Vibratory Gyroscope Research Articles

A High-Precision Method of Stiffness Axes Identification for Axisymmetric Resonator Gyroscopes.

Axisymmetric resonators are key elements of Coriolis vibratory gyroscopes (CVGs). The performance of a CVG is closely related to the stiffness and damping symmetry of its resonator. The stiffness symmetry of a resonator can be effectively improved by electrostatic tuning or mechanical trimming, both of which need an accurate knowledge of the azimuth angles of the two stiffness axes of the resonator. Considering that the motion of a non-ideal axisymmetric resonator can be decomposed as two principal oscillations with two different natural frequencies along two orthogonal stiffness axes, this paper introduces a novel high-precision method of stiffness axes identification. The method is based on measurements of the phase difference between the signals detected at two orthogonal sensing electrodes when an axisymmetric resonator is released from all the control forces of the force-to-rebalance mode and from different initial pattern angles. Except for simplicity, our method works with the eight-electrodes configuration, in no need of additional electrodes or detectors. Furthermore, the method is insensitive to the variation of natural frequencies and operates properly in the cases of either large or small frequency splits. The introduced method is tested on a resonator gyroscope, and two stiffness axes azimuth angles are obtained with a resolution better than 0.1°. A comparison of the experimental results and theoretical model simulations confirmed the validity of our method.

A Robust Angular Rate Sensor Utilizing 2:1 Auto-Parametric Resonance Excitation.

This paper presents a single-axis angular rate sensor that is robust to variations in its operating voltage and frequencies. The sensor is developed to overcome the shortcomings of conventional mode-matched Micromachined Vibratory Gyroscopes in open loop operations, namely narrow frequency bandwidths and unstable scale factors. The developed sensor utilizes inherent forcing and inertial nonlinearities from electrostatic forces and fabrication imperfections to auto-parametrically excite the sense mode via 2:1 auto-parametric resonance, which yields a broader bandwidth frequency response for the sensor’s sense mode. The experimental results demonstrated frequency bandwidth of , a scale factor of , and a dynamic range of .

Noise analysis of mode matched vibratory gyroscopes

Noise analysis of mode matched vibratory gyroscopes

Design and Simulation of a Novel Single-Chip Integrated MEMS Accelerometer Gyroscope

This paper presents the design and simulation of a single-chip integrated MEMS accelerometer gyroscope by integrating a Coriolis vibratory ring gyroscope and a differential resonant accelerometer into one single-chip structure, measuring both the acceleration and the angular velocity (or the angle). At the same time, it has the advantages of small volume, low cost, and high precision based on the characteristics of a ring gyroscope and resonant accelerometer. The proposed structure consists of a microring gyroscope and a MEMS resonant accelerometer. Tthe accelerometer is located inside the gyroscope and the two structures are concentric. The operating mechanisms of the ring gyroscope and the resonant accelerometer are first introduced. Then, the whole structure of the proposed single-chip integrated accelerometer gyroscope is presented, and the structural components are introduced in detail. Modal analysis shows the resonant frequencies of upper and lower DETFs in resonant accelerometer are 28,944.8 Hz and 28,948.0 Hz, and the resonant frequencies of the ring gyroscope (n=2) are 15,768.5 Hz and 15,770.3 Hz, respectively. The scale factor of the resonant accelerometer is calculated as 83.5 Hz/g by the analysis of the input–output characteristic. Finally, the thermal analysis fully demonstrates that the single-chip integrated accelerometer gyroscope has excellent immunity to temperature change.

Influence of Parametric Nonlinearities on Closed-Loop Operated MEMS Gyroscopes

The influence of parametric nonlinearities on the mode matching of closed-loop operated MEMS gyroscopes is investigated. Accurate resonance tuning of mechanical detection modes is essential for optimal noise suppression in closed-loop resonators. Large deflections of the drive mode lead to a geometric nonlinearity, which induces a phase-dependency in the mode-matching procedure. Those effects are known to amplify signal-to-noise ratio in open-loop vibratory MEMS gyroscopes. Predicted and measured tuning voltages and folded response of a sense mode in a prototype gyroscope are compared. Using simulations, it is shown that the pilottone with a 90° phase can confine the crosstalk of the Coriolis and quadrature channel to the quadrature channel exclusively. When applying a quadrature compensation in the simplified model, nonlinear amplification is prohibited in the output channel even for low gain of the force-to-rebalance loop. Furthermore, it is shown that in a simulation with idealized drive motion and demodulation signals the cross-coupling nonlinearity by itself does not have a major impact on standard noise suppression capabilities. [2021-0232]

Analysis of an inverse weak-value tiltmeter in the kilohertz regime.

