Gyroscopic Systems Research Articles

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

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

Nonsingular Terminal Sliding Mode Control of Uncertain Chaotic Gyroscope System Based on Disturbance Observer

Based on disturbance observer, this paper develops a nonsingular terminal sliding mode control method for uncertain chaotic gyroscope system. Firstly, fuzzy logic system (FLS) is used to estimate the unknown function; then disturbance observer (DOB) is constructed to estimate the mixed disturbance, which consists of the fuzzy estimation error, external disturbance, and dead-zone input error. Subsequently, by using a nonsingular terminal sliding mode function, the control method proposed in this paper can achieve the sliding mode variable approaching a small neighborhood of zero and reduce chattering phenomenon of the tracking error and controller. Finally, comparative simulation results confirm the effectiveness of the method proposed in this paper.

Neuro-observer based control of double gimbal control moment gyro systems

In this paper, a new third-order nonlinear dynamics solving the mismatched problem is proposed for double gimbal control moment gyros (DGCMGs) affected by friction and coupling torques, unmodeled dynamics, or parameter uncertainties; the new nonlinear dynamics with the control inputs and the disturbances into the same equations should not be linearized and any control method handling multivariate systems with cross-coupling between channels can be then used to design a controller. Secondly, a feed-forward neural network based observer with disturbance rejection ability is proposed to estimate both the exogenous/endogenous disturbances and the states of the system, the number of necessary sensors being decreased. Thirdly, in order to control the rotations of the inner/outer gimbals, compensate the disturbances, enhance the robustness of the control system, and handle the channel interferences, we design, evaluate, and compare two novel control architectures using the Lyapunov theory, the backstepping method or the dynamic inversion control technique. Each of the two control architectures uses two interconnected controllers (an inner gimbal controller and an outer gimbal controller), a neuro-observer, and two reference models to generate the necessary fictive control signals. The simulation results show that the proposed control approaches provide very good angular rate precision of the DGCMG system and successfully handle a wide range of disturbances, parameter uncertainties, and channel interferences. The smaller fluctuations of the rotation angles, angular rates, and angular accelerations in the gimbal channels indicate that the backstepping control provides better ability to reject disturbances, smaller overshoot and convergence time than the dynamic inversion control technique.

Determine the dynamic parameters in mechanical system of the crab-shaped MEMS vibratory gyroscope

Determine the dynamic parameters in mechanical system of the crab-shaped MEMS vibratory gyroscope

Analysis for vortex superposition state evolution of microcavity exciton polariton excited by ring-shaped pump

Owing to its light effective mass, polariton can easily realize Bose-Einstein condensates (BEC) and can also produce gyro effect under external drive. Therefore, it has a promising application prospect. Based on the Gross-Pitaevskii equation, the evolution of the exciton polaron BEC system in the annular microcavity is studied. Two key parameters affecting the characteristics of the exciton polaron system, namely the size of the microcavity and the configuration of the ring-shaped pumped beam, are investigated. The size of microcavity often directly affects the volume and power consumption of integrated devices. In addition, the number of coherent petals of exciton polariton superposition state matter wave propagated in microcavity is closely related to the precision and sensitivity of gyro, and the size of microcavity has a direct effect on the number of coherent petals. At the same time, whether the pumping region is continuous or not also has a key effect on the evolution of the system, and different pump configurations will affect the evolutions of the system. We find that in the microcavity radius on a micron scale, the annular microcavity can excite the petal of vortex superposition state when pumped by pumping light, and the petals can be stable, but circular cavity with a certain radius can “accommodate” a limited vortex quantum number, when vortex quantum number is too large, the system will be unstable and unable to support the formation of stable petals. However, with the increase of the radius of the annular microcavity, the superposition petal number of the exciton polariton system contained in the annular region will also increase, and the maximum petal number contained in the exciton polariton system has a positive linear correlation with the inner radius of the annular microcavity. At the same time, we find that when the pump laser configuration is changed, the system will evolve into a special form of steady state. The calculation results show that when microcavity parameters are the same but for only changing the radial width of single pump, the number of petals obtained is three times that before changing the radial width. In such a case, the number of superposition petals not only exceeds the previously calculated maximum number of petals accommodated by the annular cavity under the radius but also there appear the multiple petals combined radially. Under the double-ring pump system, changing the width of the hollow ring may produce not only the new exciton polariton condensation in the hollow ring, but also vortex states in the original petal. Under each of the three-ring and four-ring pumping condition, the evolution of the system finally presents a multi-petal state in the radial direction. Because these vortex superposition states contain the information about the density and the phase, it has important guiding significance for designing the new system of gyroscope. Therefore, these special evolutionary results open a new direction for studying the new system gyroscope.

