Microelectromechanical Systems Gyroscope Research Articles

Design and Analysis of Mode-Matched Decoupled Mass MEMS Gyroscope with Improved Thermal Stability

Abstract This paper presents an efficient design approach for microelectromechanical systems (MEMS) gyroscope considering the design constraint of MEMSCAP's Silicon-on-Insulator Multi-User MEMS Processes (SOIMUMPs). A design for a decoupled mass MEMS resonant gyroscope with tuning electrodes is presented to minimize cross-axis coupling and optimize the gyroscope's performance. The device features a size of 1.8 ×2.772 mm^2. A decoupled mass MEMS gyroscope has been designed using a novel mechanical beam configuration that optimizes the structural design to reduce unwanted interactions between drive and sense axes motions. Mode order has been achieved by obtaining the first two modes as drive and sense modes at 9946.3 Hz and 10202.7 Hz, respectively. Parallel plate electrostatic tuning electrodes have been added to adjust and match the drive and sense modes at the resonant frequencies of 9946 Hz. This mode matching is crucial for optimizing gyroscope performance, accuracy, and sensitivity. The effects of temperature variation on the performance of the designed decoupled mass MEMS gyroscope have been investigated, particularly in terms of its mode-matched operation achieved using tuning electrodes. Finite Element Method (FEM) simulations were conducted, demonstrating that thermal stability was achieved, and mode-matched operation was maintained within the temperature range of -40 ºC to 80 ºC. The gyroscope exhibits enhanced performance compared to existing MEMS gyroscopes under mode-matched conditions, featuring a lower temperature coefficient of frequency (TCF) at 0.0415 Hz/ºC in the drive mode and 0.0165 Hz/ºC in the sense mode. FEM analysis for the fabrication process tolerances has been done, where MEMS gyroscope’s resonant frequencies, output capacitance, output displacement, and sense mode quality factor have shown negligible changes to fabrication process tolerances. Transient analysis was conducted using CoventorWare MEMS+ 3D schematic, which was integrated with MATLAB Simulink to measure the MEMS gyroscope’s output response, which corresponded with the varying input angular velocity signal.

Modeling and Reliability Analysis of MEMS Gyroscope Rotor Parameters under Vibrational Stress.

Vibrational environments can cause drift or changes in Micro-Electro-Mechanical System (MEMS) gyroscope rotor parameters, potentially impacting their performance. To improve the effective use of MEMS gyroscopes, this study introduced a method for evaluating the reliability of parameter degradation under vibration. We analyzed the working principle of MEMS gyroscope rotors and investigated how vibration affects their parameters. Focusing on zero bias and scale factor as key performance indicators, we developed an accelerated degradation model using the distributional assumption method. We then collected degradation data for these parameters under various vibration conditions. Using the Copula function, we established a reliability assessment approach to evaluate the degradation of the MEMS gyroscope rotor's zero bias and scale factor under vibration, enabling the determination of reliability for these parameters. Experimental findings confirmed that increasing stress levels lead to reduced failure times and increased failure rates for MEMS gyroscope rotors, with significant changes observed in the zero bias parameter. Our evaluation method effectively characterizes changes in the reliability of the MEMS gyroscope rotor's scale factor and zero bias over time, providing valuable information for practical applications of MEMS gyroscopes.

Robust Orientation Estimation from MEMS Magnetic, Angular Rate, and Gravity (MARG) Modules for Human-Computer Interaction.

While the availability of low-cost micro electro-mechanical systems (MEMS) accelerometers, gyroscopes, and magnetometers initially seemed to promise the possibility of using them to easily track the position and orientation of virtually any object that they could be attached to, this promise has not yet been fulfilled. Navigation-grade accelerometers and gyroscopes have long been the basis for tracking ships and aircraft, but the signals from low-cost MEMS accelerometers and gyroscopes are still orders of magnitude poorer in quality (e.g., bias stability). Therefore, the applications of MEMS inertial measurement units (IMUs), containing tri-axial accelerometers and gyroscopes, are currently not as extensive as they were expected to be. Even the addition of MEMS tri-axial magnetometers, to conform magnetic, angular rate, and gravity (MARG) sensor modules, has not fully overcome the challenges involved in using these modules for long-term orientation estimation, which would be of great benefit for the tracking of human-computer hand-held controllers or tracking of Internet-Of-Things (IoT) devices. Here, we present an algorithm, GMVDμK (or simply GMVDK), that aims at taking full advantage of all the signals available from a MARG module to robustly estimate its orientation, while preventing damaging overcorrections, within the context of a human-computer interaction application. Through experimental comparison, we show that GMVDK is more robust to magnetic disturbances than three other MARG orientation estimation algorithms in representative trials.

