Attitude control for part actuator failure of agile small satellite

The stability and singularity problem of agile small satellite （ASS） with actuator failure is discussed in this paper. Firstly, the three-axis stabilized controller of an ASS is designed, where micro control moment gyros （MCMG＇s） in pyramid configuration （PC） is used as the actuator. By using the same controller and steering law, the control results before and after one gyro fails are compared by simulation. The variation of singular momentum envelope before and after one gyro fails is also compared. The simulation results show that the failure intensively decreases the capacity of output torque, which leads to the emergence of more singular points and the rapid saturation of MCMG＇s. Finally, the parameters of system controller are changed to compare the control effect.     

Steering laws analysis of SGCMGs based on singular value decomposition theory

The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.     

Underactuated spacecraft angular velocity stabilization and three-axis attitude stabilization using two single gimbal control moment gyros

Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.     

Error analysis and a new steering law design for spacecraft control system using SGCMGs

Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gimbal control moment gyros (SGCMGs) as the actuator for the attitude control system.The expression of output-torque error is given at the point of singularity,proving the incompatible relationship between the gimbal rate and the output-torque error.The method of establishing a balance between the gimbal rate and the output-torque error is discussed,and a new steering law is designed.Simulation results show that the proposed steering law can effectively drive SGCMGs to escape away from singularities.     

The output torque estimation of MCMG for agile satellites

Studied in this paper are the attitude control law design and the output torque estimation problem of micro control moment gyros （MCMGs） for the agile satellites executing rapid attitude maneuver mission. An algorithm is proposed for estimating the output torques and the gimbal angular rates of MCMGs, which can help engineers to choose reasonable size for actuators so that the cost of satellite can be decreased. According to some special maneuver missions, a numerical example of attitude control system for a small satellite with MCMGs in pyramid configuration is studied, and the simulation results validate the proposed estimation algorithm.     

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro(VSCMG), which supplies only two internal torques.Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically,when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilibrium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and derivative controller, using the generalized dynamic inverse(GDI)method. The steady-state instability inherent in the GDI controller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude stabilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efcacy of the proposed control strategy.     

Attitude maneuver of liquid-filled spacecraft with a flexible appendage by momentum wheel

Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied.The dynamic equations are derived by conservation of angular momentum and force equilibrium principle.A feedback control strategy of the momentum wheel is applied for the attitude maneuver.The residual nutation of the spacecraft in maneuver process changes with some chosen parameters,such as steady state time,locations of the liquid container and the appendage,and appendage parameters.The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for placing the liquid containers and the appendage than other locations if they can be placed randomly.Higher density and thicker cross section are better for lowering the residual nutation if they can be changed.Light appendage can be modeled as a rigid body,which results in a larger residual nutation than a flexible model though.The residual nutation decreases with increasing absolute value of the initial sloshing angular height.     

Deformable micro-continua in which quantum mysteries reside

Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale.At every instant, the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass, the velocity, the internal stress, and the intrinsic angular momentum. The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field. It is shown that these microcontinua are endowed with the following unique response features:(i) the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable;(ii) this fundamental dynamic equation and this complex field variable are just the Schr¨odinger equation and the complex wave function in quantum theory; and,accordingly,(iii) the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered, thus following objective and deterministic response patterns for quantum entities, in which the physical origins and meanings of the wave function and the Schr¨odinger equation become self-evident and, in particular, any probabilistic indeterminacy becomes irrelevant.     

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variational principle,a sub-region mixed ver- sion of the newly-developed semi-analytical‘finite element method of lines’(FEMOL)is pro- posed in this paper for accurate and efficient computation of stress intensity factors(SIFs)of two-dimensional notches/cracks.The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used,with the sought SIFs being among the unknown coefficients.The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements.A mixed system of ordinary differential equations(ODEs) and al- gebraic equations is derived via the sub-region generalized variational principle.A singularity removal technique that eliminates the stress parameters from the mixed equation system even- tually yields a standard FEMOL ODE system,the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver.A number of numerical examples,including bi-material notches/cracks in anti-plane and plane elasticity,are given to show the generally excellent performance of the proposed method.     

