Stability analysis of a new class of MEMS gyroscopes with parametric resonance

In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is demonstrated that the stability of the origin always contributes to a zero response for the sensor, and hence the instability of origin is required for the occurrence of parametric resonance. In contrast, stability of a periodic orbit does not necessarily guarantee a resonant response for the gyroscope, and again it is the instability of the origin which is required for this purpose. Because in the case of linear stiffness—linear parametric excitation the instability of the origin results in instability of the system, it is concluded that nonlinearities are required for a parametrically actuated gyroscope.     

Towards a biomimetic gyroscope inspired by the fly's haltere using microelectromechanical systems technology

Flies use so-called halteres to sense body rotation based on Coriolis forces for supporting equilibrium reflexes. Inspired by these halteres, a biomimetic gimbal-suspended gyroscope has been developed using microelectromechanical systems (MEMS) technology. Design rules for this type of gyroscope are derived, in which the haltere-inspired MEMS gyroscope is geared towards a large measurement bandwidth and a fast response, rather than towards a high responsivity. Measurements for the biomimetic gyroscope indicate a (drive mode) resonance frequency of about 550 Hz and a damping ratio of 0.9. Further, the theoretical performance of the fly''s gyroscopic system and the developed MEMS haltere-based gyroscope is assessed and the potential of this MEMS gyroscope is discussed.     

基于阿伦方差的微机电陀螺误差建模及其粒子滤波

基于Allan方差对微机电陀螺的随机漂移误差进行分析和建模,并通过粒子滤波提高了微机电陀螺的零偏稳定性.实验结果表明,这种方法比较简单而切实可行,可以明显提高微机电陀螺仪的零偏稳定性.     

时滞位移反馈作用下多自由度微陀螺的刚度非线性及控制研究

为揭示多自由度微陀螺非线性系统中位移反馈项对系统动力学特性的影响规律,探索对非线性的控制方法,以一类四自由度静电驱动微机械陀螺为研究对象,采用多尺度法对微陀螺受控系统在频域和时域中的动力学特性进行了分析。研究发现:时滞量为整周期或半周期时反馈增益可有效的对系统共振频率进行调节;时滞量为四分之一或四分之三周期时,反馈增益主要影响幅值大小,共振频率基本保持不变;反馈控制参数选取得当可消除非线性引起的多稳态解,增加陀螺的灵敏度稳定性,选取不当会导致系统出现复杂的概周期运动使灵敏度稳定性遭到破坏。     

伪随机调制在全数字闭环光纤陀螺中的应用

伪随机调制信号的抗干扰能力强,获得同样的信号,对系统正常运行的干扰程度比其他测试信号低。光纤陀螺的输出信号微弱,背景噪声强,在频域随机分布,增加了信号处理的难度。结合伪随机调制的优势,在原有的数字闭环信号处理的基础上,提出了一种新的信号处理方案:伪随机调制解调方案,与数字闭环方案相互配合,有效提取环境因变量,反馈至系统使之实时做出补偿,提高陀螺稳定性。     

Modal Coupling in Micromechanical Vibratory Rate Gyroscopes

The authors present modeling approaches to describe the coupling of modes in a resonant vibratory rate gyroscope. Modal coupling due to off-diagonal stiffness and damping terms is considered. Three analytical modeling approaches are presented in the context of a$z$-axis micromechanical vibratory rate gyroscope fabricated in an integrated polysilicon surface-micromachining process. The first approach is based on frequency-response analysis of the gyroscope output. The second approach takes the route of state-space-based system identification to identify the modal-coupling parameters. A third approach based on measured vibration data identifies the coupling parameters due to stiffness and damping. These three methods are then applied to predict the extent of displacement and force coupling between the drive and the sense axes of an existing device as a function of varying degrees of matching between the resonant frequencies associated with the drive and the sense modes. Experimental data show that as the resonant frequencies of the drive and sense modes are brought closer together, an improvement in overall resolution and scale factor of the device is obtained at the expense of an enhanced coupling of forces to displacements between the two axes and the onset of instability for an open-loop sensing implementation.     

Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation

The asymptotic Lyapunov stability with probability one of a Duffing system with time-delayed feedback control under bounded noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original system, and the asymptotic Lyapunov stability with probability one of the original system can be determined approximately by using the Lyapunov exponent. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. The theoretical results are well verified through digital simulation.     