We present a follow-on experiment to the recent study from The University of Rochester [Opt. Lett.42, 2479 (2017)OPLEDP0146-959210.1364/OL.42.002479], which reported a new architecture for an inverse weak-value tiltmeter. We recreate the Rochester tiltmeter and specifically investigate mirror oscillations in the low-kilohertz frequency regime, which is relevant to certain potential applications, such as Coriolis vibratory gyroscopes. We find that the inverse weak-value amplification effect persists in this regime, although our measured noise floors are higher than those obtained in the Rochester experiment-approximately 2prad/Hz for mirror oscillation frequencies between 1 and 25 kHz.

Online Compensation of Phase Delay Error Based on P-F Characteristic for MEMS Vibratory Gyroscopes.

In this paper, an online compensation method of phase delay error based on a Phase-Frequency (P-F) characteristic has been proposed for MEMS Coriolis Vibratory Gyroscopes (CVGs). At first, the influences of phase delay were investigated in the drive and sense mode. The frequency response was acquired in the digital control system by collecting the demodulation value of drive displacement, which verified the existence and influence of the phase delay. In addition, based on the P-F characteristic, that is, when the phase shift of the nonresonant drive force through the resonator is almost 0° or 180°, the phase delay of the gyroscope is measured online by injecting a nonresonant reference signal into the drive-mode dynamics. After that, the phase delay is self-corrected by adjusting the demodulation phase angle without affecting the normal operation of the gyroscopes. The approach was validated with an MEMS dual-mass vibratory gyroscope under double-loop force-to-rebalance (in-phase FTR and quadrature FTR) closed-loop detection mode and implemented with FPGA. The measurement results showed that this scheme can detect and compensate phase delay to effectively eliminate the effect of the quadrature error. This technique reduces the zero rate output (ZRO) from −0.71°/s to −0.21°/s and bias stability (BS) from 23.30°/h to 4.49°/h, respectively. The temperature sensitivity of bias output from −20 °C to 40 °C has reached 0.003 °/s/°C.

Online asymmetry estimation for whole angle mode coriolis vibratory gyroscopes by high frequency injection

The whole angle mode gyroscope (WAMG) is considered to be the next generation architecture, but it is suffered from the asymmetry errors to conduct real products. This paper proposes a novel high frequency injection based approach for the error parameters online identification for the WAMG. The significance is that it can separate physical and error fingerprints to enable online calibration. The nonlinear WAMG dynamics are discretized to meet the requirement of numerical precision and computation efficiency. The optimized estimation methods are then constructed and compared to track asymmetry error parameters continuously. In the validation part, its results firstly prove that the proposed scheme can accurately identify constant asymmetry parameters with an overall tracking error of less than 1 ppm and the extreme numerical convergence can reach 10−12ppm. Under the dynamic asymmetry variation condition, the root mean square errors (RMSE) indicate that the tracking accuracy can reach the level of 10−3, which shows the robustness of the proposed scheme. In summary, the proposed method can effectively estimate the WAMG asymmetry errors online with satisfied performance and practical values.

A novel tracking control approach of amplitude signals for vibratory gyroscopes suppressing high-frequency disturbance

Vibratory gyroscopes are the most ideal novel inertial sensors in the 21st century. The amplitude is an important index of vibratory gyroscopes. The high-frequency disturbance is a common and intricate problem in vibratory gyroscopes. The paper investigates a novel tracking control approach that tracks the reference amplitude signal and suppresses the high-frequency disturbance for vibratory gyroscopes. First, the original dynamic system is transformed into an interval type-2 (IT2) fuzzy system such that the nonlinearity and uncertainty of the system are well handled. To reduce the conservatism of the asymptotic stability condition, a novel coupling-factors-dependent Lyapunov function is constructed, in which the system state depends on coupling factors. Then, to track the reference amplitude signal and suppress the high-frequency disturbance simultaneously, a doubly-fed tracking controller with nonfragile property is developed such that the state error system is asymptotically stable with a prescriptive performance. Finally, the comparative results of a vibratory gyroscope are done to show that the proposed control approach can greatly improve the control precision of amplitude signals, which demonstrates the effectiveness of the proposed control approach.

