Transient attitude dynamics of satellites with deploying flexible appendages

The paper presents a general formulation for librational dynamics of satellites with an arbitrary number, types, and orientation of deploying flexible appendages. The generalized force term is incorporated making the formulation applicable to a wide variety of situations where aerodynamic forces, solar radiation, earth's magnetic field, etc. become significant. In particular, the case of a beam-type flexible appendage deploying from a satellite in an arbitrary orbit is considered. The corresponding nonlinear, non-autonomous equations for in-plane and out-of-plane vibrations are derived, allowing for the variation of mass density and flexural rigidity along the length with time dependent deployment velocity and spin rate. Next, the attention is focused on the linearized analysis of the in-plane vibrational equation using the assumed-mode method and its substantiation through numerical integration. Finally, the paper presents results for both steady-state and transient attitude behaviour for a representative gravity gradient configuration for a range of initial conditions and system parameters. Results show the combined effect of flexibility and deployment on the dynamics of the system to be substantial. Disturbance of the appendage can excite large amplitude librations. On the other hand, the converse situation is not necessarily true. Furthermore, Coriolis loading, induced by the extending appendages, can become a limiting factor in arriving at a deployment strategy; an effect not pointed out in the literature.     

簇状卫星姿态控制方程的通用建模方法

当前卫星通常都由一个中心刚体和其他挠性附件构成，每个挠性附件都与中心刚体直接相连，组成了一个簇状的刚柔耦合的多体系统。随着挠性附件的数目的不同，卫星系统的拓扑构型也将有所不同。即使对于同一颗卫星而言，在展开过程的不同阶段，卫星系统具有不同的拓扑构型。本文利用柔性多体系统动力学的单向递推组集方法，提出了一套通用的解决方案，以推导具有不同拓扑构型的簇状卫星的姿态控制方程，得出了姿态控制方程的系数矩阵。     

跟踪与数据中继卫星柔性动力学建模

研究了大型跟踪与数据中继卫星动力学建模问题。首先结合模态综合和混合坐标方法介绍了中继卫星柔性动力学一般模型建立过程;根据工程需要重点对所建立的一般动力学模型利用模态综合进行降阶处理,给出了工程实用的低阶动力学模型和各耦合系数的计算表达式;最后通过一个工程实例对模型进行了验证。     

柔性空间飞行器的振动抑止控制

本文提出了一种带有柔性附件的卫星的振动主动抑止方法,给出了能抑止任意阶振动谐波的条件.作为举例,分析了太阳帆板的转动控制,在使帆板平稳旋转的同时,还使卫星姿态稳定无振.     

含板类柔性附件的充液航天器动力学研究

对含有板类柔性附件和曲壁轴对称充液储腔的复杂航天器系统进行动力学建模和耦合机理研究。首先,采用Kirchhoff-Love薄板理论对航天器的板类柔性附件进行研究,通过D’Alembert原理得到柔性附件的振动方程,运用模态假设法将混合方程转换为常微分方程。其次,通过推导充液航天器储腔内任意点的运动,得到储腔液体的牵连速度势函数,采用Gauss超几何级数得到液体相对速度势函数的解析形式,通过Hamilton变分原理推导液体晃动的运动方程,以及液体速度势函数模态系数的控制方程。最后采用准坐标Lagrange方程得到耦合航天器系统的状态方程,通过数值仿真校验系统动力学模型的有效性。研究结果表明,刚性平台、液体、柔性附件的相互耦合效应使得航天器系统存在复杂动力学行为,在复杂航天器系统动力学建模过程中需要充分考虑液体晃动和柔性附件振动的影响,柔性附件的安装位置对于耦合航天器系统的动力学行为也有着重要影响。     