Nonresonant micromachined gyroscopes with structural mode-decoupling

This paper reports a novel four-degrees-of-freedom (DOF) nonresonant micromachined gyroscope design concept that addresses two major MEMS gyroscope design challenges: eliminating the mode-matching requirement and minimizing instability and drift due to mechanical coupling between the drive and sense modes. The proposed approach is based on utilizing dynamical amplification both in the 2-DOF drive-direction oscillator and the 2-DOF sense-direction oscillator, which are structurally decoupled, to achieve large oscillation amplitudes without resonance. The overall 4-DOF dynamical system is composed of three proof masses, where second and third masses form the 2-DOF sense-direction oscillator, and the first mass and the combination of the second and third masses form the 2-DOF drive-direction oscillator. The frequency responses of the drive and sense direction oscillators have two resonant peaks and a flat region between the peaks. The device is nominally operated in the flat regions of the response curves belonging to the drive and sense direction oscillators, where the gain is less sensitive to frequency fluctuations. This is achieved by designing the drive and sense anti-resonance frequencies to match. Consequently, by utilizing dynamical amplification in the decoupled 2-DOF oscillators, increased bandwidth and reduced sensitivity to structural and thermal parameter fluctuations and damping changes are achieved, leading to improved robustness and long-term stability over the operating time of the device.     

An exact solution of the first-exit time problem for a class of structural systems

The mean time to escape from a region of desired operations is one the basic reliability measures in stochastic dynamics. In general, a precise solution of the first-exit time problem is unavailable. This paper demonstrates an exact solution of the mean exit time problem for a multidimensional non-dissipative Lagrangian system excited by additive Gaussian white noise. We identify the Fokker–Planck equation whose solution characterizes the mean time needed to reach a critical energy and explicitly construct the solution. For illustration, we apply the developed theory to engineering examples. We calculate the mean time of the standard operation for a flexural nanotube with likely noise-induced buckling and analyze the mean time of the stable functioning for a gyroscope subjected to random and dissipation torques. It is demonstrated that the solution of the first-exit time problem for a non-dissipative system gives a quite good approximation to a numerical solution of a similar problem for a system with small dissipation.     

激光陀螺随机噪声参数估计和滤波方法研究

激光陀螺(RLG)中随机噪声是影响其精度的一个重要因素,针对其噪声的特殊性质,采用小波方法去除随机噪声,提高激光陀螺的精度。通过小波分析的参数估计方法获得噪声参数,并用小波阈值滤波方法去除噪声,对某型号的RLG的滤波结果表明了该方法的有效性。     

Stochastic properties of a system of point vortices

The dynamic and stochastic properties of a system of point vortices occurring at the vertices of a regular N-gon have been investigated. The time of reversibility of the phase trajectories was determined and their stability was studied. It is established that such a system exhibits stochastic properties only in the presence of a local instability, which is possible for N≥8.     

基于环形激光陀螺调制输出的寻北系统

利用环形激光陀螺对角速度输入量具有较高灵敏度的特点,提出了一种新型的激光陀螺寻北系统,将一环形激光陀螺垂直安3 水平的恒速转台上,使输入轴与台面平行,通过测量地球自转角速度的向向分量,实现寻北过程,通过与其对称放的加速度计可以测量出由于轴系安装和系统调平引起的台面倾斜误差,从而对激光陀螺的数据出量进行补偿,同时采用单周期多位置采集技术和多周期重复测量的方法,有效地抑制了激光陀螺的测量噪声,最大限度地减少了随机误差和系统误差的影响,提出了系统的寻北精度,适合多种领域的需要。     

Generation of fast charged particles in a superposition of oscillating electric fields with stochastically jumping phases

The motion of a nonrelativistic charged particle in an alternating electric field representing a superposition of monochromatic waves with phases described by stochastic jumplike functions of time has been studied. Statistical analysis is performed in the framework of an exactly solvable model, in which the phases are treated as independent random telegraph signals. The mean kinetic energy of the charged particle is calculated. It is shown that there is a manifold of characteristics of stochastically jumping phases (shift amplitudes and mean frequencies) for which the oscillating mean energy grows with the time. For time periods much greater than the characteristic decay time of phase correlations, the mean kinetic energy linearly increases with time (stochastic heating). The growth rate nonmonotonically depends on the parameters of phase jumps, and the maximum increment is proportional to the number of harmonics.     

谐振式光纤陀螺的数字检测方案及其优化设计

提出了一种基于 DSP 芯片实现的双频率数字调制谐振式光纤陀螺系统的闭环检测方案。在此方案中,利用带通滤波器从探测器的输出光强信号中提取其基波频率的正弦信号,通过相关检测原理去掉干扰的噪声,并利用低通滤波器提取与探测器输出光强幅度直接成正比的直流信号,将其转换成相应的谐振频差,利用此频差即可求得陀螺的旋转角速度。此方案检测线路简单,操作方便,基于 DSP 芯片的实现则大大提高了系统处理速度。同时,还利用 Matlab 软件对检测系统中的滤波器参数进行了优化设计,提高了系统的检测精度。     

Direct control method for improving stability and reliability of nonlinear stochastic dynamical systems

