Stability of Gyro with Harmonic Nonlinearity in Spinning Vehicle

A stability analysis of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain angular velocity ?z about the spin axis of the gyro is presented. The complete nonlinear equation of motion, which includes the fundamental and second harmonic nonlinear terms, arising due to ?z, is considered. For time-varying ?z(t), using the circle criterion, it is shown that the gimbal motion is globally asymptotically stable if the Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. For the case of uncertain constant ?z, using the Lyapunov approach, conditions for global asymptotic stability (GAS) and asymptotic stability are derived. Stable regions in parameter space of the gyro and state space are obtained. Analytical relations for the selection of gyro parameters are derived.     

Stability of Gyro in a Vehicle Spinning with Uncertain Angular Velocity

The analysis of a single-axis rate gyroscope mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using circle criterion, it is shown that the gimbal motion is globally asymptotically stable if Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. A simple analytical relation for the selection of gyro parameters for stability is derived.     

Gyro Motion Boundedness under Uncertain Angular Acceleration about Vehicle Output Axis

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which has uncertain time-varying acceleration and deceleration ?x(t) about the output axis of the gyro is presented. Using a Lyapunov function, a condition for boundedness of the gyro motion is derived. It is shown that by a proper selection of the parameters of the gyro, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in ? - ? plane after a certain finite interval of time for any bounded uncertain ?x(t). Analytical relations for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ?x within desirable limits are derived.     

Gyro Motion Boundedness under Uncertain Vehicle Spin and Acceleration

An analysis is presented of the motion of a single axis rate gyroscope mounted in a space vehicle, which is simultaneously accelerating and spinning about the output and spin axis, respectively, of the gyro. The time-varying acceleration and deceleration ?x(t) and the spin rate ?z(t) of the vehicle are unknown but bounded functions of time t. It is shown that the motion of the gyro remains bounded if the bound ?*2 on the uncertainty in ?z(t) does not exceed some threshold ?*2 and that this threshold depends on the various parameters of the gyro. Furthermore, by a proper selection of the gyro parameters, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in ?-? plane after a certain finite interval of time for any bounded uncertain ?x(t) and ?z(t). Analytical relations are derived for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ?x and ?z within any given limit.     

Stability of 2-Degree-of-Freedom Gyro in a Spinning Vehicle

Using the Lyapunov approach, the conditions are presented for the stability of the spin axis of a 2-degree-of-freedom gyro which is mounted in a spinning vehicle.     

Transient Performance of Gyro in Spinning Spacecraft

Transient performance of a single-axis rate gyroscope mounted in a spacecraft which is spinning about the spin axis of the gyro is presented. Analytical expressions for various time-domain and frequency-domain specifications as functions of the spin rate of the vehicle are obtained. Numerical results are presented which are useful in selecting the gyro parameters if it is to be used for the measurements of the angular velocity in spinning space vehicles.     

陀螺动力学系统计算机仿真

推导出了适于计算机仿真的陀螺完整运动方程式并给出了仿真曲线,可看出在外力矩作用下陀螺仪从起动到稳定这一段时间内的转动角速度和转角的变化规律。通过降低陀螺转速并减小外力矩,使无锁紧机构的陀螺仪消除起动时的剧烈抖动而达到平稳起动的目的。     

一种提升空间三轴激光陀螺性能的谐振腔方案研究

针对现有空间三轴机抖激光陀螺因通道间放电耦合引入了零偏误差导致陀螺性能损失的问题,提出了一种高精度空间三轴谐振腔改进设计实现方案.该方案从空间三轴激光陀螺与单轴激光陀螺放电系统的差异出发,分析了空间三轴激光陀螺不同放电状态引入零偏误差的机理,明确了高精度空间三轴激光陀螺各通道的放电电流控制需求.同时,分析结果表明,减小通道间的放电耦合可降低该型陀螺的零偏耦合误差项,因此需对空间三轴谐振腔进行放电结构的去耦合优化设计.最后,针对提出的空间三轴谐振腔改进设计方案,开展了陀螺性能试验验证,试验结果表明,空间三轴机抖激光陀螺的精度提升了5.7％以上.     