Double Recurrent Perturbation Fuzzy Neural Network Fractional-Order Sliding Mode Control of Micro Gyroscope

In this paper, a fractional-order sliding mode control method based on a double recurrent perturbation fuzzy neural network (DRPFNN) is proposed for a micro gyroscope system with parameter uncertainty and external disturbance. The DRPFNN is used to realize the adaptive estimation of the unknown part, which ensures that the controller is independent of the accurate mathematical model. The sine-cosine perturbation membership function is used to deal with the uncertainty of rules in neural network, increasing the accuracy, reduce the calculation load, and simplifying computational complexity. In addition, double recurrent links are added to transmit more information with superior dynamic ability. Then, the proposed control system is composed of a DRPFNN estimator and a fractional-order sliding mode controller (FSMC). The fractional calculus operator is introduced into the sliding surface to improve the controller flexibility. The parameter adaptive laws in the neural network are designed to be adaptively stabilized to the optimal value. Finally, simulation studies verify the effectiveness of the proposed control method, showing it can obtain higher control accuracy and enhance robustness than the traditional sliding mode control method.

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

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

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

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

Recent development of resonant micro cavity in resonant micro-optical gyro

Resonant micro-optical gyros (RMOG) based on Sagnac effect has great potential in integration, miniaturization and sensitivity, which has broad application prospects in the fields of micro nano satellite attitude control, robot control, medical diagnosis and detection instruments, and has become a research hotspot in recent years. Resonant micro cavity as the core sensing element of resonator micro optical gyroscope, the optical characteristics of which are closely related to the performance of gyroscope system. The research progress of resonator has seriously restricted the development of RMOG. At present, integrated optical technology, micro nano optical processing technology and the application of new materials can reduce the weight and size of the resonator, reduce the cost and power consumption, and increase the reliability and performance index of the system. Combined with the information disclosed by periodical conference and related research institutions, the development status, basic principle and characteristic parameters of resonant micro optical gyroscope were briefly introduced. Various new structure designs of resonant micro cavity at home and abroad were listed, and the characteristics and potential of different structures were analyzed. In addition, the new materials for fabrication of resonant micro cavity at home and abroad were reviewed, and the optical properties of different materials were summarized. The future development direction and technical development path of resonator micro cavity for resonator micro optical gyroscope were preliminarily discussed.

0.015 Degree-Per-Hour Honeycomb Disk Resonator Gyroscope

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

A Filtering Algorithm of MEMS Gyroscope to Resist Acoustic Interference.

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

Optimization and Fabrication of an MOEMS Gyroscope Based on a WGM Resonator.

In this paper, the characterization of a whispering gallery mode (WGM) resonator applied in a novel micro-opto-electro-mechanical system (MOEMS) gyroscope was investigated. The WGM optical transmission coupling model was analyzed and compared by adjusting key parameters, such as the cavity radius, the waveguide width, and the gap between them for silicon and silicon nitride materials in simulations, which will greatly affect the quality factor (Q) of the WGM resonator. Furthermore, the structural parameters of the disk resonant gyroscope were also optimized. Then, the fabrication process was optimized to overcome the difficulties in the realization of micro-optical devices. Finally, a gyroscope prototype with the integrated WGM resonator was verified experimentally. The scale factor and bias instability performance of the MOEMS gyroscope was 2.63 mv/°/s and 4.0339°/h, respectively.

