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This paper demonstrates the developments toward a high performance monolithic wheeled structure horizontal dual-axis (pitch (X-axis) and roll (Y-axis)) microelectromechanical system (MEMS) gyroscope based on off-plane coupling suppression silicon gratings. Gyroscopes have been fabricated with a silicon-on-glass fabrication process with vacuum-sealed in a metal packaging. The featured gyroscope operates in split-mode with the bandwidths of two axes devices both ~70Hz. By unitizing two individual active restraining control loops that adjust the quadrature amplitude via differentially biasing the silicon gratings in real-time, the off-plane mechanical couplings of the two sense modes are significantly reduced by ~95 and ~30 times, which enables ~25-fold and ~56-fold improvements in the bias instability for a typical dual-axis device. Tactical-grade performances are achieved for both the X-axis and Y-axis gyroscopes with angle random walk (ARW) of 0.02 deg/h and 0.045 deg/h along with in-run bias instability (BI) of 0.26 deg/h and 0.65 deg/h respectively without any temperature compensation. The current preliminary results show great potential to achieve navigation grade precision by employing the mode-matching technique in the future. The use of silicon gratings for out-of-plane coupling reduction also provides an effective way to build a high performance planar monolithic chip inertial measurement unit (IMU).

In this paper, we propose a radially pleated disk resonator for gyroscopic application. The structure is made up of concentrically nested radially pleated rings that are interconnected by straight spokes, which has the potential to provide higher thermo-elastic quality factor and larger vibration amplitude. Decaying time constant of 31 s is experimentally obtained at resonant frequency of 3 kHz. A frequency-tuning model is proposed and verified, based on which, the frequency-tuning characters of the radially pleated disk resonator are thoroughly investigated. The Coriolis coupling factor κ of the radially pleated disk resonator is precisely measured by constructing a concise quadrature frequency-modulation operation, which gives the values of κ = 0.7687 and agrees well with the calculated value of 0.7768. This work provides a new strategy for designing high performance MEMS gyroscope structure, and gives a good template for gyroscopic resonator characterization. [2021-0096]

This article proposes a serial-parallel estimation model (SPEM)-based sliding mode control (SMC) of MEMS gyroscope. For the system nonlinearity, the linear-in-parameterized dynamics are formulated and the updating law of the parameter vector is given. For the system uncertainty, the radial basis function (RBF) neural network (NN) is utilized. To improve the approximation accuracy of the compound nonlinearity, the updating laws of the parameter vector and RBF NN weight are constructed by the tracking error and the filtered modeling error derived from SPEM. Furthermore, the fast terminal (FT) SMC is employed to achieve finite-time convergence. The simulation results show that the proposed controller obtains higher tracking accuracy and faster convergence, while the compound nonlinearity approximation is with higher precision.

We propose a MEMS gyroscope system working with a fixed resonance frequency which combines resonant constant-frequency (RCF) driving and real-time automatic mode-matching technique with the help of linear tuning triangular capacitors. The special tuning capacitors are implemented in both the gyroscope drive mode and sense mode as drive-mode frequency-tuning (DFT) and sense-mode frequency-tuning (SFT), respectively. RCF assures that the drive-mode equivalent resonance frequency after tuned can keep with the given constant excitation frequency, while real-time automatic mode-matching further eliminates mismatches between the drive-mode and sense-mode equivalent resonance frequencies. As a result, the gyroscope system achieves constancy and equality of the excitation frequency and two modal resonance frequencies. Performance evaluations show that the gyroscope with the sense mode quality factor of 26.7k reaches bias instability of 0.09°/h and angle random walk of 0.0087°/ $\surd \text{h}$ under room temperature without any compensation, and is capable of detecting an angular rate as low as 0.001°/s.

10.1119/10.0005889.1The toppling motion of a uniform rectangular block is investigated as a function of the friction between its pivot edge and the horizontal surface on which it rests. Initially, the edge of the block remains stationary, but it inevitably slips before the block lands. The inclination angle at which slipping occurs and the direction of slip depend on the coefficient of static friction. The toppling motion of a granite block was monitored at 400 Hz with MEMs gyro/accelerometers at the center of mass and at the pivot edge, as well as by “Tracker” analysis of video recorded at 240 fps.

This article investigates a neurodynamic quantized control problem with improved transient performances for microelectromechanical system (MEMS) gyroscopes subject to lumped disturbances induced by parameter uncertainties, dynamic coupling, and external disturbances. First, a modified prescribed performance control mechanism based on a hyperbolic cosecant performance function is proposed to specify the transient behavior of tracking errors with an arbitrarily small overshoot. Then, to eliminate the lumped disturbances with a better identification property, a novel echo state network approximator that uses the estimation error to learn neural weights is designed with the aid of a minimal learning parameter technique, which not only can exclude the poor transient behaviors occurring extensively in the existing neural control with a large adaptive gain, but also dramatically reduce the number of parameters to be updated online. Furthermore, contrasting to the available tracking results assuming a continuous control updating, a hysteresis quantizer is introduced to provide discrete values of control signals, supporting the use of digital devices in MEMS gyroscope implementations to realize a closed-loop error stabilization. Finally, ultimately uniformly bounded stability of closed-loop system is proved with the aid of Lyapunov function and nonsmooth analysis technique, while not only simulations but also experimental results are performed to validate the effectiveness of the proposed scheme.