基于拉索的航天器挠性部件在轨增频技术研究

航天器上的太阳电池阵等挠性部件基频较低、低频模态密集,可能会与器上活动部件产生耦合和共振,对航天器姿态及载荷工作等产生不良影响。针对此问题,文章提出用主动张紧拉索装置来调节挠性部件的频率。在调研国内外技术的基础上,分析了悬臂梁模型中支撑刚度对系统模态的影响,建立拉索增频的动力学模型并进行仿真;依据原理性试验仿真结果,设计了器上增频机构,并完成了相关地面试验验证和在轨飞行验证。本研究对于航天器挠性部件的增频和错频等技术措施的实施具有参考价值。     

Planar oscillations of a vibrating dumbbell-like body in a central field of forces

The problem of planar motions of a dumbbell-like body of variable length in a central field of Newtonian attraction is considered both in the exact formulation and in satellite approximation. In the satellite approximation the true anomaly of the center of mass is used as an independent variable, which has allowed us to represent the equation of planar oscillations of the dumbbell in the form similar to the Beletskii equation. Some exact solutions to the inverse problem are given both in the complete formulation and in satellite approximation. Under an assumption of small orbit eccentricity and amplitude of the dumbbell vibrations the conditions of existence are found for families of almost periodic motions and splitting separatrices. The phenomena of alternation of regular and chaotic motions are established numerically, as well as chaos suppression with increasing frequency of vibrations. Using the method of averaging the stabilization of tangent equilibria is proved to be impossible.     

Operational modal analysis via image based technique of very flexible space structures

Vibrations represent one of the most important topics of the engineering design relevant to flexible structures. The importance of this problem increases when a very flexible system is considered, and this is often the case of space structures. In order to identify the modal characteristics, in terms of natural frequencies and relevant modal parameters, ground tests are performed. However, these parameters could vary due to the operative conditions of the system. In order to continuously monitor the modal characteristics during the satellite lifetime, an operational modal analysis is mandatory. This kind of analysis is usually performed by using classical accelerometers or strain gauges and by properly analyzing the acquired output. In this paper a different approach for the vibrations data acquisition will be performed via image-based technique. In order to simulate a flexible satellite, a free flying platform is used; the problem is furthermore complicated by the fact that the overall system, constituted by a highly rigid bus and very flexible panels, must necessarily be modeled as a multibody system. In the experimental campaign, the camera, placed on the bus, will be used to identify the eigenfrequencies of the vibrating structure; in this case aluminum thin plates simulate very flexible solar panels. The structure is excited by a hammer or studied during a fast attitude maneuver. The results of the experimental activity will be investigated and compared with respect to the numerical simulation obtained via a FEM-multibody software and the relevant results will be proposed and discussed.     

航天器附件展开动力学仿真

用Newton-Euler法建立了中心刚体带挠性附件的航天器动力学方程, 进行挠性附件展开的动力学仿真,研究附件展开对主体姿态的影响。当航天器 附件展开机构失效时,利用航天器姿态抖动来帮助展开附件。本文用ADAMS软 件建立了航天器的虚拟物理模型,用ADAMS和Matlab/Simulink联合仿真了航 天器姿态抖动过程。仿真结果表明此方法是有效的。     

Rapid rotations of a satellite with a cavity filled with viscous fluid under the action of moments of gravity and light pressure forces

Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of moments of gravity and light pressure forces. Orbital motions with an arbitrary eccentricity are supposed to be specified. The system, obtained after averaging over the Euler-Poinsot motion and applying the modified averaging method, is analyzed. The numerical analysis in the general case is performed, and the analytical study in the axial rotation vicinity is carried out. The motion in the specific case of a dynamically symmetric satellite is considered.     