THE SINGULAR BEHAVIOUR IN THE VICINITY OF INTERSECTION BETWEEN THE BODY AND FREE SURFACE

The singular behaviour in the vicinity of intersection between the body and free surface is presented.It is shown that in the linear regime the singularity of velocity potential for transient problem is in d~2|nd.The singular behaviour for harmonic problem is the same as the result for the transient problem.In particular,the singularity for the harmonic problem with infinite frequency is in d~2 lnd for velocity potential(d is the distance between field point and intersection).     

Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes

To study the stability of steady rotations of a control moment gyro system with internal dissipation, we use the Barbashin-Krasovskii theorem and the relation, established in [1], between the Lyapunov function and steady motions. Taking into account the special properties of the original problem, we reduce it to a lower-dimensional problem.We give a detailed presentation of an algorithm for analyzing the stability of steady motions of a gyrostat and use this algorithm to perform a complete study for two systems consisting, respectively, of one and two gyros whose gimbal axes are parallel to the principal axis of inertia of the system. Each steady motion is identified as either asymptotically stable or unstable. We find periodic motions that exist only in the presence of dynamic symmetry and which are regular precessions. For the system with two gyros, we prove the asymptotic stability of quiescent states and prove that in the angular momentum range where these states are defined the system does not have any other stable motions.     

一种用于无陀螺捷联惯导系统的角速度融合算法

无陀螺捷联惯导系统(GFSINS)是用加速度计的合理空间组合解算出载体的角速度。载体角速度的解算精度是GFSINS的技术关键。在分析GFSINS九加速度计配置方案的基础上,提出一种新的角速度融合算法,消除该方案解算过程中开方计算及符号判断带来的误差。该算法还明显抵消了加速度计输出中包含的常值零点偏移误差和温度漂移误差等,具有实时性好、计算量小、通用性强的优点。仿真计算表明该算法可行,并能在一定程度上提高系统解算精度。     

气体介质对动力调谐陀螺仪性能的影响机理及调整措施

在动力调谐陀螺研制和生产过程中发现，陀螺从启动到稳定所需时间较长，在长时间随机漂移测试中，有明显的斜坡漂移。这在很大程度上降低了陀螺的性能，影响了陀螺的应用，经研究发现，陀螺的内部气体在这当中起着重要作用。本文详细分析了陀螺内部气体对动力调谐陀螺性能影响的机理，并提出了解决方法。     

Topology of the Integral Manifolds of the N-Body Problem with Positive Energy

The integral manifolds of the N-body problem are the level sets of energy and angular momentum. For positive energy and non-zero angular momentum, all level sets are diffeomorphic to a non-zero level set of angular momentum on the unit tangent bundle of the configuration space. The one complication that arises in attempting to describe this level set explicitly is the degeneracy at the syzygies of the equations that define angular momentum. In this work, we analyze the behavior of the angular momentum near syzygies, and show how to construct local coordinates near the syzygies. In particular, we show that the projection of the integral manifold onto the configuration space _c is a homotopy equivalence, and use this to compute the homology of the integral manifolds.     

循环干涉型光纤陀螺及其光源

介绍了一种新型光纤陀螺及其关键器件。包括：（1）循环干涉型光纤陀螺的系统方案；（2）大功率超辐射发光二极管；（3）多功能光学发收模块，它们是国内光纤陀螺研制中急待解决的关键技术。采用模块化结构和微光电机系统（MOEMS）是国外光纤陀螺的发展方向。     

On limit motions of a system of control moment gyros with intrinsic dissipation in a homogeneous gravitational field

We study the limit motions of a free rigid body bearing n two-degree-of-freedom control moment gyros with dissipation in the gyro gimbal suspension axes. We show that, in the absence of dynamic symmetry, the limit motions of the system are only steady rotations at a constant angular velocity. In the case of dynamic symmetry, the gyros can be arranged so that, in addition to steady rotations, the system exhibits limit motions that are regular precessions.