A z-axis decoupled multi-frame vibration MEMS gyroscope (DMFVMG) is presented in this paper. Firstly, the decoupled principle is employed and the sense frame, Coriolis frame and drive frame are arranged through inner fame, intermediate frame and outer frame, and the movement characteristic analysis indicates that the structure is fully decoupled. The structure is simulated through mode analysis, harmonic response and drop shock response. The simulation results show that the resonant frequencies of the Sense Mode and Drive Mode are 10094Hz and 10162Hz, and the maximum deformation and stress with the shock analysis is 7.14 $\mu {\mathrm{ m}}$ and 235.19MPa (among three different directions). Then, the structure is fabricated through MEMS processing, and P-type single-crystalline silicon wafer and 7740 glass wafer are used. After that, the structure is packaged in a ceramic vacuum tube shell and the resonant frequencies and quality values of the sense and drive mode are 10354.21Hz and 5364, 10438.23Hz and 5219, the error between fabrication and simulation is 2.58% and 2.72%. And the monitoring system of DMFVMG prototype is established by analog circuit with drive closed-loop and sense open-loop. Then, the DMFVMG prototype is tested through turntable, and the range, scale factor and intercept are ±300°/s, −19.06mV/°/s and 95.43mV respectively. Finally, five repeated bias tests are arranged and the angular random walking values and bias stability are 0.2408°/ $\surd \text{h}$ , 0.2358°/ $\surd \text{h}$ , 0.2413°/ $\surd \text{h}$ , 0.2397°/ $\surd \text{h}$ and 0.2480°/ $\surd \text{h}$ , 2.858°/h, 3.159°/h, 3.428°/h, 1.891°/h and 3.467°/h respectively.

In this paper, the usability of the classical Harmonic Balancing method (cHB) to calculate the weakly nonlinear motion of phase- and amplitude controlled MEMS resonators is demonstrated. A polynomial mechanical stiffness description and linearized electrostatic effects are considered, which allow determining the Jacobian analytically. The effects of amplitude and phase control are taken into account by applying boundary conditions in the iteration process. With a customized cHB, it is possible to efficiently simulate the behavior of a MEMS gyroscope undergoing nonlinear resonance with higher parasitic modes. The presented results of a virtual model compare very well with solutions obtained with the Shooting method. Furthermore, we compare the measurement of a drive frequency discontinuity, taken from a different prototype, with the prediction from our linear extrapolated model and from a model with artificially fitted parameters. The cHB approach yields an order of magnitude speed-up in comparison to the transient simulation method. Besides some restrictions, customized cHB methods are interesting candidates for fast system-type simulation considering the MEMS-ASIC interface. [2021-0028]

In this paper, a fuzzy wavelet neural control scheme with improved prescribed performance is investigated for micro-electro-mechanical system (MEMS) gyroscope in the presence of uncertainties and input quantization. A hysteresis quantizer (HQ) is introduced in the controller design to generate input signal in a finite set, which can greatly reduce the actuator bandwidth without decreasing the control accuracy, and avoid the undesirable chattering occurring universally in other quantizers. To guarantee the output tracking with better prescribed transient behavior, a modified prescribed performance control (MPPC) consisting of asymmetric performance boundaries and an error transformation function is explored, such that arbitrarily small overshoot can be assured without retuning design parameters. Unlike the traditional neural network that suffers from explosion of learning, a fuzzy wavelet neural network (FWNN) based on minimal-learning-parameter (MLP) is designed to identify uncertainties with slight computational burden. A robust quantized control scheme is synthesized to compensate for quantization error and achieve prescribed ultimately uniformly bounded (UUB) tracking. Finally, extensive simulations are presented to verify the effectiveness of proposed control scheme.

The output values Gyroscope measures will contain Bias, so errors gradually accumulate. Considering this point, a study on multi-sensors was conducted. An analysis of Gyroscope noise characteristics was carried out, and the modeling for Kalman Filter was performed based on the analysis. Afterwards, data values were extracted and analyzed through an experiment. Gyroscope’s Angle Random Walk and Rate Random Walk were derived using Allan Variance, and based on this, Kalman Filter covariance matrix was formed. Data reception algorithms were constructed using Matlab Simulink, and an experiment was conducted using MicroLabBox and Rate Table. The final research objective is to apply the results of this study to 2-Axis Small Gimbal to improve stabilization precision.