带挠性附件的航天器系统动力学特性研究

本文研究了带挠性附件的航天器系统动力学特性。带挠性附件的航天器系统建模为刚性主体带挠性附件（挠性附件的末端带有刚性质量），根据拟坐标下的Ｌａｇｒａｎｇｅ定理建立了主刚体姿态运动与挠性附件振动相互耦合的动力学状态方程。针对一类带挠性附件的航天器系统编制了有关计算软件，利用该软件以ＳＣＯＬＥ模型（ＳＣＯＬＥ是ＳｐａｃｅｃｒａｆｔＣｏｎｔｒｏｌＬａｂｏｒａｔｏ－ｒｙＥｘｐｅｒｉｍｅｎｔ的缩写，其系统构形可参见文献［２］［３］）为例进行动力学分析，我们得到了与ＮＡＳＡ有关报告几乎完全一样的结果。本项研究为一类带挠性附件的航天器控制系统设计提供了一种合适的动力学理论模型。     

基于多柔体动力学的飞行器多目标优化设计

研究了柔性航天器总体设计中基于结构与姿态控制的多目标优化问题。利用拉格朗日 方程建立了刚柔耦合系统动力学模型,提出以附件质量和微分矩阵最大实特征值为目标函数 的多目标优化问题;采用非支配排序进化求解算法（NSGA-II）,对某柔性航天器进行了多目 标优化分析设计;最优决策为具有一定规律性的空间曲线,该优化结果对柔性卫星的总体分 析设计具有一定的指导意义。
     

三轴气浮台挠性航天器动力学模拟方法研究

本文研究利用气浮台上的动量轮执行机构,模拟卫星上挠性附件振动产生的干扰力矩的卫星物理仿真实验方法,以克服三轴气浮台不能直接安装挠性附件进行仿真的局限性.本实验方法通过设计一个跟踪控制器,令气浮台的姿态角速度跟踪挠性卫星参考动力学,并由动量轮产生控制力矩,该力矩即是实验模拟的挠性振动干扰力矩.理论和仿真研究表明:(1)本文提出的挠性干扰力矩模拟方法可以较好地模拟低阶挠性振动干扰力矩;(2)理论上当控制器的增益参数越大,系统能够模拟的干扰力矩频率就越大,但是由于测量噪声的影响,反馈增益不能选得过大;(3)本方法模拟的干扰力矩与真实干扰力矩存在一定的相位延迟,这是由于控制器和执行机构的固有延迟造成的.通过引入超前-滞后校正网络可以有效减小延迟的影响.     

Regularization of the Limit Problem of Satellite Librations in a Keplerian Orbit Taking Light Pressure into Account

The planar librations of a satellite whose center of mass moves along an elliptic orbit are considered. It is assumed that not only the gravitational moment but also the forces of light pressure act upon the satellite. Account is taken of the fact that the right-hand sides of the differential equations are nonanalytic functions of the phase variables. When e 1, e being the orbit's eccentricity, the deformations of solutions are considered for the case of a satellite moving along a highly elongated orbit. Such transformation of the initial system of differential equations is carried out so that the new system becomes regular up to the value e = 1. A limit problem corresponding to the case e = 1 is considered. When the azimuth angle of the light source coincides with the direction to the pericenter, the dynamical system is reversible. In this case, the known families of the periodic solutions to the problem can be continued up to the limit case.     

On the stability of spinning satellites

We study the directional stability of rigid and deformable spinning satellites in terms of two attitude angles. The linearized attitude motion of a free system about an assumed uniform-spin reference solution leads to a generic MGK system when the satellite is rigid or deformable. In terms of Lyapunov’s stability theory, we investigate the stability with respect to a subset of the variables. For a rigid body, the MGK system is 6-dimensional, i.e., 3 rotational and 3 translational variables. When flexible parts are present the system can have any arbitrary dimension. The 2×2 McIntyre–Myiagi stability matrix gives sufficient conditions for the attitude stability. A further development of this method has led to the Equivalent Rigid Body method. We propose an alternative practical method to establish sufficiency conditions for directional stability by using the Frobenius–Schur reduction formula. As practical applications we discuss a spinning satellite augmented with a spring–mass system and a rigid body appended with two cables and tip masses. In practice, the attitude stability must also be investigated when the spinning satellite is subject to a constant axial thrust. The generic format becomes MGKN as the thrust is a follower force. For a perfectly aligned thrust along the spin axis, Lyapunov’s indirect method remains valid also when deformable parts are present. We illustrate this case with an apogee motor burn in the presence of slag. When the thrust is not on the spin axis or not pointing parallel to the spin axis, the uniform-spin reference motion does not exist and none of the previous methods is applicable. In this case, the linearization may be performed about the initial state. Even when the linearized system has bounded solutions, the non-linear system can be unstable in general. We illustrate this situation by an instability that actually happened in-flight during a station-keeping maneuver of ESA’s GEOS-I satellite in 1979.     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

