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^(-12)ppm.Under the dynamic asymmetry variation condition,the root mean square errors(RMSE)indicate that the tracking accuracy can reach the level of10^(-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.

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.

Influence of flexible solar arrays on vibration isolation platform of control moment gyroscopes

A high-performance vibration isolation platform （VIP） has been developed for a cluster of control moment gyroscopes （CMGs）. CMGs have long been used for satellite attitude control. In this paper, the influence of flexible solar arrays on a passive multi-strut VIP of CMGs for a satellite is analyzed. The reasonable parameters design of flexi- ble solar arrays is discussed. Firstly, the dynamic model of the integrated satellite with flexible solar arrays, the VIP and CMGs is conducted by Newton-Euler method. Then based on reasonable assumptions, the transmissibility matrix of the VIP is derived. Secondly, the influences of the flexible solar arrays on both the performance of the VIP and the stability of closed-loop control systems are analyzed in detail. The parameter design limitation of these solar arrays is discussed. At last, by selecting reasonable parameters for both the VIP and flexible solar arrays, the attitude stabilization performance with vibration isolation system is predicted via simulation.

Finite-time stabilization of uncertain non-autonomous chaoticgyroscopes with nonlinear inputs

Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes （VSCMGs） with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account, a feedback control law is designed for the system based on a method of nonlinear model predictive control （NMPC）. The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.

A Statistical Parameter Analysis and SVM Based Fault Diagnosis Strategy for Dynamically Tuned Gyroscopes

Gyro's fault diagnosis plays a critical role in inertia navigation systems for higher reliability and precision. A new fault diagnosis strategy based on the statistical parameter analysis (SPA) and support vector machine (SVM) classification model was proposed for dynamically tuned gyroscopes (DTG). The SPA, a kind of time domain analysis approach, was introduced to compute a set of statistical parameters of vibration signal as the state features of DTG, with which the SVM model, a novel learning machine based on statistical learning theory (SLT), was applied and constructed to train and identify the working state of DTG. The experimental results verify that the proposed diagnostic strategy can simply and effectively extract the state features of DTG, and it outperforms the radial-basis function (RBF) neural network based diagnostic method and can more reliably and accurately diagnose the working state of DTG.

Design and Fabrication of MEMS Gyroscopes on the Silicon-on-insulator Substrate with Decoupled Oscillation Modes

The mode coupling is a major factor to affect the precision of the micro electromechanical systems（MEMS） gyroscope. Currently, many MEMS gyroscopes with separate oscillation modes for drive and detection have been developed to decrease the mode coupling, but the gyroscope accuracy can not satisfy the high-precision demand well. Therefore, high performance decoupled MEMS gyroscopes is still a hot topic at present. An innovative design scheme for a MEMS gyroscope is designed, and in this design, the inertial mass is divided into three parts including the inner mass, the outer mass and the main frame mass. The masses are supported and separated by a set of mutually orthogonal beams to decouple their movements. Moreover, the design is modelled by multi-port-element network（MuPEN） method and the simulation results show that the mode coupling of the gyroscope between driving and sensing mode was eliminated effectively. Furthermore, we proposed a new silicon-on-insulator（SOI） process to fabricate the gyroscope. The scale factor of the fabricated gyroscope is 8.9 mV/（（~）os） and the quality factor（Q-factor） is as high as 600 at atmosphere pressure, and then, the resonant frequency, scale factor and bias drift has been test. Process and test results show that the proposed MEMS gyroscope are effective for decrease mode coupling, furthermore, it can achieve a high performance at atmosphere pressure. Furthermore, the MEMS gyroscope can achieve a high performance at atmosphere pressure. The research can be taken as good advice for the design and fabrication of MEMS gyroscope, meanwhile, it also provides technical support for speeding up of MEMS gyroscope industrialization.

A Low-Noise Readout Circuit for Gyroscopes

In order to suppress the noise of gyroscopes,the method based on lock-in amplifier and capacitor matching of the low-noise readout circuit is proposed. Firstly,the principle to suppress the noise by lock-in amplifier is analyzed,and the noise model of front end is proposed. Secondly,the noise optimization for the charge amplifier is presented according to the noise model of front end. Finally,a readout circuit is constructed by this approach. The measurement results show that the parasitic capacitance of front end is 18 p F,and the noise at resonant frequency( 4 k Hz) is 133 n V / Hz1 / 2,and the overall bias stability is 30° /h,and the noise level is 0. 003° /( s·Hz1 / 2). The noise of the gyroscope with the low-noise readout by this method is suppressed effectively.

