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.

Design and simulation of a silicon-based hybrid integrated optical gyroscope system

By combining a silicon-based lithium niobate modulator and a silicon-based Si3N4resonator with silicon-based photonics technology,a highly systematic design of a hybrid integrated optical gyroscope with enhanced reciprocity sensitivity and a dual micro-ring structure is proposed for the first time in this paper.The relationship between the device's structural parameters and optical performance is also analyzed by constructing a complete simulation link,which provides a theoretical design reference to improve the system's sensitivity.When the wavelength is 1550 nm,the conversion frequency of the dual-ring optical path is 50 MHz,the coupling coefficient is 0.2,and the radius R is 1000μm,the quality factor of the silicon-based Si_(3)N_(4)resonator is 2.58×10^(5),which is 1.58 times that of the silicon-on-insulator resonator.Moreover,the effective number of times the light travels around the ring before leaving the micro-ring is 5.93,which is 1.62 times that of the silicon-on-insulator resonator.The work fits the gyro dynamic output diagram,and solves the problem of low sensitivity at low speed by setting the phase offset.This results provide a basis for the further optimization of design and chip processing of the integrated optical gyroscope.

Parameter analysis for a nuclear magnetic resonance gyroscope based on ^(133)Cs–^(129)Xe/^(131)Xe

We theoretically investigate several parameters for the nuclear magnetic resonance gyroscope based on ^（133）C_（s–）^（129）Xe/^（131）Xe. For a cell containing a mixture of ^（133）Cs at saturated pressure, we investigate the optimal quenching gas（N_2） pressure and the corresponding pump laser intensity to achieve 30% ^（133）Cs polarization at the center of the cell when the static magnetic field B0 is 5 μT with different ^（129）Xe/^（131）Xe pressure. The effective field produced by spin-exchange polarized ^（129）Xe or ^（131）Xe sensed by ^（133）Cs can also be discussed in different^（129）Xe/^（131）Xe pressure conditions. Furthermore,the relationship between the detected signal and the probe laser frequency is researched. We obtain the optimum probe laser detuning from the D2（6~2S_（1/2）→ 6~2P_（3/2）） resonance with different ^（129）Xe/^（131）Xe pressure owing to the pressure broadening.

INVESTIGATION OF SENSITIVITY FOR SILICON MICROMECHANICAL TUNING-FORK GYROSCOPE

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谐振式光纤陀螺谐振腔传输模型仿真方法

谐振式光纤陀螺(RFOG)是一种以光纤环形谐振腔为核心敏感器件的惯性传感器。为提高仿真效率和适用性,提出了一种谐振式光纤陀螺快速运算仿真方法,搭建了谐振式光纤陀螺信号处理和闭环控制模型,其中模拟谐振腔多圈干涉耦合采用多核并行运算,包含光场叠加和传递函数两种形式。仿真结果表明所提方法仿真效率较高,平均在16s左右完成仿真,相比于原始模型的锁频程序运行效率提升了57.6%。同时两种仿真形式均适用于精度范围0.0001~1(°)/√h的谐振光纤陀螺仿真,有效适应不同仿真参数的测试要求。其中传递函数形式相较于光场叠加形式仿真效率提升了5.4倍,在±600(°)/s动态范围内标度因数非线性度降低了17%,而光场叠加形式的零偏不稳定性减小到0.652(°)/h,易于观察偏振波动误差特性。

宽谱光源谐振式光纤陀螺谐振特性分析

为优化宽谱光源谐振式光纤陀螺(RFOG)谐振腔设计,进行了RFOG谐振特性分析。首先,根据光场传输理论完成了宽谱RFOG光场传输特性分析,建立了宽谱RFOG谐振频差曲线模型,给出了谐振特性参数表达式。理论证明了宽谱RFOG的陀螺精细度和半高全宽约为谐振腔光谱曲线的1/2和2倍。其次,基于宽谱RFOG光场理论模型,分析了耦合器交叉耦合系数、附加损耗和谐振腔腔长等谐振腔关键光学参数对陀螺精细度和极限灵敏度的影响。最后,实验验证了谐振特性理论分析的正确性,并通过优化谐振腔参数实现陀螺零偏不稳定性0.059°/h,对谐振式光纤陀螺工程设计具有理论指导意义。