Command filter-based event-triggered control for stochastic MEMS gyroscopes with finite-time prescribed performance

This paper proposes an adaptive neural control strategy for stochastic microelectromechanical system (MEMS) gyroscopes, aiming to achieve a prescribed performance in a finite time. The radial basis function neural network is introduced to address the system’s unknown nonlinear dynamics and stochastic disturbances. Then, the technology of finite-time prescribed performance function, along with the method of command-filtered backstepping design, is utilized to ensure both transient and steady-state performance and simultaneously solve the problem of "explosion of complexity." Moreover, a switching threshold event-triggered control law is proposed to cut down on communication resources and eliminate corresponding parametric inequality restrictions. The proposed adaptive state feedback control strategy is able to guarantee that the output tracking error converges to a prescribed, arbitrarily small residual set. Additionally, the closed-loop system’s signals can be semi-globally ultimately uniformly bounded in probability. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed strategy.

A toroidal SAW gyroscope with focused IDTs for sensitivity enhancement

A surface acoustic wave (SAW) gyroscope measures the rate of rotational angular velocity by exploiting a phenomenon known as the SAW gyroscope effect. Such a gyroscope is a great candidate for application in harsh environments because of the simplification of the suspension vibration mechanism necessary for traditional microelectromechanical system (MEMS) gyroscopes. Here, for the first time, we propose a novel toroidal standing-wave-mode SAW gyroscope using focused interdigitated transducers (FIDTs). Unlike traditional SAW gyroscopes that use linear IDTs to generate surface acoustic waves, which cause beam deflection and result in energy dissipation, this study uses FIDTs to concentrate the SAW energy based on structural features, resulting in better focusing performance and increased SAW amplitude. The experimental results reveal that the sensitivity of the structure is 1.51 µV/(°/s), and the bias instability is 0.77°/s, which are improved by an order of magnitude compared to those of a traditional SAW gyroscope. Thus, the FIDT component can enhance the performance of the SAW gyroscope, demonstrating its superiority for angular velocity measurements. This work provides new insights into improving the sensitivity and performance of SAW gyroscopes.

Design and Analysis of Optomechanical Micro-Gyroscope for Angular-Vibration Detection

Micro-gyroscopes based on the Coriolis principle are widely employed in inertial navigation, motion control, and vibration analysis applications. Conventional micro-gyroscopes often exhibit limitations, including elevated noise levels and suboptimal performance metrics. Conversely, the advent of cavity optomechanical system technology heralds an innovative approach to micro-gyroscope development. This method enhances the device’s capabilities, offering elevated sensitivity, augmented precision, and superior resolution. This paper presents our main contributions which include a novel dual-frame optomechanical gyroscope, a unique photonic crystal cavity design, and advanced numerical simulation and optimization methods. The proposed design utilizes an optical cavity formed between dual oscillating frames, whereby input rotation induces a measurable phase shift via optomechanical coupling. Actuation of the frames is achieved electrostatically via an interdigitated comb-drive design. Through theoretical modeling based on cavity optomechanics and finite element simulation, the operating principle and performance parameters are evaluated in detail. The results indicate an expected angular rate sensitivity of 22.8 mV/°/s and an angle random walk of 7.1 × 10−5 °/h1/2, representing superior precision to existing micro-electromechanical systems gyroscopes of comparable scale. Detailed analysis of the optomechanical transduction mechanism suggests this dual-frame approach could enable angular vibration detection with resolution exceeding state-of-the-art solutions.