Purpose To reduce the influence of temperature on MEMS gyroscope, this paper aims to propose a temperature drift compensation method based on variational modal decomposition (VMD), time-frequency peak filter (TFPF), mind evolutionary algorithm (MEA) and BP neural network. Design/methodology/approach First, VMD decomposes gyro’s temperature drift sequence to obtain multiple intrinsic mode functions (IMF) with different center frequencies and then Sample entropy calculates, according to the complexity of the signals, they are divided into three categories, namely, noise signals, mixed signals and temperature drift signals. Then, TFPF denoises the mixed-signal, the noise signal is directly removed and the denoised sub-sequence is reconstructed, which is used as training data to train the MEA optimized BP to obtain a temperature drift compensation model. Finally, the gyro’s temperature characteristic sequence is processed by the trained model. Findings The experimental result proved the superiority of this method, the bias stability value of the compensation signal is 1.279 × 10–3°/h and the angular velocity random walk value is 2.132 × 10–5°/h/vHz, which is improved compared to the 3.361°/h and 1.673 × 10–2°/h/vHz of the original output signal of the gyro. Originality/value This study proposes a multi-dimensional processing method, which treats different noises separately, effectively protects the low-frequency characteristics and provides a high-precision training set for drift modeling. TFPF can be optimized by SEVMD parallel processing in reducing noise and retaining static characteristics, MEA algorithm can search for better threshold and connection weight of BP network and improve the model’s compensation effect.

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.

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.

Purpose A 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/approach A 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. Findings The 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/value This 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.

The noise signal in the gyroscope is divided into four levels: sampling frequency level, device bandwidth frequency level, resonant frequency level, and carrier frequency level. In this paper, the signal in the dual-mass MEMS gyroscope is analyzed. Based on the variational mode decomposition (VMD) algorithm, a novel dual-mass MEMS gyroscope noise reduction method is proposed. The VMD method with different four-level center frequencies is used to process the original output signal of the MEMS gyroscope, and the results are analyzed by the Allan analysis of variance, which shows that the ARW of the gyroscope is increased from 1.998*10−1°/√h to 1.552*10−4°/√h, BS increased from 2.5261°/h to 0.0093°/h.

The applications of Inertial Measurement Unit (IMU) based on Micro Electro Mechanical System (MEMS) are widely used because of its low-cost, small volume and low energy consumption. Unlike the accelerometers and magnetometers, which are respectively sensitive to vibrations and ferrous materials interference, MEMS type gyroscope is able to provide stable orientation information for a short period of time. Compared with these two sensors, gyroscopes are neither disturbed by vibrations nor affected by metallic materials, and therefore it would be one of the primary sensors for industrial applications. Reviewing the most recently related works, accurate attitude estimations are usually obtained by fusing gyro integration. However, it is well known that series drifts will be induced after a long-term integration. Furthermore, according to the literature and the associated experiments, they all demonstrated that MEMS type gyroscopes have strong temperature correlation because of the silicon structure. Put it simply, the temperature variations will give rise to gyro drifts severely and thereby degrade the orientation estimation precision. To address this problem, this article proposed a temperature modeling technique and a real-time drift pre-compensation procedure by applying autoregressive moving average (ARMA) technology. Different from the traditional modeling methods, the proposed method is able to describe transient drifting behaviors as well as steady state ones. Moreover, comparison studies using artificial neural networks (ANNs) are also presented. Experiments show that the proposed method provides a stable and reliable temperature-caused gyroscope drift pre-compensation. The developed method is also very suitable for the realization in a low-cost embedded system.

This paper reports a rate integrating gyroscope (RIG) using independently controlled clockwise (CW) and counter clockwise (CCW) modes on a single MEMS resonator. The rotation angle is read out by the phase difference between these modes. A CW/CCW mode separator was used to independently contol these modes superposed on the resonator. The frequency and Q-factor mismatches were compensated by the phases and amplitudes of driving signals. A control system including the mode separator, feedback controllers, signal generators, mismatch compensators were implemented in a field programmable gate array (FPGA). Using the proposed mismatch compensation technique, the equivallent aniso-damping term became 1/100. As a result, the scale factor became constant and the non-linearity became less than 0.2% even when the slow angular rate region around 5°/s. In addition, the temperature coefficient of scale factor as small as −1.84 ± 0.62 ppm/K was achieved without any temperature correction. [2020-0011]

Traditional denoising methods for Micro-electromechanical Systems (MEMS) gyro signal are required to obtain a priori noise statistical properties, which result in poor denoising performance in MEMS gyro utilized in Micro-Inertial Measurement While Drilling (MWD), due to the unknown and complex noise characteristics in MWD. According to this problem, a kind of gyro signal denoising method based on sparse decomposition without a requirement of the priori noise characteristics, utilizing a newly designed atom dictionary, is proposed. Firstly, the MEMS gyro output differential equation is established on the basis of the physical mechanism of the MEMS gyro, then the real MEMS gyro output signal characteristics are analyzed according to the solution of the differential equation. Secondly, the characteristic wave atom most similar to the gyro output signal is designed. Finally, the gyro signal sparse decomposition denoising experiments based on the designed atom dictionary are conducted, compared with the wavelet threshold method and Kalman filter. The experiment results show that the proposed denoising method based on sparse decomposition utilizing the newly designed atom dictionary outperforms wavelet threshold method and Kalman filter in MEMS gyro signal processing of MWD, especially when the noise statistical properties of gyro signal are completely unknown.