Coupled Field Analysis of Hemispherical Resonator Gyroscope

This work deals with the electromechanical analysis of the Hemispherical Resonator Gyroscope (HRG). The HRG is a type of Coriolis vibratory gyroscope (CVG), which uses Coriolis force to measure the input angular rate. For any CVG drive and sense mode, frequencies play a critical role, which decides the sensitivity and bandwidth of a sensor. In this study, we carry out modal analysis to evaluate the natural frequencies and corresponding mode shapes of an HRG. As HRG is an electromechanical structure, the device is driven at resonance in the drive direction, and the Coriolis force leads to motion in the sense direction. In this study, we present the piezoelectric based HRG; coupled field simulations are carried out to evaluate the performance characteristics of a sensor.

Field-programmable gate array (FPGA) based programmable digital emulator of vibratory microelectromechanical systems (MEMS) gyroscopes.

This paper presents a hardware emulator of microelectromechanical systems (MEMS) vibratory gyroscopes that can be used for characterization and verification of control/interface electronics by means of hardware-in-the-loop testing, thus speeding up design cycles by decoupling these tasks from the often longer MEMS design and fabrication cycles. The easily re-configurable hardware emulator is completely synthesized on a field-programmable gate array board. The emulator is shown to successfully model the Coriolis effect along with the prominent error sources present in typical MEMS gyroscopes, namely, quadrature error, spring nonlinearity, and thermo-mechanical, electronic, and environmental noise. Preliminary experimental results characterizing the noise and nonlinearity models based on a prototype with user-controllable device parameters synthesized on the Xilinx Zynq®-7020 SoC (Digilent ZYBO Z7 board) are presented.

Modeling and neural sliding mode control of mems triaxial gyroscope

In this paper, a neural sliding mode control approach is developed to adjust the sliding gain using a radial basis function (RBF) neural network (NN) for the tracking control of Microelectromechanical Systems (MEMS) triaxial vibratory gyroscope. First a sliding mode control with a fixed sliding gain is proposed to assure the asymptotic stability of the closed loop system. Then a RBF neural network is derived to adjust the sliding gain using a gradient method in a switching control law. With the adaptive sliding gain using the learning function of RBF neural network, the chattering phenomenon is eliminated. Numerical simulation is investigated to verify the effectiveness of the proposed neural sliding mode control scheme.

Effect of EAM on Capacitive Detection of Motion in MEMS Vibratory Gyroscopes

The Electromechanical Amplitude Modulation (EAM) is frequently used to eliminate feed-through signals between forcer and pick-off electrodes of resonant microstructures. However, there are some undesirable effects of EAM that need to be considered. This work studies the contribution of EAM on dissipation of energy and appeared non-linear dynamics in MEMS Coriolis Vibratory Gyroscopes (CVGs). We presented an analytical model, capturing the effect of AC carrier signal on amplitude-frequency coupling, scale factor instability, and in-run noise performance of CVGs. The effect of EAM on a Dynamically Amplified dual-mass Gyroscope (DAG) was experimentally demonstrated and compared to the simulation results of the analytical model. We concluded that the AC carrier signal in EAM influences the amplitude-frequency couplings along both the drive and sense modes of the gyroscope through modifying the non-linear electrostatic stiffnesses, which was also proven to be one of the dominant sources of both the scale factor nonlinearity and frequency instability in the near-mode-matched DAG, operating in the open-loop rate mode.

Impact of outgassing and its corrective methods to improve the vacuum stability in the Coriolis Vibratory Gyroscope

Coriolis Vibratory Gyroscope (CVG) is an inertial angular rate measurement sensor. CVG sensor comprises of metal coated hemispherical quartz vibrating structure as the rotation sensing element. It is forced to vibrate at one of its resonant modes by electrostatic excitation. Because of the limited flexibility of the quartz sensing element, the amplitude is limited to the submicron level. An ultra-high vacuum environment is required for the sensing element to sustain vibration for a long time. The criticality in the sensor development is to maintaining an ultra-high vacuum environment for the sensing element. Sensor suffers a problem of vacuum instability during the operation due to the outgassing from its components. This paper presents a novel approach in the identification of various outgassing sources that exist in the sensor, mitigation plan to minimize outgassing rate by selection of suitable raw material, suitable fabrication process of the components, and the surface characterization etc. The research work also presents the cost-effective experimental methodology to measure the outgassing rate from the sensor components to assess the CVG vacuum life, the requirement of the getter to maintain the ultra-high vacuum level throughout the CVG operation.