Design of a Shock-Protected Structure for MEMS Gyroscopes over a Full Temperature Range.

Impact is the most important factor affecting the reliability of Micro-Electro-Mechanical System (MEMS) gyroscopes, therefore corresponding reliability design is very essential. This paper proposes a shock-protected structure (SPS) capable of withstanding a full temperature range from -40 °C to 80 °C to enhance the shock resistance of MEMS gyroscopes. Firstly, the shock transfer functions of the gyroscope and the SPS are derived using Single Degree-of-Freedom and Two Degree-of-Freedom models. The U-folded beam stiffness and maximum positive stress are deduced to evaluate the shock resistance of the silicon beam. Subsequently, the frequency responses of acceleration of the gyroscope and the SPS are simulated and analyzed in Matlab utilizing the theoretical models. Simulation results demonstrate that when the first-order natural frequency of the SPS is approximately one-fourth of the gyroscope's resonant frequency, the impact protection effect is best, and the SPS does not affect the original performance of the gyroscope. The acceleration peak of the MEMS gyroscope is reduced by approximately 23.5 dB when equipped with the SPS in comparison to its counterpart without the SPS. The anti-shock capability of the gyroscope with the SPS is enhanced by approximately 13 times over the full-temperature range. After the shock tests under the worst case, the gyroscope without the SPS experiences a beam fracture failure, while the performance of the gyroscope with the SPS remains normal, validating the effectiveness of the SPS in improving the shock reliability of MEMS gyroscopes.

Thermal Stabilization of Quality Factor for Dual-Axis MEMS Gyroscope Based on Joule Effect In Situ Dynamic Tuning

Quality factor has played a crucial role in determining the temperature and anti-shock performance of a microelectromechanical system (MEMS) gyroscope. This paper presents an innovative approach to enhance the thermal stability of quality factor for a micro resonant sensors based on Joule effect in-situ dynamic tuning for the first time. By unitizing an active control loop that adjusts the dissipation energy of a resistive element connected to the mechanical structure via monitoring the driving voltage, the device damping can be effectively tuned in real-time, thus stabilizing the quality factor. The proposed method is demonstrated on a vacuumed sealed monolithic dual-axis gyroscope. The results show that the relative variation of the Q-factor significantly reduced by more than 3000× down to ∼150ppm from -40℃ to +60℃, which achieves only ∼30ppm of driving voltage stability with ∼3500× reduction. Benefiting from the quality factor precise control capability, the electrical coupling from the drive mode to the sense mode is therefore suppressed, exhibiting more than three-fold times improvement of the zero bias thermal drift over 100℃ range. This technique is also promising for enhancing the anti-shock performance.

A hybrid denoising method for gyroscopes based on multiple screening

To reduce the random error of microelectromechanical system (MEMS) gyroscope, a hybrid method combining improved empirical mode decomposition (EMD) and least squares algorithm (LS) is proposed. Firstly, based on the multiple screening mechanism, intrinsic mode functions (IMFs) from the first decomposition are divided into noise IMFs, strong noise mixed IMFs, weak noise mixed IMFs and signal IMFs. Secondly, according to their characteristics, they are processed again. IMFs from the second decomposition are divided into noise IMFs and signal IMFs. Finally, useful signal is gathered to obtain the final denoising signal. Compared with some other denoising methods proposed in recent years, the experimental results show that the proposed method has obvious advantages in suppressing random error, greatly improving the signal quality and improving the accuracy of inertial navigation.

