Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.     

有扰情况下欠驱动刚性航天器旋转轴稳定研究

研究欠驱动刚性航天器受到正弦干扰力矩作用时的旋转轴指向稳定控制问题。采用欧拉-泊松形式描述航天器的运动方程,然后分别针对轴对称情况和非轴对称情况设计控制律,并结合Lyapunov直接法和LaSalle不变性定理证明控制律的全局渐近稳定性。理论分析和仿真结果都表明新的控制律能够实现旋转轴指向全局渐近稳定。     

航天器的起旋和消旋运动

本文利用轴对称刚体在自身力矩作用下,绕定点运动的一阶正规型运动微分方程代替欧拉方程,讨论航天器的起旋和消旋运动。给出两个卡尔丹角为小量时运动方程的解析积分,由此直接导出航天器相对质心的动量矩矢量及自旋轴在起旋和消旋运动中的变化规律。并以伽里略航天器作为具体对象进行了数值计算。     

欠驱动刚性航天器姿态的非完整运动规划粒子群算法

研究欠驱动刚性航天器姿态的非完整运动规划问题。众所周知航天器利用三个动量飞轮可以控制其姿态和任意定位，当其中一轮失效，航天器动力学方程表现为不可控。在系统角动量为零的情况下，系统的姿态控制问题可转化为无漂移系统的运动规划问题。基于粒子群优化技术设计了欠驱动刚性航天器姿态的非完整运动规划算法。通过数值仿真，并和遗传算法进行了比较，结果表明该方法对欠驱动航天器姿态运动规划是有效的。     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

万有引力场中带挠性太阳帆板航天器的姿态稳定性

本文讨论带双侧挠性太阳帆板航天器在万有引力场中的姿态运动，建立带挠性帆板航天器的欧拉方程和帆板强迫振动方程。利用Ｇａｌｅｒｋｉｎ方法对动力学方程离散化，利用Ｋｅｌｖｉｎ－Ｔａｉｔ－Ｃｈｅｔａｙｅｖ定量判断航天器在轨道坐标系内相对平衡的稳定性。导出适用于任意阶模态的解析形式稳定性充分条件。     

大角速度柔性航天器动力学模型修正

将拉格朗日方程及其准坐标形式用于中心刚体加柔性附件航天器的拉格朗日函数,推导了中心刚体加柔性附件航天器动力学模型。针对航天器大角速度,分析中心刚体角速度对角动量方程的影响,对传统动力学模型进行修正。航天器绕惯量主轴大角速度自旋仿真结果验证了修正后的动力学模型对于大角速度航天器的有效性。     

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。     

Physico-chemical state of the air at the stagnation point during the atmospheric reentry of a spacecraft

Hypersonic flows around spatial vehicles during their reentry phase in planetary atmospheres are characterized by intense aerothermal phenomena. The aim of this work is to analyze high temperature flows around an axisymmetric blunt body taking into account chemical and vibrational non-equilibrium for air mixture species. For this purpose, a finite volume methodology is employed to determine the supersonic flow parameters around the axisymmetric blunt body, especially at the stagnation point and along the wall of spacecraft for several altitudes. Our code permits to capture the detached shock wave with exactitude before a blunt body placed in supersonic free stream. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, along with CFL coefficient and mesh size level are selected to ensure numerical convergence, sought with an order of 10^?8.     

大型空间结构的自适应控制

本文将Bar-Kana等人的模型参考自适应控制法(MRAC)用于柔性结构的自适应控制中,原方法要求系统的输入维数等于输出维数。对于柔性的大型空间结构(LSS),观测量的数目往往大于输入量的数目。本文采用组合LSS各观测点的信号,形成综合输出矢量Y_P,以满足自适应控制系统中,用较少的控制输入达到控制LSS结构中较多观测点的要求。为了克服跟踪误差,本文建议用最优返馈增益阵作为输出阵C_P,并采用LQR理论以求C_P。 本文将大型空间结构的实例简化成离散模型,进行模拟计算,计算结果说明系统有较好的跟踪特性,当LSS的柔度变化较大时,系统具有跟踪的鲁棒性。     

Study of the mode of angular velocity damping for a spacecraft at non-standard situation

Non-standard situation on a spacecraft (Earth’s satellite) is considered, when there are no measurements of the spacecraft’s angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft’s attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft’s angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft’s angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft’s rotational motion.     