Approximation method for frequency split calculation of coriolis vibrating gyroscope resonator

One of the main characteristics influencing the accuracy of Coriolis Vibrating Gyroscopes (CVG) is the frequency split caused by various manufacturing defects. It is well known that in most cases, the largest part of the frequency split is determined by the circumferential harmonic of a defect with the number k=2n (where n is a circumferential wave number). Also, frequency split is strongly influenced by the meridional distribution of the kth defect harmonic because the resonator shell has both the circumferential and meridional directions. Meridional defects of different distribution can appear because of manufacturing inaccuracies and because of different balancing methods. This paper presents a new simple, fast and accurate frequency split calculation technique for various meridional defect functions. The frequency split can be calculated as a linear function of a defect’s meridional ordinates (as a simple dot product of two vectors). The proposed approach is based on the linearity of the relationship between the frequency split and a defect’s kth harmonic. The proposed approach also allows estimating the sensitivity of frequency split to the location of a defect on the meridian of the resonator shell. Besides, the calculation simplicity, accuracy, and speed enable the optimization of frequency split balancing parameters. The paper considers cylinder and bell-shaped resonators, and the proposed calculation approach was validated for meridional defect distributions. The results obtained using the proposed method are in good agreement with the results obtained using FEM.

Vibratory Gyroscope Scale Factor and Bias on-Run Self-calibration

А new method for on-run periodic scale factor and bias self-calibration of vibratory gyroscopes in an inertial measurement unit with a redundant number of sensors is proposed. Self-calibration uses predefined virtual positive and negative angle rates to calibrate the SF, and the bias of the gyroscope that is in calibration mode, while the others, at least three gyroscopes of an inertial measurement unit, whose sensitivity axes do not lie in the same plane, operate in the measurement mode to measure the real angle rate of a vehicle. The projection of the current angle rate onto the sensitivity axis of the gyroscope being calibrated is computed from the results of measuring the full angle rate vector by the other three gyroscopes, creating conditions for the calibration procedure. In contrast to known methods, such as single-axis or multi-axis rotation of an inertial measurement unit and vibration modes reversal, the proposed method does not use mechanical rotation, which requires additional devices, and does not require a reorientation of the vibrating wave, which entails the need to align the parameters of the two measuring channels. The scale factor and bias calibration procedure using this method is the same for any gyroscope of an inertial measurement unit and can be applied to several gyroscopes at the same time. Therefore, the proposed method has great potential for an application not only for small-sized 4-gyro inertial measurement unit based on vibratory gyroscopes but also for multi-gyro inertial measurement unit based on micro-electro-mechanical gyroscopes. Experimentally shown that using the proposed method a gyro requirements mitigation coefficient can be substantially increased and can provide high accuracy for autonomous navigation systems based on low-cost, small-sized, and micro-electro-mechanical gyroscopes.

Python-Based Open-Source Electro-Mechanical Co-Optimization System for MEMS Inertial Sensors.

The surge in fabrication techniques for micro- and nanodevices gave room to rapid growth in these technologies and a never-ending range of possible applications emerged. These new products significantly improve human life, however, the evolution in the design, simulation and optimization process of said products did not observe a similarly rapid growth. It became thus clear that the performance of micro- and nanodevices would benefit from significant improvements in this area. This work presents a novel methodology for electro-mechanical co-optimization of micro-electromechanical systems (MEMS) inertial sensors. The developed software tool comprises geometry design, finite element method (FEM) analysis, damping calculation, electronic domain simulation, and a genetic algorithm (GA) optimization process. It allows for a facilitated system-level MEMS design flow, in which electrical and mechanical domains communicate with each other to achieve an optimized system performance. To demonstrate the efficacy of the methodology, an open-loop capacitive MEMS accelerometer and an open-loop Coriolis vibratory MEMS gyroscope were simulated and optimized—these devices saw a sensitivity improvement of 193.77% and 420.9%, respectively, in comparison to their original state.

Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes.

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension.

Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

Characterization of Modal Frequencies and Orientation of Axisymmetric Resonators in Coriolis Vibratory Gyroscopes

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.