Adaptive Fractional Prescribed Performance Control for Micro-Electromechanical System Gyros Using a Modified Neural Estimator

In this paper, a neural fractional order prescribed performance control is proposed for micro-electromechanical system (MEMS) gyros. Gyros tend to become smaller in size and more precise in structure with the development of micro-manufacturing technology. The operational security for MEMS gyros in cases of disturbances and parameter uncertainties becomes a challenging problem that has attracted much attention. The proposed method incorporates a prescribed performance technique to accomplish a bounded (within 10% of the vibration amplitude) gyro trajectory tracking error dynamic to secure the gyro’s operation. Meanwhile, fractional calculus is integrated into the controller’s design to provide precise adjustments to the gyro’s motion and thus further improve gyro control performance (shortening error convergence time by 20%). Furthermore, to enlarge the application scope and to improve gyro system robustness, a modified neural network estimator with a constrained input mapping mechanism is proposed to approximate unknown time-varying angular-velocity-related gyro dynamics. Notably, the constrained input mapping mechanism can help guide neural parameter initialization to avoid a time-consuming parameter adjustment process. The stability of the closed-loop gyro control system is proved in the framework of Lyapunov stability theory, and comparisons of simulation results are presented to demonstrate the effectiveness of the proposed method.

A method for compensating random errors in MEMS gyroscopes based on interval empirical mode decomposition and ARMA

The random error in micro-electro-mechanical systems (MEMS) gyroscopes is one of the major aspects that limit measurement accuracy. In order to address the inaccurate extraction of noise and trend during the signal preprocessing, as well as the subjectivity in autoregressive moving average (ARMA) model ordering, this paper proposes a method based on interval empirical mode decomposition and ARMA model. In the proposed method, the original signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual through empirical mode decomposition (EMD). Based on the Hellinger distance and autocorrelation function, IMFs are then classified into noise IMFs, hybrid IMFs, and signal IMFs. The improved sand cat swarm optimization is utilized to optimize the ordering process of the ARMA model. The improved adaptive filter is adopted to compensate the random error, and the compensated signal is reconstructed with the signal IMFs and residual to obtain the final output. Experiments show that under static conditions, the proposed method could reduce the root mean square error (RMSE) by 52.6% and 33.3%, respectively, compared with the traditional EMD and ARMA methods. Under dynamic conditions, the proposed method could reduce the RMSE by 51.1% and 37.1%, respectively, compared with the traditional EMD and ARMA methods. The proposed method could effectively compensate the random error and improve the measurement accuracy of MEMS gyroscopes.

ROEKF-MPC Estimator for Satellite Attitude and Gyroscope Bias Estimation

Micro-electro-mechanical system (MEMS) based gyroscopes are commonly used for satellite's attitude determination and control system in recent years. They are packaged in a small form factor and have lower power consumption. They provide a low-cost solution to the emerging NewSpace industry. MEMS gyroscopes exhibit time-zero null bias with variation over temperature. To overcome this problem, this paper proposes a technique for self-calibration of gyroscope bias based on reduced order Extended Kalman Filter (EKF) working alongside an estimator based on the model predictive control (MPC) approach. The proposed technique is referred as the ROEKF-MPC Estimator. Both simulation results and experimental verification using an in-house developed spacecraft simulator are presented. Unlike the EKF method, the proposed method can estimate the gyroscope bias instantly and it is robust against changes in temperature. In addition, the proposed method employing a reduced order EKF is 28.4% computationally more efficient than the typical higher order EKF method. Results show that the pointing performance is better than 0.35deg making the proposed method very attractive for most NewSpace applications. While the proposed method allows for self-calibration of gyroscope bias, its performance is affected by the gyroscope noise and requires the satellite's attitude to be nearly in steady state. This limitation will be addressed in detail.

A Method to Identify Different Comb Gaps for MEMS Gyroscope at the Wafer Level Based on Negative Electrostatic Stiffness

For high-accurate micro-electro-mechanical systems (MEMS) gyroscopes, comb gap errors influence the mechanical coupling errors and limit performance. In this study, an in situ method was proposed to identify the gaps of drive combs, drive-sense combs, and sense combs in MEMS gyroscopes that can be applied at the wafer level. Negative electrostatic stiffness of combs was considered in the model construction of the sense mode and the Y-axis in-phase mode, and the frequency change caused by this was applied to characterize the comb gaps. Eight chips in different positions of a wafer were selected for verification of this method. The results shows that errors of drive comb gaps, drive-sense comb gaps, and sense comb gaps in the chip near the wafer center were 0.67 μm, 0.60 μm, and 0.53 μm, respectively, and those in the chip at the wafer edge were 0.96 μm, 0.95 μm, and 0.71 μm, respectively. The variation of comb gaps was 0.08 μm in a single chip near the wafer center, and 0.03 μm in a single chip at the wafer edge. This work provides a method for the fabless designers to explore the effect of wafer process on the structures and reduce it through careful design.