谐振式光纤陀螺系统建模及其应用研究

谐振式光纤陀螺作为高精度角速度传感器,以其集成化高、成本低以及抗干扰性强等独有优势,逐渐成为下一代光学陀螺研究发展的热点。通过对谐振式光纤陀螺工作原理的分析,建立了陀螺数字信号处理系统可视化模型,并对系统谐振曲线和同步解调曲线等开环输出以及锁频反馈下闭环输出进行了模拟仿真。利用仿真模型分析了正弦波调制下谐振谱分裂现象,并搭建实验装置对其进行了验证。结果表明,实验中正弦信号调制频率高于系统谐振输出半高全宽一半,即对应2 MHz时,谐振谱分裂会导致同步解调输出线性区域出现明显失真,严重恶化了标度因数线性度。因此,搭建的谐振式光纤陀螺仿真模型能够准确而有效地模拟系统的工作状态,在系统噪声抑制和精度提升方面具有指导性意义。

谐振式光学陀螺噪声抑制技术研究现状(特邀)

谐振式光学陀螺仪利用光学谐振腔在时空上对光波极强的局域增强效应,有望成为兼具高精度和小体积的光学陀螺。然而,谐振式陀螺转动产生的Sagnac效应相对微弱,容易受到陀螺系统内非互易性以及互易性噪声的干扰,成为其精度提升的瓶颈。在陀螺的小型化过程中这一问题更加凸显。因此,对谐振式光学陀螺仪进行噪声抑制显得尤为重要。本文详细综述了谐振式光学陀螺中非互易性和互易性两大类噪声的原理及其抑制方法,总结了该领域近来年的研究现状及未来挑战与发展趋势,为我国谐振式光学陀螺发展提供参考。

基于FPGA的硅微陀螺数字测控和温补技术研究

硅微陀螺仪由陀螺结构和测控电路组成,随着模拟接口电路的日臻完善,陀螺仪性能的提升主要靠数字电路中的测控和补偿算法;目前硅微陀螺测控电路正在向芯片化方向发展,为了加速硅微陀螺测控电路芯片化进程,用Verilog硬件描述语言设计了AGC和PLL对陀螺幅度和相位进行闭环控制,科氏力平衡进行闭环检测;对因加工造成的正交误差,设计了正交校正闭环;根据温度对陀螺仪的影响,对标度因数进行线性补偿,对零偏进行了BP神经网络补偿;实验结果表明,该控制系统下AGC相对稳定性为124 ppm,PLL相对稳定性为79.1 ppm,常温零偏稳定性为2.9°/h;在0~65℃内补偿前零偏稳定性为17.7°/h,补偿后零偏稳定性为9.1°/h,标度因数温度灵敏度降低1个数量级,不仅提升了硅微陀螺仪的性能,也为陀螺ASIC设计奠定了良好基础。

Y波导温致半波电压特性对谐振式光纤陀螺的影响

针对基于宽谱光源的谐振式光纤陀螺(resonant fiber optic gyroscope, RFOG)中Y波导调制器半波电压的温度影响,开展了Y波导温致半波电压特性对谐振式光纤陀螺影响的研究。建立了Y波导温致半波电压特性对基于宽谱光源的谐振式光纤陀螺系统标度因素的影响规律模型,模型表明:Y波导调制器的温致半波电压特性会导致基于宽谱光源的谐振式光纤陀螺系统的标度因素发生变化。搭建了用于宽谱光源的Y波导调制器半波电压测试系统,系统测试精度达1 mV。实验测试了全温范围内Y波导的温致半波电压特性在基于宽谱光源的谐振式光纤陀螺系统中的影响,测试结果表明:Y波导调制器的半波电压与温度呈线性负相关;Y波导调制器的温致半波电压特性导致基于宽谱光源的谐振式光纤陀螺系统的标度因素的最大相对变化误差为1 266.01×10^(-6)。