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

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

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

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

Denoising Method of MEMS Gyroscope Based on Interval Empirical Mode Decomposition

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

Nanophotonic optical gyroscope with sensitivity enhancement around “mirrored” exceptional points

Unavoidable thermal fluctuation and fabrication error severely compromise the sensing performance of nanophotonic optical gyroscope devices in practice. In this paper, we theoretically propose a doubly-coupled-ring gyroscope system that not only takes advantage of exceptional point enhanced rotation sensitivity but also improves the robustness against thermal fluctuation and fabrication error. In the doubly-coupled-ring gyroscope with gains, two mirrored exceptional point supermodes experience opposite responses to rotation but same response to thermal fluctuation and fabrication error. Thus, differential readout of the frequency splitting from the two mirrored exceptional point supermodes results in a nearly 100% common-mode noise rejection and remarkably enhances the measurement precision and sensitivity of the photonic optical gyroscope. The proposed doubly-coupled-ring system is a promising platform for not only the novel photonic optical gyroscope but also the next-generation exceptional point sensor in general.

Research on frequency stability of narrow linewidth laser in resonant optical gyro

In this study, to measure the frequency drift characteristics of the narrow-linewidth laser, we provide a method with high accuracy and adjustable measuring range that can be applied in a resonant optical gyro (ROG) system. In an ROG system, the laser frequency drift characteristics, such as fluctuation range and frequency, influence the performance of the closed-loop frequency-locked module. To measure the above performance of the laser, we proposed a novel measurement system based on the Fabry–Pérot cavity. We proved the feasibility of the scheme through theory and simulation. Then, the calibration of the experimental device and the measurement of the tested laser were completed. The measurement accuracy of this method is 1.2 kHz, and the measurement range reaches ±60 MHz, which can be adjusted by the modulation index. The results show that the laser has a frequency fluctuation of 30 MHz in the stabilization stage, and there is mainly a low-frequency component under 5 Hz in the frequency domain of the laser frequency fluctuation. Furthermore, this measurement scheme can be applied in other fiber sensor systems to evaluate the effect of laser frequency fluctuation on system output performance.

A discrete-time self-clocking complex electromechanical ƩΔM gyroscope with quadrature error cancellation

In this work, a new self-clocking electromechanical sigma-delta modulator (ƩΔM) quadrature error cancellation scheme for MEMS mode-matching gyroscopes is presented. The proposed techniques allow to decompose the gyroscope sense mode into in- and quadrature-phase signals and process it with two high-order sigma-delta control loops, achieving efficient noise shaping and error suppression. Furthermore, the system was designed with a self-clocking calibration scheme to provide temperature-independent turn-on bias output. Simulation results proved its robustness, a significant improvement for linearity and achieving over 80 dB attenuation of quadrature error. The hardware implementation comprising a discrete interface circuit and a wheel gyroscope was demonstrated. Measurement results validate the inherent loop quadrature cancellation scheme and demonstrate a sub-1°/hr bias instability (BI), with 5.5X and 3X improvement of BI and angle random walk (ARW) compared with a conventional single-loop ƩΔM gyroscope system. Combined with real-time self-clocking control, it yields an improvement of turn on bias error (1800s) and output linearity, achieving 1°/h and 0.021 %, respectively.

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

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

Nonlinear Performance of MEMS Vibratory Ring Gyroscope

Micro-electro-mechanical system (MEMS) gyroscopes are an important sort of inertial sensor for identifying parameters of spinning structures, such as the spinning speed and angular deviation, based on the Coriolis effect. In this paper, the nonlinear mechanism of MEMS vibratory ring gyroscopes is analyzed by applying a fully coupled nonlinear model, in which the gyroscopic coupling and geometrically and structurally nonlinear couplings are all taken into account. The coupled differential equations governing the drive and sense motions are established via the Lagrangian equations. Numerical simulation is conducted, and the key nonlinear components and energy transfer behaviors between the drive and sense modes are elucidated. It is revealed that the cubic rigidity nonlinearity is another significant factor leading to the coupling between the drive and sense modes other than the gyroscopic coupling. Perturbation analysis is also carried out by using the method of multiple scales. The nonlinear frequency–amplitude responses of the drive and sense vibrations are obtained, and comprehensive parametric studies are performed. The significant effects of system damping, excitation amplitude, drive amplitude and spinning speed on the responses are discussed, which will facilitate to improve the nonlinear performance and sensitivity of the gyroscope.