The rising demand for mobile devices with photo cameras that has the same stability as that of a high-end camera has led to the need for introducing image stabilizing devices that must be inexpensive and efficient. This problem is often addressed using miniature Micro-Electro-Mechanical Sensors (MEMS). The application of resonance MEMS as inertial sensors in navigation systems of low accuracy grade is also relevant. Such devices are manufactured using well-developed microelectronic technologies of silicon processing to obtain layers up to 100 µm thick. Today, much attention is paid to the issues of a sensitive element development for a MEMS gyro with high sensitivity and a minimum possible size. This paper reports one such comb driven, single perforated proof mass MEMS-based Tuning-Fork Gyroscope (TFG) using PolyMUMPs process. In this paper, initially, a full description of design and simulation is done using predictive modelling methods. We propose a miniature perforated mass sized 500*500 µm, highly sensitive to the input signal, with small displacements along the axis of primary oscillations. The value of this work is that it considers a full cycle of a MEMS-based gyroscope’s design, starting from the mathematical model description and up to the study of a manufactured prototype.

Because the dual-mass MEMS gyroscope’s output is greatly influenced by temperature, which can lead to errors that cannot be ignored. To solve this problem, a novel compensation method is proposed: a parallel processing algorithm, which integrates the Permutation entropy (PE), Local Characteristic-scale Decomposition (LCD) and Adaptive network-based fuzzy inference system (ANFIS). Firstly, LCD is used to decompose the output which contains temperature noises and drifts into a trend component and several intrinsic scale components (ISC), according to autocorrelation and complexity, three different categories will be obtained by PE: pure noise output, mixed output, and drift output. The different processes are as follows, the noise output is discarded, the mixed output is filtered by SG (Savitzky-Golay filter), then dual ANFIS is applied. Since the drift output completely reflects the temperature characteristics, the degree of non-linearity is high, the ANFIS with complex rules is used for processing. And the mixed output is composed of intermediate layer modes, containing a relatively small amount of temperature characteristics, simple rule ANFIS is adopted for processing. Finally, the signal is reconstructed. After that, the temperature error experiment is carried out, the result shows the method can effectively eliminate the error and compensate for the drift, it has a fast convergence speed and good effect, and has the advantage of good compensation efficiency.

A novel fusion algorithm is proposed based on Improved Adaptive Wavelet Threshold De-noising (IAWTD), C-means Support Vector Machine (CSVM) and Ensemble Empirical Mode Decomposition (EEMD) method to eliminate the humidity drift of MEMS gyroscope. Firstly, the IAWTD method is employed to decrease the humidity drift component in MEMS gyroscope output signal. Then, the humidity drift compensation model is established: the input elements are the relative humidity, the change rate of relative humidity and the humidity drift, and the output is the compensated MEMS gyroscope output signal by EEMD method. In order to verify the compensation effect of the fusion algorithm, the gyroscope outputs are collected and analyzed with the relative humidity ranged from 40% to 90% based on the temperature varying from 20°C to 60°C. The results show that the IAWTD-CSVM-EEMD method significantly reduces the influence of relative humidity drift on the gyroscope output, according to the quantitative analysis of Allan variance, the quantization noise of the gyroscope output decreases by 87.78%, 96.37%, 97.77%, 99.17% and 92.62% respectively under the relative humidity ranging from 40% to 90%, as the temperature rose from 20 °C to 60 °C at intervals of 10 °C. In addition, the bias stability decreases by 96.9%, 99.41%, 99.1%, 99.46%, and 99.78% respectively and the angle random walk decreases by 88.16%, 96.54%, 98.16%, 94.43%, and 92.05% respectively at different temperatures. It is worth mentioning that, to further verify the applicability of the fusion algorithm, a group of comparative experiments are added to consider the influence of temperature changes on the gyroscope output under different relative humidity. The experimental results show that the quantization noise, bias stability and angle random walk of the MEMS gyroscope are significantly reduced compared with the original output after processing by IAWTD-CSVM-EEMD. Therefore, the method proposed in this paper is beneficial to reduce the humidity drift in the MEMS gyroscope output.

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 achieving 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 the 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 $31.09\times 10^{-6\circ }$ /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.

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 $e_{4} \in [-4.657:5.565]\times 10^{-11}$ , and the maximum settling time was $T_{e3} \sim 0.144$ for the error of the $\dot {y}-$ axis and the settling time of the $\dot {x}-$ axis, respectively.

This chapter summarizes Micro‐Electromechanical Systems (MEMS) inertial sensors and their application to navigation solutions, with the goal of providing a practical introduction for those readers unfamiliar with MEMS. A MEMS accelerometer (“accel”) converts an applied force into an electrical output proportional to acceleration, just as a traditional electromechanical sensor would. As with MEMS accelerometers, the type of MEMS gyro is determined by its transduction principle, each with specific advantages and disadvantages. The chapter provides an overview of common gyroscope types. The typical MEMS inertial measurement units contains, at minimum, a 3‐axis accelerometer and a 3‐axis gyroscope. Some considerations specific to selecting and applying MEMS sensors are described. MEMS inertial sensors offer a new source of position, orientation, and motion data to navigation solutions. MEMS sensors provide an enticing option for the navigation engineer, particularly for applications in the GNSS‐denied environment.

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.

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.

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.