Design and Optimization of Hemispherical Resonators Based on PSO-BP and NSGA-II.

Although one of the poster children of high-performance MEMS (Micro Electro Mechanical Systems) gyroscopes, the MEMS hemispherical resonator gyroscope (HRG) is faced with the barrier of technical and process limits, which makes it unable to form a resonator with the best structure. How to obtain the best resonator under specific technical and process limits is a significant topic for us. In this paper, the optimization of a MEMS polysilicon hemispherical resonator, designed by patterns based on PSO-BP and NSGA-II, was introduced. Firstly, the geometric parameters that significantly contribute to the performance of the resonator were determined via a thermoelastic model and process characteristics. Variety regulation between its performance parameters and geometric characteristics was discovered preliminarily using finite element simulation under a specified range. Then, the mapping between performance parameters and structure parameters was determined and stored in the BP neural network, which was optimized via PSO. Finally, the structure parameters in a specific numerical range corresponding to the best performance were obtained via the selection, heredity, and variation of NSGAII. Additionally, it was demonstrated using commercial finite element soft analysis that the output of the NSGAII, which corresponded to the Q factor of 42,454 and frequency difference of 8539, was a better structure for the resonator (generated by polysilicon under this process within a selected range) than the original. Instead of experimental processing, this study provides an effective and economical alternative for the design and optimization of high-performance HRGs under specific technical and process limits.

Fault‐tolerant fixed‐time prescribed performance control of MEMS gyroscope

AbstractThis paper investigates a fault‐tolerant fixed‐time prescribed performance microelectromechanical system gyroscope using the adaptive backstepping method. The control protocol is designed such that not only is the system robust to even extremely harsh conditions of disturbance and actuator faults but also the performance and its settling time are user‐adjustable. Also, the system itself along with the external disturbances and actuator faults are assumed to be uncertain. Two case studies have been analyzed; the controller performance in the presence of very severe while uncertain disturbance and actuator faults, and a comparison between fixed‐time and finite‐time in this model in terms of their performance and convergence rate. First, the dynamics of the system are derived, and the prescribed performance error is defined for the analysis. Then, using the backstepping method, and adaptive estimations for the uncertainties, the algorithm is designed to converge the errors to a small set near zero with a fixed‐time convergence rate after which the stability of the system is verified via Lyapunov theory. In the end, a simulation example is presented in each case study to represent the efficacy of the proposed control scheme.

A 0.82 μVrms ultralow 1/f noise bandgap reference for a MEMS gyroscope

High-precision microelectromechanical system (MEMS) gyroscopes are significant in many applications. Bias instability (BI) is an important parameter that indicates the performance of a MEMS gyroscope and is affected by the 1/f noise of the MEMS resonator and readout circuit. Since the bandgap reference (BGR) is an important block in the readout circuit, reducing its 1/f noise is key to improving a gyroscope’s BI. In a traditional BGR, the error amplifier is applied to provide a virtual short-circuit point, but it introduces the main low-frequency noise sources. This paper proposes an ultralow 1/f noise BGR by removing the error amplifier and applying an optimized circuit topology. In addition, a simplified but accurate noise model of the proposed BGR is obtained to optimize the BGR’s output noise performance. To verify this design, the proposed BGR has been implemented in a 180 nm CMOS process with a chip area of 545 × 423 μm. The experimental results show that the BGR’s output integrated noise from 0.1 to 10 Hz is 0.82 μV and the thermal noise is 35 nV/√Hz. Furthermore, bias stability tests of the MEMS gyroscope fabricated in our laboratory with the proposed BGR and some commercial BGRs are carried out. Statistical results show that reducing the BGR’s 1/f noise can nearly linearly improve the gyroscope’s BI.