Asymptotically decoupled discontinuous control of systems andnonlinear aircraft maneuver

The question of control of a class of nonlinear systems that can be decoupled by state-variable feedback is considered. Based on variable-structure system theory, a discontinuous control law is derived that accomplishes asymptotic decoupled output trajectory-following in the presence of uncertainty in the system. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. During the sliding phase the motion is insensitive to parameter variations. Based on this result, a control law for asymptotically decoupled control of roll angle, angle of attack, and sideslip in rapid, nonlinear maneuvers is derived. Simulation results are presented to show that large, simultaneous lateral and longitudinal maneuvers can be performed in spite of uncertainty in the stability derivatives     

State space modeling of random drift rate in high-precision gyro

A state space approach for the modeling of nonstationary time series is presented. Based on the concept of smoothness priors constraint, the overall model is fitted by using the Kalman filler and Akaike's AIC criterion. Whenever an autoregressive (AR) model with time-varying coefficient is fitted in state space model, it can be used for the time-varying spectrum estimation. Some numerical results of gyro drift models are obtained for analysis of high-precision gyro. As the trend, irregular and periodic components of the observed time series can be modeled simultaneously, it is statistically more accurate and efficient than that modeled separately     

弹性飞行器纵向稳定性问题

 本文研究考虑气动弹性时飞行器的纵向稳定性问题。首先由弹性飞行器的纵向扰动运动方程出发,导出了便于计算采用的弹性飞行器纵向扰动方程的标准矩阵形式,作出作为控制对象的弹性飞行器在考虑一阶、二阶及三阶振型时的传递函数;其次分析气动弹性对整个飞行器系统的稳定性的影响,并提出对飞行器自动驾驶仪敏感元件的可能合适位置选择的要求。最后还建立了计算气动弹性对飞行器气动导数值影响的理论式。     

具有无穷时滞的序列差分方程的稳定性

通过介绍一种新的离散相空间C_d~h(C_d~h是Banach空间)研究了具有无穷时滞的序列差分方程的稳定性问题,并相应给出了一致稳定和一致渐近稳定的充要条件。     

Bifurcation analysis of polynomial models for longitudinal motion at high angle of attack

To investigate the longitudinal motion stability of aircraft maneuvers conveniently, a new stability analysis approach is presented in this paper. Based on describing longitudinal aerodynamics at high angle-of-attack (a < 50 ) motion by polynomials, a union structure of two-order differential equation is suggested. By means of nonlinear theory and method, analytical and global bifurcation analyses of the polynomial differential systems are provided for the study of the nonlinear phenomena of high angle-of-attack flight. Applying the theories of bifurcations, many kinds of bifurcations, such as equilibrium, Hopf, homoclinic (heteroclinic) orbit and double limit cycle bifurcations are discussed and the existence conditions for these bifurcations as well as formulas for calculating bifurcation curves are derived. The bifurcation curves divide the parameter plane into several regions; moreover, the complete bifurcation diagrams and phase portraits in different regions are obtained. Finally, our conclusions are applied to analyzing the stability and bifurcations of a practical example of a high angle-of-attack flight as well as the effects of elevator deflection on the asymptotic stability regions of equilibrium. The model and analytical methods presented in this paper can be used to study the nonlinear flight dynamic of longitudinal stall at high angle of attack.     