一种改进的航天器时变模态参数递推辨识方法

针对基于预测器的递推子空间辨识(RPBSID)方法在估计系统的状态变量时计算量较大的问题,提出一种改进的RPBSID方法并应用于航天器的时变模态参数辨识。与原算法相比,改进后的方法在求解状态量时不需要逐个时刻构建相应的Hankel矩阵,而是利用仿射投影算法(APA)实现状态量的递推估计,从而减少了辨识过程中的数据量。在此基础上,利用该状态变量递推得到时变系统的状态空间模型和模态参数。在数值仿真中,建立带有大型挠性附件的卫星动力学模型,分别考虑系统模态参数线性变化、突变和周期改变的情况,利用改进的RPBSID方法对结构的时变频率和阻尼比等参数进行了辨识。理论分析和数值仿真的结果表明这种改进的方法不仅能够有效地辨识系统的时变模态参数,而且与原方法相比具有更高的计算效率。     

Spacecraft detumbling using movable telescoping appendages

The dynamics of detumbling a randomly spinning spacecraft using externally mounted, movable telescoping appendages are studied both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. From an application of Lyapunov's second method, boom extension maneuvers can be determined to approach either of two desired final states: close to a zero inertial angular velocity state and a final spin rate about only one of the principal axes. Recovery dynamics are evaluated analytically for the case of symmetrical deployment. Numerical examination of other asymmetrical cases verifies the practicality of using movable appendages to recover a randomly tumbling spacecraft.     

Variable structure maneuvering control with time-varying sliding surface and active vibration damping of flexible spacecraft with input saturation

This paper presents a dual-stage control system design method for the three-axis-rotational maneuver and vibration stabilization of a spacecraft with flexible appendages embedded with piezoceramics as sensors/actuators. In this design approach, attitude control system and vibration suppression were designed separately using lower order model. The design of attitude controller was based on variable-structure control (VSC) theory leading to a discontinuous control law. To accomplish asymptotic attitude maneuvering in the closed-loop system and be insensitive to the interaction of elastic modes in the presence of unknown disturbances/uncertainty and input saturation as well, a switching mechanism is employed to design the attitude controller such that outside the sliding region VSC law with a time-varying sliding surface is implemented and inside the region the VSC law with a linear sliding surface is activated. Furthermore, a hyperbolic tangent function in conjunction with a sharpness function permitted to vary with time according to a set of user-defined parameters is implemented to offset the disadvantages of existing saturation-respecting controller and chattering. In addition, for actively damping the excited elastic vibrations during attitude maneuvering, modal velocity feedback and strain rate feedback control design methods are presented and compared by using piezoelectric materials as additional sensors and actuators bonded on the surface of the flexible appendages. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance torque, parameter uncertainty and control saturation nonlinearity.     

Motion of a satellite equipped with a pitch flywheel and magnetic coils in gravitational field

A satellite equipped with a magnetic attitude control system and a pitch flywheel has been considered. The system performance in the transient mode has been investigated. The characteristic exponent of the system have been approximated for a satellite on a circumpolar orbit. In the steady-state mode of gravitational attitude, small motions are considered in the vicinity of equilibrium. The attitude accuracy has been analyzed. The algorithm of an arbitrary but given attitude of the satellite in the orbital plane has been investigated. A numerical simulation has been performed.