On stability of a rotating spacecraft partially filled with liquid: The case of a single cavity

The problem of stability of a rotating spacecraft with a cavity partially filled with liquid to a small depth is considered with regard to the distinction in angular velocities of spacecraft and liquid rotation and their variability (the modes of the spacecraft’s stationary rotation, spin-up, and rotation deceleration). The regions of stability (in space of the characteristic parameters of an object) are found, and mathematical simulating of the disturbed motion is carried out.     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with cavities partially filled with liquid

This paper is a continuation of [1–3] and a generalization of the results for a rotating spacecraft with cavities partially filled with liquid and equipped with an operational magnetohydrodynamic (MHD) element in the loop of its attitude control. This element makes possible the creation of hingeless systems of stabilization and orientation that do not require rocket propellant consumption. The application of an MHD element is considered for stabilization in the mode of spin-up of a spacecraft not having gyroscopic stability.     

液体大幅晃动类等效力学模型研究

基于液体大幅晃动等效力学模型研究充液航天器动力学与控制问题。首先,发展并完善了模拟液体大幅晃动的运动脉动球模型（MPBM）,结合已有的液体大幅晃动运动规律和分析结论对MPBM的法向力的计算方法进行了改进;通过数值仿真结果与已有试验结果的对比证明了以上改进工作的有效性。然后,基于MPBM建立了携带多个充液储箱的航天器动力学模型,针对携带四个储箱的充液航天器进行姿态机动控制研究。研究结果表明,四个充液储箱的三种可能的空间布局对航天器姿态机动过程中的角速度、液体晃动力矩和控制力矩将产生不同的影响;此外,还研究了液体大幅晃动等效力学模型中液体晃动阻尼因素对航天器姿态机动控制的影响。     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with a spike antenna

The problem of stabilization of a rotating spacecraft with a flexible spike antenna located along the axis of spacecraft rotation is considered. A magnetohydrodynamic element is used as a final-control element in the control loop of spacecraft attitude, and the solar direction sensor serves as a measuring device. At the first stage of investigation, the problem of stability is considered for stationary and non-stationary modes of rotation of the spacecraft with a flexible antenna and with a cavity partially filled with a low-viscosity liquid.     

Controlling the motion of a spacecraft when approaching a large object of space debris

The problem of calculating the parameters of maneuvering a spacecraft as it approaches a large object of space debris (LOSD) in close near-circular noncoplanar orbits has been considered. In [1–4], the results of analyzing the problem of the flyby of the separated LOSD groups have been presented. It has been assumed that a collector spacecraft approaches the LOSD and captures it or it is inserted into the nozzle of a small spacecraft that has a proper propulsion system (PS). However, in these papers, the flight from one object to another was only analyzed and the problem of approaching to LOSD with a given accuracy was not considered. This paper is a supplement to the cycle of papers [1–4]. It is assumed that, the final stage of approaching the LOSD is implemented by maneuvering in many orbits (up to several dozens) with low-thrust engines, but the PS operating time is fairly small compared with the orbit period in order to make it possible to use impulse approximation in the calculations.     

The Effect of Dissipative Moments Caused by Liquid Body Viscosity on the Rotation Stability of a Space Object

The influence of dissipative forces in a viscous liquid that completely fills the cavities of a space object executing a rotational motion is analyzed. The Navier–Stokes equations are solved by expanding them into a series in terms of eigenfunctions of the boundary value problem on involving the resting liquid in rotation around the longitudinal axis of a cavity. The analytical solutions for coaxial cylindrical and concentric spherical cavities are obtained, in particular, for a straight circular cylinder and a sphere. The stability of the single-axis orientation of a space object filled with a viscous liquid is investigated. The dependences of rotation decay processes and drifts of the space object's longitudinal axis from a given direction are shown on the plane of constructive parameters.     