One of the inevitable problems with real-time control systems is the presence of the uncertainties and external disturbances. The existence of these uncertainties in the fabrication processes of the MEMS Gyroscope devices can deeply impact the performance of the devices. In this paper, five adaptive finite time robust control methods are employed based on SMC method for a Micro-Electro-Mechanical System (MEMS) Gyroscope with mismatched uncertainties and external disturbances to achieve trajectory tracking goal. A new Stepping SMC method is proposed in this study to improve some deficiencies of conventional and existing methods including Simple SMC, Classical SMC, Cubic SMC, and Hexagonal SMC. The upper bound of mismatched uncertainties is estimated in finite time and their estimation is utilized in the control inputs for all five control methods. The elimination of chattering phenomenon is considered in this paper. The system finite time stability proof is obtained using Lyapunov stability theory. The numerical simulation is performed in Simulink/MATLAB for the MEMS gyroscope system to demonstrate the effectiveness of our proposed control method, Stepping SMC, compared with four other methods. To make an extensive comparison among results, the performance criterion, Integral of the square value (ISV), is used.

The reliability analysis of MEMS gyroscope under long-term operating condition has become an urgent requirement with the enlargement of its application scope and the requirement of good durability. In this study we propose a lifetime prediction method for MEMS gyroscope based on accelerated degradation tests (ADTs) and acceleration factor model. Firstly, the degradation characteristic (bias instability) is extracted based on Allan variance. The effect of temperature stress on the degradation rate of bias instability is analyzed, and it shows that the degradation rate of bias instability would increase with the increase of the temperature. Secondly, the ADTs of MEMS gyroscope are designed and conducted, the degradation model of MEMS gyroscope is established based on the output voltage of MEMS gyroscope and Allan variance. Finally, the acceleration factor model of MEMS gyroscope under temperature stress is derived, and the lifetime of the MEMS gyroscope is predicted based on two group tests data under high stress level. The results show that the lifetime calculated by the acceleration factor model and mean lifetime under high stress levels is close to the mean lifetime calculated by the linear equation at normal temperature stress.

In this paper, we apply the topology optimization method to the design of MEMS gyroscopes, with the aim of supporting traditional trial and error design procedures. Using deterministic, gradient-based mathematical programming, the approach is here applied to the design of 2D in-plane single mass MEMS gyroscopes. We first focus on a benchmark academic case, for which we present and compare three different formulations of the optimization problem, considering typical industrial requirements. These include the maximization of the response of the sensor’s structure to the external angular rate, target resonant frequencies and minimum or constrained material usage. Also, a minimum length scale is imposed to the geometric features in order to ensure manufacturability, and an explicit penalization of grey elements is proposed to improve convergence to black and white layouts. Once the suitability of the method has been assessed, the formulation associated with the lowest computational cost, i.e. the one considering static estimations of the resonant frequencies, is applied to the design of a real-world MEMS gyroscope, targeting different resonant frequencies.

Aiming at the requirement of attitude information module with high precision, small size and low power consumption for the control of miniature UAV, a practical attitude estimation algorithm based on the micro-electro-mechanical sensor is proposed in this paper, which realizes the accurate estimation of the attitude of the UAV under the condition of low acceleration. A low-cost MEMS gyroscope, accelerometer, and magnetometer are used in the system. The Euler angle is obtained by the state observer method based on Direction Cosine Matrix (DCM) which can be got by fusing the sensor data. Firstly, based on the basic idea of TRIAD algorithm, a method to determine the attitude rotation matrix by accelerometer and magnetometric measurement is proposed. Compared with the traditional method, this method does not have to calculate the inverse of the matrix. Secondly, a state observer is intended to estimate the attitude of the system. The state observer doesn't have to observe the bias of the gyroscope, but still ensures the convergence of the Euler angle. Finally, the simulation based on the actual sampling data of the MEMS sensor shows that the output of the state observer designed in this paper still has high accuracy and good dynamic characteristics under the condition of gyroscope noise and bias.

In the future, smart intelligent ammunition will be widely applied in the military field. Small volume microelectromechanical system inertial measurement units (MIMUs) have become the mainstream solution for a smart intelligent ammunition navigation system; however, the accuracy of the IMU is the main factor limiting the accuracy of the strikes. To improve the navigation accuracy of the MIMU, various integrated methods have been proposed, for example, the integration of a global navigation satellite system (GNSS) and a magnetometer. In this study, a compound navigation system (CPNS) is designed to improve the navigation accuracy of the MIMU. The CPNS consists of an oblique single-axis fiber optic gyroscope (FOG), a MIMU and a GNSS. The proposed method solves two problems: the calibration of the MEMS gyro and GPS measurement lag. With a FOG as the measurement, MEMS gyro errors are calibrated online by the designed Kalman filter. Thus, the accuracy of the CPNS-IMU can be improved. When GPS measurement lag occurs, the accuracy of the traditional Kalman filter will deteriorate. To reduce the data fusion error of the CPNS under measurement lag, a distributed optimal fusion estimation method is proposed based on the multi-scale theory. The hardware-in-the-loop simulation results demonstrate that the constant bias, scale factor errors, and misalignment errors of the MEMS gyro are effectively suppressed by configuring the FOG to the MIMU. The navigation error of the CPNS-IMU is reduced by more than 50% as compared with the navigation error of the MIMU. In the CPNS with the measurement lag, the fusion error is reduced by approximately 33% in the proposed method as compared with the existing methods.

