Microelectromechanical Systems Gyroscope Research Articles

Neurodynamic Approximation-Based Quantized Control With Improved Transient Performances for Microelectromechanical System Gyroscopes: Theory and Experimental Results

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 Portable Support Attitude Sensing System for Accurate Attitude Estimation of Hydraulic Support Based on Unscented Kalman Filter.

To measure the support attitude of hydraulic support, a support attitude sensing system composed of an inertial measurement unit with microelectromechanical system (MEMS) was designed in this study. Yaw angle estimation with magnetometers is disturbed by the perturbed magnetic field generated by coal rock structure and high-power equipment of shearer in automatic coal mining working face. Roll and pitch angles are estimated using the MEMS gyroscope and accelerometer, and the accuracy is not reliable with time. In order to eliminate the measurement error of the sensors and obtain the high-accuracy attitude estimation of the system, an unscented Kalman filter based on quaternion according to the characteristics of complementation of the magnetometer, accelerometer and gyroscope is applied to optimize the solution of sensor data. Then the gradient descent algorithm is used to optimize the key parameter of unscented Kalman filter, namely process noise covariance, to improve the accuracy of attitude calculation. Finally, an experiment and industrial application show that the average measurement error of yaw angle is less than 2° and that of pitch angle and roll angle is less than 1°, which proves the efficiency and feasibility of the proposed system and method.

A Novel MEMS Gyroscope In-Self Calibration Approach.

This paper presents a novel approach for hand-held low-cost MEMS (micro-electro-mechanical system) gyroscope in-self calibration. This method does not need the support of external high-precision equipment compared with traditional calibration scheme and can be accomplished by user hand rotation. In this approach, Kalman filter is designed to perform the calibration procedure and estimate gyroscope bias error, scale factor error and non-orthogonal error. The system observability is analyzed and the dynamic rotating conditions under which the sensor errors become observable are derived. The design principles of optimal calibration procedure are provided as well. Both simulated and practical experiments are carried out to test the validation of the proposed calibration algorithm. The achieved results demonstrate that the introduced approach can provide promising calibration scheme for the low-cost MEMS gyroscope.

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

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

Effective nested Kalman fusion for improving microelectromechanical system array performance

Microelectromechanical systems (MEMS) are widely used in the navigation field due to their low cost and easy integration. Its low positioning accuracy restricts its expansion into the high-end navigation field. To improve the performance of MEMS inertial devices, this paper proposes a nested Kalman fusion (NKF) for MEMS gyroscope array data fusion applied to the virtual gyroscope. First, the algorithm processes the raw gyroscope array data through Kalman filtering. Secondly, the obtained filtered array data converge as a virtual gyroscope by support degree data fusion—the NKF experimental data collected by the actual test. The experimental results show the zero-bias instability, angular random walk and rate ramp of the original data are improved by 10.64 dB, 12.45 dB and 10.26 dB, respectively, by the NKF algorithm. NKF can adjust the gyro parameters by about 6 dB in comparison with existing MEMS optimization algorithms.

Design, Analysis and Simulation of a MEMS-Based Gyroscope with Differential Tunneling Magnetoresistance Sensing Structure.

The design, analysis, and simulation of a new Micro-electromechanical System (MEMS) gyroscope based on differential tunneling magnetoresistance sensing are presented in this paper. The device is driven by electrostatic force, whereas the Coriolis displacements are transferred to intensity variations of magnetic fields, further detected by the Tunneling Magnetoresistance units. The magnetic fields are generated by a pair of two-layer planar multi-turn copper coils that are coated on the backs of the inner masses. Together with the dual-mass structure of proposed tuning fork gyroscope, a two-stage differential detection is formed, thereby enabling rejection of mechanical and magnetic common-mode errors concurrently. The overall conception is described followed by detailed analyses of proposed micro-gyroscope and rectangle coil. Subsequently, the FEM simulations are implemented to determine the mechanical and magnetic characteristics of the device separately. The results demonstrate that the micro-gyroscope has a mechanical sensitivity of 1.754 nm/°/s, and the micro-coil has a maximum sensitivity of 41.38 mOe/µm. When the detection height of Tunneling Magnetoresistance unit is set as 60 µm, the proposed device exhibits a voltage-angular velocity sensitivity of 0.131 mV/°/s with a noise floor of 7.713 × 10−6°/s/ in the absence of any external amplification.

Fuzzy wavelet neural control with improved prescribed performance for MEMS gyroscope subject to input quantization

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.

A cross product calibration method for micro-electro mechanical system gyroscope in unmanned aerial vehicle attitude determination system

This paper presents a novel calibration method for micro-electro mechanical system gyroscope in attitude measurement system of small rotor unmanned aerial vehicles. This method is based on an observation vector and its cross product, which is especially valuable for the in-field calibration without the aid of external equipment. By analysing the error model of the tri-axial gyroscope, the principle of calibration is proposed. Compared with other algorithms, numerical simulations are performed to evaluate the effectiveness of integral form of the cross product calibration method. Experiment on the hex-rotor unmanned aerial vehicle platform shows that the proposed method has great advantages in low-cost integrated navigation system.