测量不确定的充液航天器自适应鲁棒容错控制

针对三轴稳定充液航天器控制系统中同时存在外部未知干扰,参数不确定,测量不确定和执行器部分失效故障的鲁棒容错姿态机动控制问题进行研究。首先将部分充液贮箱内的晃动液体燃料等效为粘性球摆模型,采用动量矩守恒定律推导出航天器的刚-液耦合动力学方程。然后将变结构控制策略结合范数自适应估计算法设计了自适应鲁棒容错控制器,其中设计的范数自适应控制算法用于有效估计由测量不确定产生的集总扰动的未知上界;自适应估计算法则用于有效估计贮箱内的液体晃动位移变量。提出的控制策略不依赖精确的故障信息,并且在故障信息值不确定的情况下可以实现期望的姿态机动任务。基于Lyapunov稳定性分析方法证明了容错闭环系统状态变量的一致最终有界性。采用数值方法验证了所提控制方法的有效性和鲁棒性。     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

航天器贮箱大幅液体晃动三维质心面等效模型研究

针对航天器贮箱内的大幅液体晃动建立了三维质心面等效模型,此模型将贮箱内液体等效为位于液体质心处的质点,该质心点可以在质心约束面内任意运动,同时利用质心点动力学方程及接触碰撞模型近似计算液体晃动对贮箱的作用力。质心面等效模型的数值仿真结果与基于VOF方法的流体动力学数值计算结果基本吻合,从而验证了质心面等效模型用于航天器贮箱大幅液体晃动分析的有效性。     

多充液贮腔航天器耦合动力学与姿态控制

基于已有的质心面液体大幅晃动等效力学模型，采用拉格朗日方法，系统地建立了任意复杂激励下四贮腔航天器刚-液耦合动力学精确模型。由本文方法所得到的等效晃动力及晃动力矩与通过Flow3D计算出的相应结果吻合良好，验证了所建模型的可靠性。根据所建立的大幅晃动类充液航天器耦合系统动力学模型进一步研究了该类航天器在进行三轴稳定姿态机动时的主要动力学耦合特性，并设计了一类抑制姿态振荡的补偿控 制器。     

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。     

复杂结构充液航天器晃动动力学与姿态稳定性

复杂充液航天器的晃动及其对控制系统的影响是当前空间高技术的重要问题。 本文首先由力学变分原理导出充液复杂系统的方程式,其中包括流体力学方程和相应的边界条件,以及弹性连续介质力学方程;特别是,考虑了强毛细作用力的影响。其次,考查了微重条件下带有隔板的贮箱内的液体晃动、带有网孔隔板腔体内的液体晃动和粘弹性隔板对抑制晃动的作用。另外,本文将分析带有多腔充液自旋卫星的姿态稳定性,以及晃动、液体涡旋、贮箱偏置,能量耗散和哥氏加速度对卫星运动的影响。最后,讨论了多体系统充液挠性空间飞行器的稳定性问题。 同时,本文给出了数值计算结果和某些试验结果,并与理论分析作了对比。     

凹腔超声速燃烧室氢气燃烧流场数值模拟

对带长深比为10的凹腔结构的燃烧室二维氢燃烧流场进行数值模拟,燃料喷注方式采用凹腔上游喷注加辅加凹腔前壁、底壁、后壁喷注。采用三阶MUSCL格式求解二维含组分守恒N-S方程组,湍流模型采用剪切修正的RNGk-ε湍流模型,对喷氢燃烧工况进行了计算研究,并分别分析了凹腔中不同燃料喷注方式对燃烧特性的影响。结果表明：凹腔是火焰驻留的主要区域;凹腔上游喷注氢,可以使燃料在凹腔中混合燃烧,辅加凹腔中喷氢的三种方式对燃烧状况产生一定的影响。在凹腔前壁、底面辅加喷氢,没有增强凹腔的稳焰特性,对整个燃烧状态影响不大;在凹腔后壁喷氢,能够增加凹腔中的燃料含量,加强了回流效果,对燃烧状态影响较大。三种喷注方式都没有从根本上改变凹腔燃烧流场的特性。     

横向激励下液体大幅晃动建模分析

研究部分充液球形贮箱内的液体在横向推力作用下发生大幅晃动的等效力学模型,建模过程同时考虑平动和转动激励。建立一种新的等效模型,首次提出液体的静平衡表面垂直于等效重力方向的假设,将液体的大幅运动分解为跟随等效重力的整体运动和在此基础上的小幅晃动,该等效模型能够更好地模拟液体大幅晃动情形。将仿真得到的晃动力和力矩与传统等效模型及Flow-3d的结果进行对比,验证了新模型的有效性和准确性。该模型可应用于探月软着陆悬停避障过程等实际工程问题中。     