Temperature compensation method for low cost three-axis MEMS digital angular rate gyroscopes

In recent years,a large number of small volume,low cost micro electro mechanical systems（MEMS）digital three-axis angular rate gyroscopes have been developed and widely used in civil and military fields.However,these kinds of gyroscopes have poor performances in initial zero-bias,temperature drift,In-Run bias stability,bias repeatability,etc.,their output errors need to be compensated before being used.Based on a lot of experiments,the temperature drift and the initial zero-bias are the major error sources in the MEMS gyroscopes output data.Due to the poor repeatability of temperature drift,the temperature compensation coefficients need to be recalculated every time before using.In order to recalculate parameters of the temperature compensation model quickly,a 1st-order polynomial model of temperature is established,then a forgetting factor recursive least squares estimator will be adopted to identify the model parameters in real time.Static and dynamic experimental data shows that this method removed/compensated the temperature drift and initial zero-bias from the output of the gyroscopes effectively.

GNSS gyroscopes:determination of angular velocity and acceleration with very high-rate GNSS

Although global navigation satellite systems(GNSS)have been routinely applied to determine attitudes,there exists no literature on determining angular velocity and/or angular acceleration from GNSS.Motivated by the invention of computerized accelerometers of the correspondence author and following the success of accurately recovering translational velocity and acceleration waveforms from very high-rate GNSS precise positioning by Xu and his collaborators in 2021,we propose the concept of GNSS gyroscopes and reconstruct angular velocity and acceleration from very high-rate GNSS attitudes by applying regularization under the criterion of minimum mean squared errors.The major results from the experiments can be summarized in the following:(i)angular velocity and acceleration waveforms computed by applying the difference methods to high-rate GNSS attitudes are too noisy and can be physically not meaningful and numerically incorrect.The same can be said about inertial measurement unit(IMU)attitudes,if IMU gyros are not of very high accuracy;(ii)regularization is successfully applied to reconstruct the high-rate angular velocity and acceleration waveforms from 50 Hz GNSS attitudes and significantly outperforms the difference methods,validating the proposed concept of GNSS gyroscopes.By comparing the angular velocity and acceleration results by using the difference methods and regularization,we find that the peak values of angular velocity and acceleration by regularization are much smaller by a maximum factor of 1.57 in the angular velocity to a maximum factor of 8662.53 times in the angular acceleration in the case of high-rate GNSS,and by a maximum factor of 1.26 in the angular velocity to a maximum factor of 2819.85 times in the angular acceleration in the case of IMU,respectively;and(iii)the IMU attitudes apparently lead to better regularized angular velocity and acceleration waveforms than the high-rate GNSS attitudes,which can well be explained by the fact that the former is of better accuracy than the latter.As a result,to suppress the significant amplification of noise in GNSS attitudes,larger regularization parameters have to be chosen for the high-rate GNSS attitudes,resulting in smaller peak angular accelerations by a maximum factor of 37.55 percent in the angular velocity to a maximum factor of 6.20 times in the angular acceleration in comparison of the corresponding IMU results.Nevertheless,the regularized angular acceleration waveforms for both GNSS and IMU look more or less similar in pattern or waveform shape.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

A D-optimal Multi-position Calibration Method for Dynamically Tuned Gyroscopes

This paper presents a novel experimental design to greatly improve the calibration accuracy of the acceleration-insensitive bias and the acceleration-sensitive bias of the dynamically tuned gyroscopes（DTGs）.In order to reduce experimental cost,the D-optimal criteria with constraints are constructed.The turntable positions and the number of test points are chosen to build D-optimal experimental designs.The D-optimal experimental designs are tested by multi-position calibration experiment for tactical-grade DTGs.Test results show that,with the same cost,the fit uncertainty is reduced by about 50% by using the D-optimal 8-position experimental procedure,compared to using a defacto standard experimental procedure in ANSI/IEEE Std 813-1988.Furthermore,the new experimental procedure almost achieves optimal accuracy with only 12-position which is half the cost of the widely adopted 24-position experimental procedure for achieving optimal accuracy.

Decentralized adaptive sliding mode control of a space robot actuated by control moment gyroscopes

An adaptive sliding mode control （ASMC） law is proposed in decentralized scheme for trajectory tracking control of a new concept space robot. Each joint of the system is a free ball joint capable of rotating with three degrees of freedom （DOF）. A cluster of control moment gyroscopes （CMGs） is mounted on each link and the base to actuate the system. The modified Rodrigues parameters （MRPs） are employed to describe the angular displacements, and the equations of motion are derived using Kane＇s equations. The controller for each link or the base is designed sep- arately in decentralized scheme. The unknown disturbances, inertia parameter uncertainties and nonlinear uncertainties are classified as a ＂lumped＂ matched uncertainty with unknown upper bound, and a continuous sliding mode control （SMC） law is proposed, in which the control gain is tuned by the improved adaptation laws for the upper bound on norm of the uncertainty. A gen- eral amplification function is designed and incorporated in the adaptation laws to reduce the control error without conspicuously increasing the magnitude of the control input. Uniformly ultimate boundedness of the closed loop system is proved by Lyapunov＇s method. Simulation results based on a three-link system verify the effectiveness of the proposed controller.