Perturbation solution of attitude motion under body-fixed torques

Approximate analytical solutions are established for the attitude rates and angles of a rigid body subjected to a constant body-fixed torque. The perturbation solutions obtained are valid for any arbitrary inertia parameters. The small parameter is defined as the ratio between representative transverse rotation rate and the spin or scan rate. The results should be useful for quickly evaluating the attitude response of a spin-stabilised or scanning spacecraft to a variety of torque inputs. The applicability of the theory is illustrated by means of practical examples such as the spin-down due to rate coupling of ESA's GEOS spacecraft and the prediction of the attitude drift of the HIPPARCOS satellite during payload initialisation. Furthermore, the compact first-order results should be suitable for implementation in on-board manoeuvre or attitude control software.     

带挠性附件卫星的模型化及截断

本文给出了具有中心刚体和P个挠性附件的空间飞行器姿态动力学方程式,并用约束和非约束两种模态展开,得到时域求解的状态方程式和频域中的增广姿态角对控制力矩的逆传递函数阵。推导中考虑了挠性附件对中心刚体的相对运动。本文还给出了两种模态恒等式,其中之一可用来做控制系统分析时截断高阶方程式的截断准则。     

Analytic expansions of luni-solar gravity perturbations along rotating axes for trajectory optimization—Part 2: The multipliers system and simulations

An efficient self-contained trajectory optimization software is generated by making use of de Pontécoulant's analytic lunar theory removing the need for an outside third body ephemeris program to compute the lunar and solar position vectors at each integration step. The accelerations being further resolved along the rotating Euler–Hill frame after expansion to third order in the spacecraft radial distance, the adjoint differential equations are derived in a direct manner complementing the generation of the dynamic system of equations for full compatibility. Because the variation of parameters equations are cast in terms of the nonsingular equinoctial elements with the perturbation accelerations resolved in their analytic form along the rotating axes, the adjoint equations are also derived in the same manner providing a highly efficient and accurate system of equations for rapid computations in conjunction with Aerospace Corporation's NLP2 nonlinear programming codes to search for the initial values of the multipliers that steer the spacecraft towards its target orbit in minimum time. Numerical simulations show that the solutions obtained by the analysis developed in this paper are essentially identical to the more indirect approach based on the use of inertial accelerations obtained from a separate ephemeris generator and subsequent conversions to the thrust frame and equinoctial system.     

一类挠性多体航天器快速大角度机动的动力学与控制

研究一类挠性多体航天器快速大角度机动的动力学与控制问题。考虑构形为“刚性主体 绕性梁 刚性端质量”的航天器，并假定它在一平面内作大角度旋转运动，本文利用Hamilton原理，建立了系统的非线性无穷维动力学模型，在只可测量刚性主体旋转角及其速率的情况下，设计了一种线性反馈控制方案，并证明了相应的闭环系统的渐近稳定性。     

挠性飞行器的脉冲调制控制

三轴稳定控制是大挠性飞行器有效和重要的姿态控制方式，喷嘴控制是实现三轴稳定控制的手段之一。本文针对伪速率调制器（ＰＳＲＭ）和脉冲调宽调频调制器（ＰＷＰＦＭ），采用非线性脉冲调制器线性化和描述函数两种方法来分析大挠性航天飞行器的姿态稳定性问题，并对某型卫星的远地点点火姿态控制系统进行了分析和仿真。     

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。     

Impulsive control for angular momentum management of tumbling spacecraft

We discuss an angular momentum control of a tumbling spacecraft. The proposed control method is to apply an impulse by a space robot arm, to measure and control the relative position and attitude between the target spacecraft, and then to apply another impulse until the rotational motion of the target spacecraft is well damped. A discrete controller is designed using the simplified equations of rotational motion through appropriate coordinate transformation. The stationary response under contact model uncertainty is investigated and stability condition is analytically derived. Numerical simulations are given to validate the proposed approach.     

Asymptotic theory for thrusting,spinning-up spacecraft maneuvers

We consider the problem of a spacecraft subjected to constant body-fixed forces and moments about all three axes during a spinning-up, thrusting maneuver. In applications, undesired forces and moments can arise due to thruster imbalances and misalignments and to center-of-mass offset. In previous works, approximate analytical solutions have been found for the attitude motion, and for the change in inertial velocity and inertial position. In this paper we find asymptotic and limiting-case expressions which we derive from the analytic solutions, in order to obtain simplified, practical formulas that lend insight into the motion. Specifically, we investigate how the motion evolves (1) as time grows without bound and (2) for geometric cases of the sphere, the thin rod, and the thin plate. Closed-forms or upper-bound limits are provided for angular velocities, Eulerian angles, angular momentum pointing error, transverse and axial velocities, and transverse and axial displacements. Summaries for the asymptotic limits (for zero initial conditions) are provided in tabular form. Results are verified by numerical simulations.