Constructive approach to reduce the influence of temperature on spring suspension eigenfrequencies

PurposeOne of the problems encountered by developers of inertial systems, such as gyroscopes and accelerometers, is the critical dependence of the eigenfrequencies of elastic suspensions (ES) on temperature when using substrates for sensors made of dielectric materials, such as borosilicate glass. The internal stresses arising in the ES caused by the difference in the temperature coefficients of linear expansion (TCLE) lead to deformation of the sensor and complication of the electronic part of the sensor. The purpose of this paper is to approach for in-plane and out-of-plane ES are considered that allow for minimization of the influence of internal stresses on eigenfrequencies.Design/methodology/approachAnalytical, finite element and experimental results are considered. The temperature coefficient of thermal expansion, the Young’s modulus and the Poisson ratio are given as a function of temperature. The shape of the spring elements (SEs) and the construction of the elastic suspension are the main topics of focus in this study. The authors’ out-of-plane ES based on a meander-like spring element implemented via finite element modeling show good agreement with the experimental results.FindingsMeander-like SEs have been developed that have lower temperature errors in comparison with traditional types of SEs. The main contribution to the change in the eigenfrequency from temperature is made by internal stresses that arose from the deformation of the bonded materials with different TCLE. The change of eigenfrequency from the temperatures that were calculated by finite element method did not exceed 0.15%, however, in practice, the scatter of the obtained characteristics for different samples showed a change of up to 0.3%.Originality/valueThis study shows a way to design and optimize the structure and theoretical background for the development of the microelectromechanical systems (MEMS) inertial module combining the functions of gyroscope and accelerometer. The obtained results will improve and expand the manufacturing technology of MEMS gyroscopes and accelerometers.

Recurrent-neural-network-based unscented Kalman filter for estimating and compensating the random drift of MEMS gyroscopes in real time

The presence of the stochastic errors in MEMS (Micro Electro Mechanical Systems) gyroscopes makes the improvement of the measurement precision challenging. This paper addresses a novel method to estimate and compensate the random drift of MEMS gyroscopes in real time, combining unscented Kalman filter (UKF) with recurrent neural network (RNN). In the proposed method, the random drift is regarded as a generalized nonlinear autoregressive moving average (NARMA) model, and its optimal predictor is realized by a dynamic RNN. To compensate the random drift in real time, the RNN model is brought into the framework of UKF, for establishing the state equation of the improved UKF. The novelty of this paper is that a strategy is presented to guarantee the validity of the combination of UKF and RNN. The effectiveness and superiorities of the proposed method are verified by experiments.

Chattering-Free Adaptive Finite-Time Sliding Mode Control for Trajectory Tracking of MEMS Gyroscope

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.

Sound Attenuation Study of Micro-Scale Acoustic Package

Certain microelectromechanical systems (MEMS), particularly MEMS gyroscopes, are notably susceptible to high power acoustic noise, especially when the noise is at or near its resonant frequency. A micro scale open-through dual expansion chamber (ODEC) array package with a continuous transmission loss (TL) in a wide frequency range is proposed to diminish the impact of such noise on the performance of MEMS gyroscopes. An analytical model based on planar wave propagation in stationary air has been developed with the consideration of the thermo-acoustic effect near the inner rigid boundary regarding small scale. Experiments with ODEC groups and control groups (non-ODEC) samples have been conducted to verify the model and compare the performances. The ODECs perform in the manner of low-pass filters and both the experimental and the analytical results exhibit greater TL in the higher frequency ranges as compared to the corresponding control samples. In addition, the resonance effects of the ODEC itself are also experimentally observed to be a key factor in influencing the TL.

A digital force-to-rebalance scheme for high-frequency bulk-acoustic-wave micro-gyroscopes

This paper presents a digital force-to-rebalance (FTR) control system to substantially extend the bandwidth of high-Q mode-matched high-frequency micro-electro-mechanical systems (MEMS) bulk-acoustic-wave (BAW) gyroscopes. Principle and challenges for the FTR operation of high-frequency mode-matched MEMS gyroscopes are studied and a digital implementation is demonstrated based on high speed field programmable gate arrays (FPGA) using a 4.2 MHz silicon BAW gyroscope with a Q of 144,000. By using a properly designed cascaded lead controller, the bandwidth of the mode-matched gyroscope is extended from 14 Hz to 180 Hz with no degradation in angle random walk (ARW) and an improved long-term bias stability, which will allow high-Q mode-matched gyroscopes to be used for advanced high-bandwidth high-dynamic-range applications.