This paper presents a design optimization approach for a single-drive, 3-axis Microelectromechanical Systems (MEMS) gyroscope. Mathematical models for springs are obtained and a simplified structure for single-drive, 3-axis MEMS gyroscope is proposed. In the proposed structure, concentrated spring architecture was exploited to critical mechanical elements in order to mitigate the fabrication imperfections in the design and the effect of unwanted frequencies. The number of elastic elements was also reduced, while increasing the active area efficiently. The proposed simplified, single-drive, 3-axis MEMS gyroscope is using mode split approach, having a drive resonant frequency of $$25443\mathrm{H}\mathrm{z},$$ with the $$x-\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}, y-\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}, \mathrm{a}\mathrm{n}\mathrm{d}\mathrm\ z-\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}$$ being $$25529\mathrm{H}\mathrm{z}$$ , $$25612\mathrm{H}\mathrm{z}$$ , and $$25621\mathrm{H}\mathrm{z},$$ respectively. The drive and desired sense resonant frequencies are separated by a frequency difference of less than 300 $$\mathrm{H}\mathrm{z}$$ , while the unwanted ones are above $$3 \mathrm{k}\mathrm{H}\mathrm{z}$$ .

Bias thermal stability of microelectromechanical system (MEMS) gyroscope is a significant performance parameter for industrial and tactical applications. The quadrature coupling motion and demodulation phase error are two main sources of bias drift. This work presents a MEMS tuning fork gyroscope with dedicated electrostatic correction combs finger structure that can be implemented to suppress the quadrature motion. By utilising a closed-loop control for the coupling stiffness, the temperature variation of quadrature motion achieves >260 times of magnitude reduction, resulting in the thermal bias drift decreased from 0.98 to 0.18°/s with 5.4 times improvement over the temperature from −40 to 60°C. The results indicate that the variation of the quadrature motion is the dominant factor that determines the temperature bias drift of the custom-designed gyroscope. The compensated bias stability (1σ) is measured to be ∼8.6°/h by using temperature self-sensing compensation technique over the whole temperature operating range, which demonstrates a considerably competitive result for the tactical-grade MEMS gyroscope.

Although the accuracy of MEMS gyroscopes has been extremely improved, in some aspects, such as stability of bias, they still suffer from some big error sources, like run-to-run bias, which determines the sensor price but is not negligible even inexpensive sensors. Due to the fact that run-to-run bias is a kind of stochastic parameter, it has to be measured by utilizing online methods. Utilizing a novel, fast and efficient vision-based rotation estimation algorithm for ground vehicles, we have developed a visual gyroscope that is used in our sensor fusion system, in order to estimate run-to-run bias of the MEMS gyroscope, accurately. Comparing with similar approaches that use GPS, odometer, accelerometer or magnetometer, the most important advantage of the proposed vision-based sensor-fusion framework is its accuracy in accelerated motions. Moreover, it can be used at environments that have a magnetic field, such as urban environments, without depending on external signals. We have evaluated the efficiency of the proposed system using real datasets, recorded from a car moving in urban areas. According to our experimental results, the proposed algorithm is capable of estimating bias of gyroscope after a convergence time of about 6 seconds and improving the accuracy of the MEMS gyroscope, which provides the possibility of using cheaper sensors for high-accuracy demands.

In this paper, a comparison study between gyro-based and gyroless approaches for spacecraft attitude estimation is presented. Due to its vulnerability to the model errors, the gyroless approach has not been widely focused on and there are only few comparison studies available. However, this conventional wisdom might not directly apply to CubeSat attitude estimation, where noisy MEMS gyro is usually implemented. Although the noise density can be improved by low-pass filtering, it sacrifices the bandwidth so that it can induce a discretization error when spacecraft rotates in high speed. This paper outlines expected pros and cons of gyroless attitude estimation with respect to cost and miniaturization, rotational agility, and model errors. Additionally, linearized system models for both of the attitude estimation methods are formulated and a simple guideline for tuning process noise against the model errors is proposed. Numerical results for a realistic earth observation scenario are presented to quantitatively compare the benefits and drawbacks of each attitude estimation method.

In this paper, we report a novel honeycomb-like disk resonator gyroscope (HDRG) and its comprehensive test results. HDRG inherits many advantages from traditional nested-ring disk resonator such as axisymmetric structure and huge capacitive area. In addition, HDRG owns unique characteristics and potentials due to its topology structure, namely, higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement. This new design of HDRG is based on a tradeoff between performance parameters including quality factor, decaying time constant, effective mass, effective capacitive area, transducer sensitivity and mechanical noise. The characteristics and potentials of HDRG are investigated firstly. Afterwards, the parameter optimization and frame structure optimization of HDRG are investigated. Based on the investigation, a novel HDRG is proposed. A prototype of this design is fabricated and its overall performance is tested. Results show that the quality factor of HDRG increases from 81.1k to 171.6k and the decaying time constant increases from 1.507 s to 6.973 s. The bias instability of the gyroscope reaches 0.11 °/h at room temperature without any compensation, more than eighty times smaller than the former design, exhibiting significant performance improvement. Moreover, ranging from −40 °C to 60 °C, the temperature coefficient of scale factor is 0.188%/ °C, and the maximum variations of zero offset and bias instability over temperature are 40 °/h and 0.12 °/h respectively, showing good robustness to environment disturbance. This new gyroscope has the potential to operate steadily under variable temperature conditions, offering as a new type of MEMS gyroscope with high performance and good robustness.