一种核磁共振陀螺横向磁场线圈耦合标定方法

磁场线圈是核磁共振陀螺磁场系统的核心部件,是惰性气体磁共振激励维持、主动磁补偿的核心部件。横向磁场线圈的耦合对磁补偿精度与磁共振激励都有较大影响。因此,横向磁场线圈的耦合标定尤为重要。为解决上述问题,提出了一种基于核磁共振陀螺内置磁力仪的横向磁场线圈耦合标定方法,通过理论仿真和实验设计,验证了其正确性与可行性。实验结果表明,采用所提出的耦合标定方法对X轴对Y轴耦合和Y轴对X轴耦合进行标定,分别为1.86%和3.11%。通过旋转线圈改变装配角度,表明此方法在较小旋转角度时,测量结果不受装配误差的影响。通过标定同一批次的5只线圈,根据结果从中选取耦合较小的线圈进行装配,为核磁共振陀螺线圈的筛选奠定了基础。

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.

Research progress of integrated optical gyroscope

Integrated optical gyroscopes(IOGs)have been an efficient tool for numerous applications in various fields,including inertial navigation,flight control,and earthquake monitoring.Here,we review the progress of integrated optical gyroscopes based on two categories of integrated interferometric optical gyroscopes(IIOGs)and integrated resonant optical gyroscopes(IROGs).

基于Rb-Xe体系核磁共振陀螺仪的Xe极化场测量方法

核磁共振陀螺仪具有小体积、高精度、低功耗等优点,是未来高精度微小型陀螺的主要发展方向之一。原子气室内Xe核自旋的极化是衡量原子气室性能的一个重要参数,直接影响陀螺的角随机游走,因此准确快速地测量极化场有利于研制性能更优的原子气室。为了实现Rb-Xe体系的核磁共振陀螺仪快速、原位测量Xe的极化场,提出了利用Rb电子顺磁共振频移测量Xe极化场的方法。通过激励磁场翻转Xe极化场,推导了估算Xe极化场的简单公式。实验测量了在典型核磁共振陀螺仪装置中,10nT量级的Xe极化场,结果与理论计算相符。表明这种方法能够快速有效地在核磁共振陀螺仪原位测量Xe的极化场。

宽谱光源驱动的高精度谐振式光纤陀螺

针对高精度惯性导航系统对高精度小型化光纤陀螺的发展需求,开展了宽谱光源驱动的谐振式光纤陀螺(RFOG)技术研究。首先介绍了宽谱谐振式光纤陀螺的工作原理,对比分析了该种陀螺在角度随机游走上相对于发展较为成熟的干涉式光纤陀螺的优势;讨论了受散粒噪声制约的理论角度随机游走的影响因素,并结合光纤耦合器的损耗系数和谐振腔内的光纤传输损耗,对耦合器的耦合系数进行了优化设计,获得了宽谱RFOG系统的最佳角度随机游走理论值;利用优化后的耦合系数,设计并研制了总长为1020 m、内径为15 cm的透射式光纤环形谐振腔,并完成了宽谱RFOG系统的研制和测试。测试结果表明,陀螺角度随机游走为2.1×10^(-4)(°)/h^(1/2),零偏不稳定性为4.6×10^(-4)(°)/h,达到了战略级陀螺的精度范围。

Measuring Transverse Relaxation Time of Xenon Atoms Based on Single Beam of Laser in Nuclear Magnetic Resonance Gyroscope

Nuclear magnetic resonance gyroscope (NMRG) has the characteristics of high precision and miniaturization, and is one of the main applications of quantum technology in the field of navigation. The transverse relaxation time (T_(2)) of the xenon nuclear spin in the atomic cell of the NMRG directly affects the angular random walk of the gyro. Accurate and rapid measurement of T_(2) is conducive to further improvement of gyroscope. At present, for the measurement of T_(2), the schemes of two orthogonal lasers for pumping and detecting are usually used. By applying two fast-switching orthogonal static magnetic fields and a single beam of circularly polarized laser with corresponding wavelength to pump the atomic cell, the xenon nuclear macroscopic magnetic moment Larmor precession is generated. The cesium atoms parametric magnetometer in cell is formed to detect the free induction decay signal generated by nuclear spin precession of xenon atoms. The measurement of T_(2) by a single laser simplifies the measurement equipment compared with traditional method with two lasers. The experimental results show that the T_(2) of xenon atoms is more than 10 s, and the effects of temperature are studied, which lay the foundation for the subsequent improvement of gyro performance.