Dual-Mass MEMS Gyroscope Parallel Denoising and Temperature Compensation Processing Based on WLMP and CS-SVR

For the sake of decreasing the effects of noise and temperature error on the measurement accuracy of micro-electro-mechanical system (MEMS) gyroscopes, a denoising and temperature drift compensation parallel model method based on wavelet transform and forward linear prediction (WFLP) and support vector regression based on the cuckoo search algorithm (CS-SVR) is proposed in this paper. First, variational mode decomposition (VMD) is proposed in this paper, which is aimed at dividing the output signal of the gyroscope into intrinsic mode functions (IMFs); then, the IMFs are classified into three features—drift, mixed, and pure noise features—by the sample entropy (SE) value. Second, a wavelet transform and forward linear prediction (WFLP) are combined to remove the noise from the mixed features. Meanwhile, the drift feature is compensated by support vector regression based on the cuckoo search algorithm (CS-SVR). Finally, through reconstruction, the final signal is obtained. Experimental results demonstrate that the VMD-SE-WFLP-CS-SVR method proposed in this paper can decrease noise and compensate the temperature error effectively (angular random walking value is optimized from 1.667°/√h to 0.0667°/√h and the bias stability is reduced from 30°/h to 4°/h). In terms of denoising, the performance of the WFLP algorithm is superior to the wavelet threshold and FLP, as it combines their advantages; furthermore, in terms of temperature compensation, the proposed CS-SVR algorithm uses the cuckoo search algorithm to find the optimal parameters of SVR, improving the accuracy of the model.

Thermoelastic Dissipation in Diamond Micro Hemispherical Shell Resonators

Maximizing quality factor (Q) is essential to improve the performance of micro hemispherical shell resonators (μHSRs) which can be used in microelectromechanical system (MEMS) gyroscopes to measure angular rotation. Several energy dissipation mechanisms limit Q, where thermoelastic dissipation (TED) is the major one and studied in this paper. Fully coupled thermo-mechanical equations for calculating TED are formulated, and then temperature distribution in a deformed μHSR and its quality factor related to TED (QTED) are obtained by solving the equations through a finite-element method (FEM). It has been found that different fabrication process conditions can obtain various geometrical parameters in our previous studies. In order to provide guidelines for the design and fabrication of μHSRs, the effects of their geometry on resonant frequency (f0) and QTED are studied. The change of anchor height and small enough anchor radius have no effect on both f0 and QTED, but the shell size including its radius, thickness and height has significant impact on f0 and QTED. It is found that whether a μHSR has lower f0 and higher QTED or higher f0 and higher QTED can be achieved by changing these geometrical parameters. The results presented in this paper can also be applied to other similar resonators.

Angular velocity fusion of the microelectromechanical system inertial measurement unit array based on extended Kalman filter with correlated system noises

The paper proposes an angular velocity fusion method of the microelectromechanical system inertial measurement unit array based on the extended Kalman filter with correlated system noises. In the proposed method, an adaptive model of the angular velocity is built according to the motion characteristics of the vehicles and it is regarded as the state equation to estimate the angular velocity. The signal model of gyroscopes and accelerometers in the microelectromechanical system inertial measurement unit array is used as the measurement equation to fuse and estimate the angular velocity. Due to the correlation of the state and measurement noises in the presented fusion model, the traditional extended Kalman filter equations are optimized, so as to accurately and reliably estimate the angular velocity. By simulating angular rates in different motion modes, such as constant and change-in-time angular rates, it is verified that the proposed method can reliably estimate angular rates, even when the angular rate has been out of the microelectromechanical system gyroscope measurement range. And results show that, compared with the traditional angular rate fusion method of microelectromechanical system inertial measurement unit array, it can estimate angular rates more accurately. Moreover, in the kinematic vehicle experiments, the performance advantage of the proposed method is also verified and the angular rate estimation accuracy can be increased by about 1.5 times compared to the traditional method.

MEMS gyroscope fault detection and elimination for an underwater robot using the combination of smooth switching and dynamic redundancy method

Micro Electro Mechanical System (MEMS) gyroscope sensors are used in different underwater vehicles to determine their attitude as the input of the controller system to adjust the attitude to the desired value. Fault detection and elimination are necessary for MEMS gyroscope sensors to avoid disruption of the system performance. In this paper, it is tried to study different types of gyroscope sensor faults which can be detected and eliminated by designing a new proposed dynamic redundancy scheme. The proposed method is consisted of two MEMS gyroscope sensors and is modified by considering underwater robot dynamics in threshold tuning via Monte Carlo simulations. The switch between the primary and secondary gyroscope sensors is designed by smoothing methods to eliminate undesirable behavior of switching kick. Finally, numerical and experimental simulations are performed by a three degree of freedom table to show that the proposed method is efficient for the underwater robot exposed to gyroscope sensor faults.

Modelling and optimization of single drive 3-axis MEMS gyroscope

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 $$3 \mathrm{k}\mathrm{H}\mathrm{z}$$ .

Investigation on the Measurement Method for Output Torque of a Spherical Motor

The output torque is an important performance indicator of a motor. Due to the special structure of a permanent magnet spherical motor (PMSM), it is difficult to measure its torque. This paper proposes a novel method to measure the output torque of the PMSM. The proposed method uses the microelectromechanical system (MEMS) gyroscope to measure the rotor motion acceleration, which is then used to calculate the output torque based on the rotor dynamics equation. In this paper, we firstly simulate and analyze the output torque of the PMSM. Secondly, we design a torque-measuring device to measure the output torque. Thirdly, we compare and discuss the experimental and simulation results. The comparison results show that the proposed method is feasible.

Bias thermal stability improvement of MEMS gyroscope with quadrature motion correction and temperature self‐sensing compensation

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.