This paper proposes a fractional-order nonsingular terminal sliding mode control of a MEMS gyroscope using a double loop recurrent neural network approximator. For the system stability, a nonsingular terminal sliding mode controller is formulated to guarantee the convergence. For higher accuracy and faster convergence, the fractional-order (FO) calculus is employed with additional degree of freedom. For the system robustness, the neural network is designed to approximate the lumped uncertainty. The inner recurrent loop and external recurrent loop are employed to provide a feedback signal to obtain satisfactory approximation accuracy. For higher adaptability of the neural network, the dynamic function is formulated and the updating law of the parameter is given. Furthermore, the Lyapunov stability theorem is employed to verify the asymptotical stability and convergence of system. Simulations for a MEMS gyroscope are studied to exhibit the superiority of the proposed control strategy.

In this paper, a minimum-learning-parameter (MLP) based neural control method is proposed for micro-electro-mechanical system (MEMS) gyroscope with prescribed performance and input quantization. For the first time, a logarithmic quantizer (LQ) is employed to generate smooth input control signal for MEMS gyroscope, which greatly reduces the communication data size as well as actuator bandwidth. To improve the performance of MEMS gyroscope in the presence of quantization error, a prescribed performance control scheme consisting of preselected performance boundaries and an error transformation is utilized, such that preselected transient and steady-state properties can be assured. In contrast to the neural control strategies subject to the issue of learning explosion, a MLP-based neural network (NN) is introduced to estimate the unknown uncertainties using the norm of neural weight. To eliminate the effect of quantization error induced by LQ, a robust quantized control is designed to further ensure the closed-loop system suffering from discontinuous dynamics with prescribed ultimately uniformly bounded (UUB) performance. In the end, a series of simulations are presented to validate the superiority of the proposed control methodology.

International audience; To obtain a consistent estimate when performing an identication with Prediction Error, it is important that the excitation yields informative data with respect to the chosen model structure. While the characterization of this property seems to be a mature research area in the linear case, the same cannot be said for nonlinear systems. In this work, we study the data informativity for a particular type of Hammerstein systems for two commonly-used excitations: white Gaussian noise and multisine. The real life example of the MEMS gyroscope is considered.

A closed-loop controlling system for Micro Electro Mechanical System (MEMS) gyroscope sense mode is investigated in this paper, and the controller is designed to achieve low error, wide bandwidth and low noise capability. The gyroscope monitoring system includes four independent closed-loop, and is simulated by Simulink soft to prove the speedability and stability of the sensing closed-loop. The gyroscope monitoring system is realized through 3 analog circuit boards, and is tested through temperature controlled turntable. The bias stability, angular random walking value and bias temperature coefficients improved from 2.168 °/h, 0.155°/√h and 10.59 °/h/°C to 0.415 °/h, 0.0414°/√h and 3.59°/h/°C. And the bandwidth value is improved from 13Hz to 104Hz. Meanwhile, scale factor nonlinearity, asymmetry, repeatability and temperature coefficient parameters are enhanced from 660 ppm, 430ppm, 403ppm and 180 ppm/°C to 59.3ppm, 62.4ppm, 50.4ppm and 28.7 ppm/°C respectively.

This paper investigates an event-triggered output feedback control problem with guaranteed tracking performance for microelectromechanical system (MEMS) gyroscope subject to the lumped disturbances, including parameter uncertainties, coupling between driving mode and sensing mode, and unknown external disturbances. Firstly, to make the system output tracking errors evolve within the predetermined performance envelopes, a prescribed performance control (PPC) is employed in our controller design, such that a prescribed trajectory tracking with preselected settling time and steady-state tracking accuracy can be ensured. Besides, to simultaneously realize disturbance rejection and estimation of the immeasurable velocity state, linear extended state observers (LESOs) are designed to reconstruct the lumped disturbances and immeasurable velocity states for both MEMS gyroscope driving and sensing modes. In general, excessively energy and resource consumption are fundamentally neglected in most of the existing output feedback controllers for MEMS gyroscope, which will dramatically reduce the operational time of the close-loop system. To address this problem, we embed a fixed threshold event-triggered mechanism into the controller design procedure, such that the communication data size can be drastically reduced without sacrificing the tracking accuracy. Finally, to obtain the close-loop stability for MEMS gyroscope, robust control laws are designed to compensate for the measurement error and estimation error, meanwhile Zeno phenomena can be effectively eliminated. The simulation results and comparisons validate the effectiveness of the proposed scheme.

