Asymptotically Stable Motions of a Gyro in a Spinning Vehicle

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain constant angular velocity xz about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using the Lyapunov approach, regions are obtained in the k-xz plane where k is the torsional spring constant, for asymptotic stability and for global asymptotic stability, and an estimate of the region of stability in state space is presented. Analytical relations for the selection of the 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.     

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.     

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 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.     

Magnetically suspended MEMS spinning wheel gyro

A concept of a magnetically suspended spinning wheel gyro is described. The gyro is based on a patented, planar magnetic actuator and position sensor configuration with a gyro wheel that is rotated by a multi-phase electromagnetic spin motor. The motor and actuator/sensor configurations, in addition to providing the necessary forces to suspend the spinning wheel, are amenable to fabrication using some of the developing MEMS fabrication technologies, making batch fabrication of the gyro possible. This provide the capability for high production yield in high volume through the use of batch processing, without the need for skilled hand labor, resulting in high yields, high reliability, and low cost of ownership. The gyro concept is described in detail. The high-speed rotation of the wheel, somewhat smaller than a dime, can produce an angular momentum much larger than that of the Coriolis force based MEMS gyros now receiving intensive development, and is expected to provide considerably higher performance than currently available from this class of instrument. Two axes of angular rate information and three axes of acceleration information are provided by the control loops that center the wheel within the case. Thus, two such magnetically suspended spinning wheel gyros can be used to implement a complete IMU, and can also provide redundancy in three of the five degrees of freedom     

Angular Velocity Measurement Using Rate Gyros in a Spinning Vehicle

It is shown that when the gyro spin vector is in opposition to the spin vector of the vehicle, the output differential equation of the gyro becomes unstable for large vehicle spin values. When the gyro is used with its spin vector along the spin vector of the vehicle, the steady-state response of the gyro is a nonlinear function of the roll rate of the vehicle.     

Theory of Operation of an Elastically Supported Tuned Gyroscope

Detailed derivation of the transfer function for a multigimbal, elastically supported, tuned gyro is presented and comparison made between its characteristics and those of a classical two-axis, free-rotor gyro. Knowledge of the gyro transfer function is necessary for the purpose of servo analysis of the system in which the gyro is used; also, the transfer function is a basis of evaluation of errors caused by angular inputs that occur at twice spin frequency.     

Dynamics of an Eddy-Current-Torqued Gyro-Stabilized Assembly

Prominent among the commonly encountered gyro-stabilized assemblies used in guidance and tracking are those which are eddy-current torqued. Although eddy-current-torquecd lead- computing gunsights, which use spinning mirrors, have been well known for thirty years, it has been difficult to find an analysis of the torques developed by the precession mechanism. In this paper a model configuration of the torquer is presented. The total gyro dynamics are then determined by including these torque terms in the model presented in the preceding paper.     

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。     

Coning motion instability of spinning missiles induced by the delay of strap-down seeker

The strap-down seeker, which combines the seeker’s and the onboard gyro’s measurements to obtain the target information, has been extensively applied by spinning missiles. The response delay of the strap-down seeker, a novel factor that could result in crosscoupling between the acceleration commands in the pitch and yaw channels and subsequently cause the significant deterioration in dynamic stability of the spinning missile equipped with a rate loop, is noted in this paper. The sufficient and necessary stability conditions are also analytically established based on the system equation with complex coefficient, which are further verified by numerical simulations. It could be indicated that the response delay of the strap-down seeker will greatly deteriorate the dynamic stability of the whole guidance system designed by the conventional method. It is also noticed from analysis that the stable region of the combined guidance coefficient is shrunken significantly with the increase of the spinning rate.     

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.     

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.     

A Microprocessor-Based Data-Acquisition System for Stall/Spin Research

Accurate data are necessary for the identification of aerodynamic parameters at high angle of attack and in spinning flight. Modern sensors and microelectronic devices are employed in a stall/spin data acquisition system that will be tested in a Schweizer 2-32 sailplane. This instrumentation package will use a quaternion-based ?strapdown IMU? algorithm to derive vehicle attitude from angular rate data, and it will use fault-detection logic to identify inflight sensor failures. Details of the system and flight test program are presented, together with results of preflight digital simulation analysis.     

Spectral Analysis of Optimal and Suboptimal Gyro Monitoring Filters

Gyro monitoring filters are used to estimate and correct gyro drift rates of local-level inertial navigation systems. Conventional gyro monitoring filters are usually designed based on a simplified model of gyro drift rate. Furthermore, the effectiveness of these filters-and of many filters of the "Kalman" type-is often measured in terms of the root mean square (rms) criterion in contrast to the spectral content criterion typical of classical Wiener filtering theory. This paper has two objectives: to propose a gyro monitoring filter which is based on a more detailed model of gyro drift rate; and to propose a method of filter performance evaluation which uses as criterion a measure of the spectral content of the error process. The proposed gyro monitoring filter is shown to have improved spectral contents resulting in superior navigation performance for the gyro error models used in the calculations (comparable to commercial-grade aircraft gyros).     

Modeling Random Gyro Drift Rate by Data Dependent Systems

A new modeling procedure is presented in which a mathematical model for random gyro drift rate is obtained directly from the original observations without requiring any theoretical conjectures or preprocessing of the data. The adequate model so obtained confirms the presence of a random walk component causing the "steady state" drift and a stochastic component of the nature of correlated noise. It also provides a quantitative measure of the relative contribution of each component, useful in determining the quality of the gyro in guidance over extended periods.     

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.     

Interlaced optimal-REQUEST and unscented Kalman filtering for attitude determination

 Aimed at low accuracy of attitude determination because of using low-cost components which may result in non-linearity in integrated attitude determination systems, a novel attitude determination algorithm using vector observations and gyro measurements is presented. The various features of the unscented Kalman filter (UKF) and optimal-REQUEST (quaternion estimator) algorithms are introduced for attitude determination. An interlaced filtering method is presented for the attitude determination of nano-spacecraft by setting the quaternion as the attitude representation, using the UKF and optimal-REQUEST to estimate the gyro drifts and the quaternion, respectively. The optimal-REQUEST and UKF are not isolated from each other. When the optimal-REQUEST algorithm estimates the attitude quaternion, the gyro drifts are estimated by the UKF algorithm synchronously by using the estimated attitude quaternion. Furthermore, the speed of attitude determination is improved by setting the state dimension to three. Experimental results show that the presented method has higher performance in attitude determination compared to the UKF algorithm and the traditional interlaced filtering method and can estimate the gyro drifts quickly.     

一种新型机载对地观测用三轴稳定平台陀螺安装方式

陀螺安装方式及相应的算法编排是稳定平台设计中的一项关键技术。针对机载对地观测用三轴稳定平台特点,提出了将方位陀螺安装在方位环上,俯仰陀螺和横滚陀螺安装在俯仰环上的陀螺安装方式。利用空间矢量分解理论分析了陀螺输出角速度信号的投影关系及电机控制信号的分配;基于稳定平台系统模型,对理想正交情况和考虑陀螺安装误差情况进行了仿真分析,验证了此种安装方式的可行性和优越性。分析表明,在同等条件下,所提出的安装方式减小了稳定平台的机械尺寸,降低了稳定平台的重量和功耗,实现了三维角速度的正交测量,简化了三轴解耦控制算法。研究结论可为其他三轴稳定平台结构设计和陀螺安装方式设计提供参考。