Er-doped fiber ring laser gyroscopes operating in continuous waves

A direction related polarizer was inserted into a ring laser cavity to eliminate one of the two eigen-modes as well as spatial hole burning of the gain medium in a bidirectional Er-doped fiber ring laser. Thus, a fiber ring laser gyroscope （FRLG） operating in continuous wave was demonstrated. A beat signal of over 30-dB noise was observed and a good linear relation between the beat frequency shift and cavity rotation rate was obtained.

Gyroscope Dynamic Balance Counterweight Prediction Based on Multi-Head ResGAT Networks

The dynamic balance assessment during the assembly of the coordinator gyroscope significantly impacts the guidance accuracy of precision-guided equipment.In dynamic balance debugging,reliance on rudimentary counterweight empirical formulas persists,resulting in suboptimal debugging accuracy and an increased repetition rate.To mitigate this challenge,we present a multi-head residual graph attention network(ResGAT)model,designed to predict dynamic balance counterweights with high precision.In this research,we employ graph neural networks for interaction feature extraction from assembly graph data.An SDAE-GPC model is designed for the assembly condition classification to derive graph data inputs for the ResGAT regression model,which is capable of predicting gyroscope counterweights under small-sample conditions.The results of our experiments demonstrate the effectiveness of the proposed approach in predicting dynamic gyroscope counterweight in its assembly process.Our approach surpasses current methods in mitigating repetition rates and enhancing the assembly efficiency of gyroscopes.

Response analysis of NMRG system considering Rb-Xe coupling

The dynamic range of the nuclear magnetic resonance gyroscope can be effectively improved through the closedloop control scheme,which is crucial to its application in inertial measurement.This paper presents the analytical transfer function of Xe closed-loop system in the nuclear magnetic resonance gyroscope considering Rb–Xe coupling effect.It not only considers the dynamic characteristics of the system more comprehensively,but also adds the influence of the practical filters in the gyro signal processing system,which can obtain the accurate response characteristics of signal frequency and amplitude at the same time.The numerical results are compared with an experimentally verified simulation program,which indicate great agreement.The research results of this paper are of great significance to the practical application and development of the nuclear magnetic resonance gyroscope.

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method.

Design of the low-loss waveguide coil for interferometric integrated optic gyroscopes

With the development of manufacturing technology,the propagation loss of the planar waveguide is getting lower and lower,and the shot-noise-limited sensitivity of an HOG will be greatly improved.When the propagation loss is getting lower,improper coupling-out waveguide in the waveguide coil may lead to non-ignorable bending loss and crosstalk because of the small radius of curvature and X-junction.In this paper,different couplingout waveguides have been designed.After calculation and optimization by the beam propagation method,we found the proper coupling-out waveguide having relatively low propagation loss,which can improve the sensitivity of the HOG.

The effect of parasitic charge on the output stability of MEMS gyroscopes

Output voltage drifting was observed in MEMS gyroscopes. Other than the quadrature error, frequency mismatch and quality factor, the dielectric parasitic charge was thought to be a major determinant. We studied the mechanism and variation of the parasitic charge in the MEMS gyroscopes, and analyzed the effect of the parasitic charge on the output stability. This phenomenon was extremely obvious in the Pyrex encapsulated MEMS gyroscopes. Due to the DC voltage required for the electrostatic actuation, the parasitic charge in the dielectric layer would accumulate and induce a residual voltage. This voltage had an impact on the resonant frequency of the gyroscopes, so as to affect the output stability. The theoretical studies were also confirmed by our experimental results. It was shown that the parasitic charge was harmful to the output stability of MEMS gyroscopes.

Closed loop control design for the sense mode of micromachined vibratory gyroscopes

This paper presents a novel design method of force rebalance control for the sense mode of micromachined vibratory gyroscopes.Specific theoretical deductions are performed to identify a precise linear model of the open loop system of the sense mode,which is crucial for the PI controller design.The frequency responses obtained by experimental tests agree well with those calculated with the theoretical model,indicating the accuracy of the theoretical analyses.Experimental results demonstrate that the bandwidth of the closed loop is extended to 94.8 Hz from 2.3 Hz in the open loop and the quadrature signal is suppressed by about 64 dBV in the closed loop system.The overshoot and stable time in the step response of the closed loop system are measured to be about 15% and 35 ms,respectively.The mode-splitting gyroscope with the closed loop controlled sense mode achieves a scale factor of 41.0 mV/deg/s with nonlinearity of 0.09% and asymmetry of 1%,and a bias instability of 4.0 °/h with angle random walk of 0.171 deg/h1/2.