Resonant pitch and roll silicon gyroscopes with sub-micron-gap slanted electrodes:Breaking the barrier toward high-performance monolithic inertial measurement units

This paper presents the design,fabrication,and characterization of a novel high quality factor(Q)resonant pitch/roll gyroscope implemented in a 40μm(100)silicon-on-insulator(SOI)substrate without using the deep reactive-ion etching(DRIE)process.The featured silicon gyroscope has a mode-matched operating frequency of 200 kHz and is the first out-of-plane pitch/roll gyroscope with electrostatic quadrature tuning capability to fully compensate for fabrication non-idealities and variation in SOI thickness.The quadrature tuning is enabled by slanted electrodes with sub-micron capacitive gaps along the(111)plane created by an anisotropic wet etching.The quadrature cancellation enables a 20-fold improvement in the scale factor for a typical fabricated device.Noise measurement of quadrature-cancelled mode-matched devices shows an angle random walk(ARW)of 0.63°√h^(−1) and a bias instability of 37.7°h^(−1),partially limited by the noise of the interface electronics.The elimination of silicon DRIE in the anisotropically wet-etched gyroscope improves the gyroscope robustness against the process variation and reduces the fabrication costs.The use of a slanted electrode for quadrature tuning demonstrates an effective path to reach high-performance in future pitch and roll gyroscope designs for the implementation of single-chip high-precision inertial measurement units(IMUs).

Analysis of resonance asymmetry phenomenon in resonator integrated optic gyro

Resonator integrated optic gyro （RIOG） is a high-accuracy gyroscope based on the Sagnac effect. The waveguide- type ring resonator is a key rotation sensing element in the RIOG. An asymmetric resonance line shape is found in the optic resonator. These asymmetries will induce offset errors when the phase modulation spectroscopy technique （PMST） is applied to the RIOG. The polarization errors and the difference among normal mode losses are found to be the two main sources of resonance asymmetry in an experiment. These sources are fully investigated and their contributions to the offset errors are compared. The analysis shows that proper modulation frequencies in clockwise （CW） and counterclockwise （CCW） directions can reduce an RIOG bias error. A transmissive resonator is recommended to obtain a better resonance line shape.

Suppression of backscattering induced noise by the sideband locking technique in a resonant fiber optic gyroscope

Polarization fluctuation induced noise and backscattering-induced noise are the dominant noises in resonant fiber optic gyroscopes. This Letter proposes a new method to suppress the carrier and backscattering induced noise by the sideband locking technique. Besides choosing an optimized modulation depth and different clockwise and counterclockwise modulation frequencies, the sideband is locked to the cavity resonance. With the proper modulation frequency, the carrier frequency component locates at a position far away from the resonant frequency, and then it is suppressed by the cavity itself, which can be taken as a bandpass filter. The amplitude of the carrier frequency can be suppressed by 20–25 d B additionally by the cavity and the total intensity suppression ratio can reach 115.74 d B. The backscattering induced noise can be eliminated for the adoption of different frequencies. The method can realize a stable and high suppression ratio without high requirements for parameter accuracy or device performance.

Effects of Material and Dimension on TCF,Frequency,and Q of Radial Contour Mode AlN-on-Si MEMS Resonators

This paper investigates the effects of material and dimension parameters on the frequency splitting,frequency drift,and quality factor(Q)of aluminium nitride(AlN)-on-n-doped/pure silicon(Si)microelectromechanical systems(MEMS)disk resonators through analysis and simulation.These parameters include the crystallographic orientation,dopant,substrate thickness,and temperature.The resonators operate in the elliptical,higher order,and flexural modes.The simulation results show that i)the turnover points of the resonators exist at 55°C,-50°C,40°C,and-10°C for n-doped silicon with the doping concentration of 2×1019 cm-3 and the Si thickness of 3.5μm,and these points are shifted with the substrate thickness and mode variations;ii)compared with pure Si,the modal-frequency splitting for n-doped Si is higher and increases from 5%to 10%for all studied modes;iii)Q of the resonators depends on the temperature and dopant.Therefore,the turnover,modal-frequency splitting,and Q of the resonators depend on the thickness and material of the substrate and the temperature.This work offers an analysis and design platform for high-performance MEMS gyroscopes as well as oscillators in terms of the temperature compensation by n-doped Si.