液体多模态晃动充液航天器姿态机动复合控制

主要研究多模态液体晃动时充液航天器大角度姿态机动动力学与控制问题。采用液体晃动弹簧质量等效力学模型将液体燃料前两阶液体晃动模态纳入到充液航天器耦合动力学模型中;根据动量矩守恒定律推导出充液航天器耦合系统动力学方程。针对充液航天器大角度姿态机动同时抑制燃料晃动的问题,采用自适应动态输出反馈的姿态控制方法并结合基于前馈控制的多模态ZVD输入成型器设计复合控制器。通过数值模拟给出了液体晃动响应及航天器姿态机动的时间历程图,数值仿真结果表明了本文所给出复合控制方法的有效性。     

Equivalent mechanical model for liquid sloshing during draining

For a spacecraft draining liquid fuel during a continuous thruster maneuver, a brief equivalent method is proposed to model the time-varying properties of liquid sloshing for dynamics and control design. The sloshing liquid during draining is equivalent to a set of mechanical model with variable parameters. The model parameters for sample filling ratios are determined by an efficient finite element method according to equivalent principles, while the parameters for other filling ratios are obtained by piecewise linear interpolation. Using the proposed model, forces and torques acted on a Cassini shaped tank by the inside liquid during draining are investigated undergoing several typical motions. Verifications and comparative studies are done with Computational Fluid Dynamics simulations, which confirm the accuracy of the brief model while the sloshing amplitude is small and the flow rate is low.     

航天器相对运动建模及周期性相对运动求解

面向航天器编队飞行的需求,对椭圆参考轨道航天器非线性周期相对运动条件进行研究,提出了确定椭圆参考轨道编队航天器非线性周期性相对运动条件的新方法。首先,考虑非线性、椭圆轨道等因素,通过哈密尔顿-雅可比(HJ)方程和正则摄动理论,推导了在任意非线性摄动下相对运动的模型和获得不需消耗任何燃料的周期性相对运动轨道的条件;然后,采用时域配点法,结合改进的列文伯格-马夸尔特(LM)法对周期性相对运动的初值进行求解;最后,设计数值仿真算例,利用上述条件,得到不消耗任何燃料的周期性绕飞轨道,由此验证了本文所提模型和方法的正确性。     

携带晃动燃料柔性航天器姿态机动中的同宿环分叉研究

本文研究了带液体晃动和柔性附件的耦合航天器系统在液体燃料耗散和柔性附件扭转振动的作用下,经历从最小惯量轴到最大惯量轴姿态机动中的混沌动力学行为.将液体晃动等效为球摆模型并由此建立了带柔性附件充液航天器多体耦合系统动力学模型.首先推导出耦合系统动力学方程并采用Melnikov积分预测受扰系统稳定与不稳定流形是否横截相交,得到了参数形式表达的混沌运动解析判据,这对航天器的设计有重要的指导意义.研究发现,混沌的发生依赖于刚体形状,阻尼比,充液比和扭转振动频率.此外,在经过被动再定向姿态机动后,由于液体晃动的本质非线性特性,充液航天器最终将进行大章动角的周期极限环运动而非绕着最大惯量轴自旋.     

非轴对称贮箱液体晃动的等效力学模型

针对非轴对称贮箱液体晃动问题,从一般意义上推导了作三维运动的任意三维贮箱内液体晃动的等效力学模型,采用有限元方法建立计算等效力学模型参数的数值算法,利用矩阵相似变换的性质分离液体零频以消除液体刚度矩阵的奇异性,从而将等效力学模型参数的计算归结为广义特征值问题和线性代数方程组的求解,具有较高的计算效率。通过非轴对称贮箱液体晃动的算例说明,不同的等效晃动方向可能不正交,晃动平面可能不过液体质心,因此非轴对称贮箱液体晃动的等效力学模型比轴对称贮箱液体晃动的更加复杂。最后以三棱柱形充液贮箱为例,采用商用CFD（计算流体动力学）分析软件FLOW-3D验证了在贮箱作典型三维运动时等效力学模型的有效性。
     

带空间机械臂的充液航天器姿态动力学研究

本文研究空间机械臂运动对充液航天器姿态的影响，讨论了利用机械臂调整充液航天器姿态问题、以及机械臂操作与航天器姿态稳定的协调问题。研究表明：影响充液航天器姿态的因素除了机械臂运动的路径，还有机械臂运动的时间、机械臂转角的变化规律、液体的粘性、质量和惯性张量等。其中机械臂运动时间的影响比较明显，而且机械臂运动得越慢对航天器姿态的影响越大。合理地选择机械臂操作时间和机械臂转角变化规律，可以实现机械臂操作