Precision agriculture, such as precise seeding or ploughing, is guaranteed by vehicle navigation accuracy. A steering angle plays an essential and fundamental role in the function of autonomous vehicle and the path planning because it controls the vehicle direction. However, the steering angle cannot be calibrated directly from Global Navigation Satellite System (GNSS) due to the limitation of GNSS parameters. In addition, the accuracy of steering angle obtained from the analysis of Global Position System (GPS) information cannot satisfy the accuracy requirements in engineering applications. In this paper, a novel approach to improve accuracy of steering angle is proposed. Low-cost Micro-electromechanical System (MEMS) and GPS are combined on an agriculture vehicle so that the steering angle can be calculated precisely. Unscented Kalman Filters (UKF) are used in simulations to estimate the steering angle. The simulation and experiment results show that the proposed method can achieve increased accuracy of estimation of steering angle than that based merely on GPS information. Because the cost of a MEMS gyroscope is very low, the proposed method is a practical way to achieve precision agriculture with high accuracy.

This paper presents the characterization of the modal frequencies and the modal orientation of the axisymmetric resonators in Coriolis vibratory gyroscopes based on the approaches of the frequency sweep and the ring down. The modal frequencies and the orientation of the stiffness axis are the key parameters for the mechanical correction of the stiffness imperfections. The frequency sweep method utilizes the zero and the poles in the magnitude-frequency responses of the two-dimensional transfer function to extract the modal orientation information within the frequency domain. The ring down method makes use of the peak and the valley values of the beat signals at the readout electrodes to obtain the modal orientation and the coefficient of the nonlinear stiffness directly within the time domain. The proposed approaches were verified via a silicon ring resonator designed for gyroscopic sensing and the modal information from the experiments exhibited a good agreement between the methods of the frequency sweep and the ring down.

Video stabilization is essential for long-range electro-optical systems, especially in situations when the field of view is narrow, since the system shake may produce highly deteriorating effects. It is important that the stabilization works for different camera types, i.e., different parts of the electromagnetic spectrum independently of the weather conditions and any form of image distortion. In this paper, we propose a method for real-time video stabilization that uses only gyroscope measurements, analyze its performance, and implement and validate it on a real-world professional electro-optical system developed at Vlatacom Institute. Camera movements are modeled with 3D rotations obtained by integration of MEMS gyroscope measurements. The 3D orientation estimation quality depends on the gyroscope characteristics, we provide a detailed discussion on the criteria for gyroscope selection in terms of the sensitivity, measurement noise, and drift stability. Furthermore, we propose a method for improving the unwanted motion estimation quality using interpolation in the quaternion domain. We also propose practical solutions for eliminating disturbances originating from gyro bias instability and noise. In order to evaluate the quality of our solution, we compared the performance of our implementation with two feature-based digital stabilization methods. The general advantage of the proposed methods is its drastically lower computational complexity, hence, it can be implemented for a low price independent of the used electro-optical sensor system.

In high-reliability applications, the health condition of the MEMS gyroscope needs to be known in real time to ensure that the system does not fail due to the wrong output signal. Because the MEMS gyroscope self-test based on the principle of electrostatic force cannot be performed during the working state. We propose that by monitoring the quadrature error signal of the MEMS gyroscope in real time, an online self-test of the MEMS gyroscope can be realized. The correlation between the gyroscope’s quadrature error amplitude signal and the gyroscope scale factor and bias was theoretically analyzed. Based on the sixteen-sided cobweb-like MEMS gyroscope, the real-time built-in self-test (BIST) method of the MEMS gyroscope based on the quadrature error signal was verified. By artificially setting the control signal of the gyroscope to zero, we imitated several scenarios where the gyroscope malfunctioned. Moreover, a mechanical impact table was used to impact the gyroscope. After a 6000 g shock, the gyroscope scale factor, bias, and quadrature error amplitude changed by −1.02%, −5.76%, and −3.74%, respectively, compared to before the impact. The gyroscope failed after a 10,000 g impact, and the quadrature error amplitude changed −99.82% compared to before the impact. The experimental results show that, when the amplitude of the quadrature error signal seriously deviates from the original value, it can be determined that the gyroscope output signal is invalid.

This work discusses the key issues associated with the process development for 200 μm thick structure for mechanically decoupled Silicon on Glass (SOG) MEMS gyroscope. The gyroscope discussed here is a single axis, in-plane moving device with capacitive driving, differential capacitive sensing and has an area of 2.6 × 2.4 cm2. Challenges involved in defining masks for High Aspect Ratio (HAR) etching of silicon using Bosch process to a depth of 200 μm through an opening of 8 μm are discussed. The HAR etching of silicon is achieved by using a novel approach of having dual layer masks of Aluminum and photoresist.

MEMS inertial devices are important sensors for measuring angle and acceleration. Due to the drift of the gyroscope output caused by temperature, it is difficult to improve the precision of the hemispherical resonator gyroscope, so it is necessary to compensate the error of the gyroscope. Firstly, the mechanism of zero drift is analyzed based on the working principle of HRG. In this paper, we introduce the principle of BP neural network and the advantages of immune algorithm in improving BP neural network. The neural network is trained by the zero point data of MEMS gyroscope at different temperatures, and the error is compensated. The conclusion shows that IA-BP algorithm has shorter training time and better error compensation effect than BP algorithm.