Research on A Gyro Error Calibration Method Based on Dynamic Compensation

Gyroscopes in Micro-Electro-Mechanical Systems (MEMS) technology have high accuracy, convenient use, and broad application prospects. In practical applications, it is found that angular rate error is one of the main reasons that affect the output accuracy of gyroscopes. In the angular rate error calibration of MEMS gyroscopes, the method of calibrating the gyroscopes only by changing the bias and scale coefficients obtained by fitting cannot meet the angular rate error calibration of MEMS gyroscopes whose dynamic range exceeds . Therefore, the research proposes an improved calibration method to solve the problem of angular rate error, using dynamic compensation algorithms to achieve dynamic compensation for the angular rate of MEMS gyroscopes. Experiments show that using the dynamic compensation calibration method proposed in this paper, the root mean square error of the angular rate of MEMS gyroscopes has decreased by 52.37% compared to the previous one, verifying the feasibility of this method.

A Traceability Localization Method of Acoustic Attack Source for MEMS Gyroscope

The malicious acoustic attack can easily cause the failure of micro-electro mechanical systems (MEMS) sensors. It can use ultrasonic waves to attack the MEMS gyroscope over long distances. This type of attack is highly hidden and harmful. Therefore, the purpose of this letter is to locate malicious sources and facilitate the eradication of the threat. We designed a prototype system to simulate an ultrasonic attack on an MEMS gyroscope, which can collect and analyze the state of the gyroscope after being attacked. Furthermore, we proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -standard deviation-based feature extraction, and then designed a neural-network-based traceability location method to seek for attacker’s location. The experimental results indicate that our approach can effectively and accurately locate the malicious acoustic source location.

Calibration Method of MEMS Gyroscopes Using a Robot Manipulator

Inertial measurement units composed of microelectromechanical systems (MEMS) gyroscopes are widely used sensors for small spacecraft and nanosatellite attitude estimation, control, and orientation. This is due to the fact that when developing nanosatellites, it is convenient to use devices of small dimensions and low energy consumption, which are advantages of MEMS sensors. However, one of the significant disadvantages of these measuring devices is their relatively low accuracy, which is related to systematic and random errors. For this reason, this article proposes a method for calibrating MEMS-based angular rate sensors using a robot manipulator for partial elimination of these errors. There are high-precision rotary calibration stands on the market that are designed to set angular rates and orientations when testing products of various types and accuracy classes. Similarly, a robot manipulator represents a possible option for performing this task. As a result, a modified six-position method as a sequence for performing laboratory calibration using a robot joint for high-precision rotation is proposed. The features of the results of processing experimental measurement data of tests have been validated on MEMS angular rate sensors. After calibration, the quality of MEMS gyroscope output data using this calibration approach was significantly improved.

An Interface ASIC Design of MEMS Gyroscope with Analog Closed Loop Driving.

This paper introduces a digital interface application-specific integrated circuit (ASIC) for a micro-electromechanical systems (MEMS) vibratory gyroscope. The driving circuit of the interface ASIC uses an automatic gain circuit (AGC) module instead of a phase-locked loop to realize a self-excited vibration, which gives the gyroscope system good robustness. In order to realize the co-simulation of the mechanically sensitive structure and interface circuit of the gyroscope, the equivalent electrical model analysis and modeling of the mechanically sensitive structure of the gyro are carried out by Verilog-A. According to the design scheme of the MEMS gyroscope interface circuit, a system-level simulation model including mechanically sensitive structure and measurement and control circuit is established by SIMULINK. A digital-to-analog converter (ADC) is designed for the digital processing and temperature compensation of the angular velocity in the MEMS gyroscope digital circuit system. Using the positive and negative diode temperature characteristics, the function of the on-chip temperature sensor is realized, and the temperature compensation and zero bias correction are carried out simultaneously. The MEMS interface ASIC is designed using a standard 0.18 μM CMOS BCD process. The experimental results show that the signal-to-noise ratio (SNR) of sigma-delta (ΣΔ) ADC is 111.56 dB. The nonlinearity of the MEMS gyroscope system is 0.03% over the full-scale range.