飞控系统的模糊模型及其研究

在Takagi-Sugeno模型的基础上,建立了飞控系统的模糊模型。讨论了该模型的整体渐近稳定性,给出了判定该模型的整体渐近稳定的充分条件和满足一定条件的控制器的设计方法。最后对国产某飞机的纵向短周期运动系统的分析说明本文的模型是合适的,方法是有效的。     

某型方位旋转平台惯导系统转速模型分析与验证

某型平台惯导系统采用方位旋转调制技术,通过对台体匀速转动的控制调制陀螺的漂移。台体的转速不是固定值,是随惯导系统所在地区而改变的,且台体转速异常必伴随方位陀螺故障。为了正确判断台体转速的理论是否正常,文章推导了转速的理论计算公式,不同地区惯导系统的实测数据表明实测值与理论计算值一致,验证了转速计算公式的正确性,为监控方位陀螺状态提供了技术途径。     

Accurate INS Transfer Alignment Using a Monitor Gyro and External Navigation Measurements

A particular alignment mechanization for a nonmaneuvering vehicle is described which uses a monitor gyro to estimate the slave inertial navigation system (INS) equivalent east gyro drift rate and thus improves azimuth alignment. A state-space model of the dynamic system with measurements is developed. Results of covariance simulations employing Kalman filter estimation are presented for two master INS position update scenarios, one involving frequent and very accurate updates and the other including infrequent and coarse updates. The ef fects of position updates and the monitor gyro on the quality of transfer alignment are demonstrated and analyzed.     

Gyro Misalignment and Encoder Quantization Effects During Multi-Axis Evaluation of Strapdown Gyros

This paper presents a quantitative discussion of two error sources which affect the accuracy of data comparison between instrument outputs and reference angle computations during multi-axis evaluation of strapdown gyros. The error due to misalignment of gyro input axes is formulated in terms of closed-form solutions for typical relationships between the three table gimbal rotation histories. If the angular positions of the table gimbal axes are measured by shaft encoders, then any measurement has an uncertainty in the range from plus to minus one-half of the quantization level. It is shown that the effect of encoder quantization error on the computer transformed angles in the bodyfixed coordinate system can be divided into two parts: the initial uncertainty of the zero positions of the gimbals before table motion is begun, and all subsequent error contributions during table test. Typical data for gyro misalignment and encoder quantization error effects are presented.     

有攻角细长旋成体极端地面效应分析

本文用匹配摄动方法研究了细长旋成体贴近地面运动时诱导的不可压缩势流问题,它是经典细长体理论的推广和发展。文中将流场分为内外两个渐近区域,建立了问题的匹配摄动理论,并利用文献[1]中的双圆诱导不可压缩势流的精确解,给出了该问题的首阶解析解。然后又导出了细长体上的吸力和俯仰力矩的计算公式。在此基础上,文中对细长旋成体极端地面效应的运动学规律和动力学规律作了定性和定量两个方面的分析。     

光纤陀螺惯导稳定平台与旋转调制方法

光纤陀螺仪在随机误差方面表现出极佳的性能优势,但受限于其标度因数不理想的现实。针对航海用长航时、高精度光纤陀螺惯导系统的使用需求,设计了基于光纤陀螺数字信号实现载体三维角运动隔离的同时完成惯性测量装置的旋转调制功能,可有效减小光纤陀螺标度因数误差与载体运动角速度的耦合误差,同时充分发挥光纤陀螺随机游走小的精度优势。理论仿真验证了光纤惯导稳定平台加旋转调制方法的优越性和可行性,为光纤陀螺惯导系统在高精度导航领域中的应用提供了技术基础。     

Dynamics of a Solenoidal-Torqued Gyro-Stabilized Seeker Assembly for Guidance and Tracking

Several low-cost gyro-stabilized, bang-bang seeker assemblies for missile guidance and tracking applications have used similar physical structures. A magnetic dipole is an integral part of the gyro rotor assembly. The nominal spin axis of the gyro is colinear with the axis of a cylinder about which is wound a helix of wire. By properly modulating the current that is passed through that helix, the precession torque acting upon the gyroscope is controlled. One rather generalized model of such a seeker assembly is modeled, the equations of motion are derived, and the dominant error sources are identified and parametrically evaluated. Because this is such a commonly encountered structure, yet no such analysis has been published, to the author's knowledge, it is hoped that this is a useful contribution to the literature.