the noise. A new denoising method of interval empirical mode decomposition (IEMD) is proposed. Firstly, the traditional EMD algorithm is used to decompose the signal into a finite number of intrinsic mode functions (IMFs). Based on the Bhattacharyya distance analysis and the characteristics of the autocorrelation function, a screening mechanism is proposed to divide IMFs into three categories: noise IMFs, mixed IMFs, and signal IMFs. Then, the traditional modelling filtering method is used to filter the mixed IMFs. Finally, the mixed IMFs after modelling and filtering and signal IMFs are reconstructed to obtain the denoised signal. In the experimental analysis, the static denoising experiment of the turntable, the Allan variance analysis, dynamic denoising experiment, and vehicle experiment are set up in this paper, which fully proves that the method has obvious advantages in denoising and greatly improves the quality of signal and the accuracy of the inertial navigation system solution.

Sensitivity Analysis of Single-Drive, 3-axis MEMS Gyroscope Using COMSOL Multiphysics.

In this paper, a COMSOL Multiphysics-based methodology is presented for evaluation of the microelectromechanical systems (MEMS) gyroscope. The established finite element analysis (FEA) model was successfully validated through a comparison with analytical and Matlab/Simulink analysis results. A simplified single-drive, 3-axis MEMS gyroscope was analyzed using a mode split approach, having a drive resonant frequency of 24,918 Hz, with the x-sense, y-sense, and z-sense being 25,625, 25,886, and 25,806 Hz, respectively. Drive-mode analysis was carried out and a maximum drive-displacement of 4.0 μm was computed for a 0.378 μN harmonic drive force. Mechanical sensitivity was computed at 2000 degrees per second (dps) input angular rate while the scale factor for roll, pitch, and yaw was computed to be 0.014, 0.011, and 0.013 nm/dps, respectively.

Gyrocardiography: A Review of the Definition, History, Waveform Description, and Applications.

Gyrocardiography (GCG) is a non-invasive technique of analyzing cardiac vibrations by a MEMS (microelectromechanical system) gyroscope placed on a chest wall. Although its history is short in comparison with seismocardiography (SCG) and electrocardiography (ECG), GCG becomes a technique which may provide additional insight into the mechanical aspects of the cardiac cycle. In this review, we describe the summary of the history, definition, measurements, waveform description and applications of gyrocardiography. The review was conducted on about 55 works analyzed between November 2016 and September 2020. The aim of this literature review was to summarize the current state of knowledge in gyrocardiography, especially the definition, waveform description, the physiological and physical sources of the signal and its applications. Based on the analyzed works, we present the definition of GCG as a technique for registration and analysis of rotational component of local cardiac vibrations, waveform annotation, several applications of the gyrocardiography, including, heart rate estimation, heart rate variability analysis, hemodynamics analysis, and classification of various cardiac diseases.

Random Error Reduction Algorithms for MEMS Inertial Sensor Accuracy Improvement-A Review.

Research and industrial studies have indicated that small size, low cost, high precision, and ease of integration are vital features that characterize microelectromechanical systems (MEMS) inertial sensors for mass production and diverse applications. In recent times, sensors like MEMS accelerometers and MEMS gyroscopes have been sought in an increased application range such as medical devices for health care to defense and military weapons. An important limitation of MEMS inertial sensors is repeatedly documented as the ease of being influenced by environmental noise from random sources, along with mechanical and electronic artifacts in the underlying systems, and other random noise. Thus, random error processing is essential for proper elimination of artifact signals and improvement of the accuracy and reliability from such sensors. In this paper, a systematic review is carried out by investigating different random error signal processing models that have been recently developed for MEMS inertial sensor precision improvement. For this purpose, an in-depth literature search was performed on several databases viz., Web of Science, IEEE Xplore, Science Direct, and Association for Computing Machinery Digital Library. Forty-nine representative papers that focused on the processing of signals from MEMS accelerometers, MEMS gyroscopes, and MEMS inertial measuring units, published in journal or conference formats, and indexed on the databases within the last 10 years, were downloaded and carefully reviewed. From this literature overview, 30 mainstream algorithms were extracted and categorized into seven groups, which were analyzed to present the contributions, strengths, and weaknesses of the literature. Additionally, a summary of the models developed in the studies was presented, along with their working principles viz., application domain, and the conclusions made in the studies. Finally, the development trend of MEMS inertial sensor technology and its application prospects were presented.

Influence of fabrication tolerances on performance characteristics of a MEMS gyroscope

Fabrication of high aspect ratio microelectromechanical systems (MEMS) like comb drive structures are mostly done by DRIE (Deep Reactive Ion Etching) process. Bosch process is a type of DRIE which involves alternate repetition of plasma etching and side wall passivation to achieve deep vertical structures. A continued plasma etching may lead to tapered wall due to some lateral etching. Although, a straight and smooth wall is expected due to combined alternate processes of etching and passivation, very often the resulting walls are having surface undulations called as scalloping. So, due to slanting, scalloping and combined slanting and scalloping defects the working and performance of a MEMS device get affected. MEMS gyrocope is one such widely comercialized device, which is required to measure angular rotation wth certain accuracy. We take a simple single-axis MEMS vibratory gyroscope to study the effect on these defects on its dynamics performance. The study presented in the paper may be useful for including undesirable effects in designing MEMS vibratory gyroscopes.

High-sensitivity tunneling magneto-resistive micro-gyroscope with immunity to external magnetic interference

Micro-electro-mechanical system (MEMS) gyroscopes have numerous potential applications including guidance, robotics, tactical-grade navigation, and automotive applications fields. The methods with ability of the weak Coriolis force detection are critical for MEMS gyroscopes. In this paper, we presented a design of MEMS gyroscope based on the tunneling magneto-resistance effect with higher detection sensitivity. Of all these designed parameters, the structural, magnetic field, and magneto-resistance sensitivity values reach to 21.6 nm/°/s, 0.0023 Oe/nm, and 29.5 mV/Oe, thus, with total sensitivity of 1.47 mV/°/s. Multi-bridge circuit method is employed to suppress external magnetic interference and avoid the integration error of the TMR devices effectively. The proposed tunneling magneto-resistive micro-gyroscope shows a possibility to make an inertial grade MEMS gyroscope in the future.