Optimal control for improving the stability and reliability of nonlinear stochastic dynamical systems is of great significance for enhancing system performances. However, it has not been adequately investigated because the evaluation indicators for stability (e.g. maximal Lyapunov exponent) and for reliability (e.g. mean first-passage time) cannot be explicitly expressed as the functions of system states. Here, a unified procedure is established to derive optimal control strategies for improving system stability and reliability, in which a physical intuition-inspired separation technique is adopted to split feedback control forces into conservative components and dissipative components, the stochastic averaging is then utilized to express the evaluation indicators of performances of controlled system, the optimal control strategies are finally derived by minimizing the performance indexes constituted by the sigmoid function of maximal Lyapunov exponent (for stability-based control)/the reciprocal of mean first-passage time (for reliability-based control), and the mean value of quadratic form of control force. The unified procedure converts the original functional extreme problem of optimal control into an extremum value problem of multivariable function which can be solved by optimization algorithms. A numerical example is worked out to illustrate the efficacy of the optimal control strategies for enhancing system performance.     

单轴光纤陀螺光学结构的研究与实现

针对实际系统中的单轴干涉式光纤陀螺仪结构与稳定性问题,提出将Lyot消偏器引入到陀螺光学结构中,新结构在不改变原陀螺光路高精度特性的基础上,使系统输入极低偏振度的自然光,提高了单轴光纤陀螺的精度和稳定性.利用琼斯矩阵与干涉矩阵建立了单轴干涉式光纤陀螺的系统模型,对该陀螺的输出及零点偏移情况进行了仿真分析和实验研究.结果表明,该设计结构在提高了陀螺系统的精度与稳定性的同时,还在一定程度上降低了系统对光源偏振度的要求.     

具有栅结构与静电梳齿驱动的电容式微机械陀螺的仿真、设计与测试

电容式陀螺仪是一种振动式陀螺仪,由于加工的特殊性使其具有了传统的陀螺无法比拟的优点,从而拓宽了其应用领域.为了提高陀螺仪的检测精度,本文提出了一种静电梳齿驱动、栅结构的电容式检测的微机械陀螺仪的设计方法,并分析了其工作原理.运用ANSYS软件对陀螺结构进行了仿真和模态分析,仿真结果与理论计算结果相接近.所设计的陀螺结构采用体硅标准工艺方法进行了设计,并对其进行了流片加工和封装,最终得到了电容式微机械陀螺仪.实验测试的结果表明,陀螺驱动模态的固有频率为4.06kHz,灵敏度为0.027 9 v/((°)s-1).     

非线性时变结构随机地震响应最优多项式控制

以随机地震动作用下具有Bouc-Wen滞回特性的非线性结构系统为受控对象,开展了最优多项式控制算法研究：包括系统矩阵中Maclaurin展开取初始零值衍生的具有时不变增益矩阵的控制律,和系统矩阵中Maclaurin一阶展开衍生的具有时变增益矩阵的控制律。研究表明,受控结构层间位移响应的变异性明显降低,结构的安全性显著提高。同时,基于时不变增益矩阵的控制律的控制效果在一定程度上受制于控制力施加的大小与系统稳定性之间的平衡关系,而考虑了每一个时间步位移和速度对增益矩阵影响、基于时变增益矩阵的控制律则能以较小的控制出力获得较好的控制效果。     

Stochastic stability of SDOF linear viscoelastic system under wideband noise excitation

The stochastic moment stability and almost-sure stability of a single-degree-of-freedom (SDOF) viscoelastic system subject to parametric fluctuation is investigated by using the method of higher-order stochastic averaging. The stochastic parametric excitation is modeled as a wideband noise, which is taken as Gaussian white noise and real noise. The viscoelastic material is assumed to follow ordinary Maxwell linear constitutive relation. For small damping and weak stochastic fluctuation, analytical expressions are derived for the moment Lyapunov exponent and the Lyapunov exponent, which indicate moment stability and almost-sure stability respectively. The effects of various system and loading parameters on the stochastic stability are discussed. Both analytical and simulation results show that higher-order stochastic averaging improves the accuracy compared with the first-order stochastic averaging. However, results of the third-order averaging are almost overridden by those of second-order averaging and the third-order averaging involves far more calculation. It is advisable to consider a balance between accuracy achievement and calculation endeavor when using higher-order stochastic averaging.     

用于微小型飞行器姿态估计的四元数扩展卡尔曼滤波算法

针对MEMS陀螺、加速度计、磁强计组合的姿态确定系统,笔者设计了用于微小型飞行器姿态估计的四元数扩展卡尔曼滤波算法．取姿态误差四元数和陀螺随机漂移构建滤波状态向量,通过误差四元数微分方程和陀螺随机误差模型建立了卡尔曼滤波状态方程;采用改进的高斯-牛顿算法将传感器观测量转化为四元数,通过与利用陀螺信息估计的四元数相乘,得到姿态误差四元数作为卡尔曼滤波量测值,显著减小了机动加速度对姿态估计的影响．仿真实验显示：四元数静态估计误差小于0．22％,在动态情况下,四元教估计值能够较好地跟踪真实值的变化,表明该滤波算法能够有效提高姿态估计的精度．