Stability of spinning satellite under axial thrust and internal mass motion

This paper considers a spinning rigid body and a particle with internal motion under axial thrust. This model is helpful for gaining insights into the nutation anomalies that occurred near the end of orbit injections performed by STAR-48 rocket motors. The stability of this system is investigated by means of linearized equations about a uniform spin reference state. In this model, a double root does not necessarily imply instability. The resulting stability condition defines a manifold in the parameter space. A detailed study of this manifold and the parameter space shows that the envelope of the constant solutions is in fact the stability boundary. Only part of the manifold defines a physical system and the range of frequency values that make the system unstable is restricted. Also it turns out that an increase of the spring stiffness, which restrains the internal motion, does not necessarily increase the stability margin. The application of the model is demonstrated using the orbit injection data of ESA's Ulysses satellite in 1990.     

FY-2C星控制分系统设计

介绍了风云二号(FY-2)气象卫星双自旋稳定控制分系统的组成、功能和技术指标,以及卫星起旋控制、章动角与摇摆角控制、敏感器设计和消旋子系统设计等关键技术.C星在轨运行情况表明,控制分系统工作正常、性能稳定,圆满完成了起旋、主动章动控制、测定姿、姿态机动、转速调整、定点捕获和天线消旋对地定向等任务,技术指标满足任务书要求.     

Study of a bunch of three algorithms for magnetic control of attitude and spin rate of a spin-stabilized satellite

We consider the angular motion of an axi-symmetrical satellite equipped with an active magnetic attitude control system. Dynamics of the satellite is studied on the entire control loop, consisting of a bunch of three successively used algorithms. The control cycle includes the stages of nutation damping, spinning up the satellite about its symmetry axis, and reorienting the symmetry axis into a preset direction in the inertial space. The results are confirmed by numerical simulations.     

Stability of large damped flexible spacecraft with stored angular momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.     

空间绳系机器人抓捕非合作目标的质量特性参数辨识

针对空间绳系机器人抓捕非合作目标/空间垃圾后需要对其进行回收/拖曳的精确控制问题,提出了一种利用抓捕后保持阶段的振动特性辨识目标参数的方法。首先,根据质量特性参数辨识的需要,推导了系统的动力学模型。不同于以往将本体卫星和被抓捕目标简化为质点的动力学模型,本文针对任意的目标抓捕位置,在考虑重力梯度影响的基础上,利用拉格朗日法获得系统各广义坐标的动力学公式。然后,分析非合作目标和系绳在后抓捕保持阶段的姿态运动。最后,在非合作目标与本体卫星没有任何信息交互的情况下,利用后抓捕阶段目标卫星和系绳特有的振动,并使用具有鲁棒性可遗忘因子的递推最小二乘法,提出了包括转动惯量和质心到任意抓捕点距离在内的质量特性参数辨识算法。     

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.     

One method of gravitational attitude control of a rotating satellite

The mode of spinning up a low-orbit satellite in the plane of its orbit is studied. In this mode, the satellite rotates around its longitudinal axis (principal central axis of the minimum moment of inertia), which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around the longitudinal axis is several tenths of a degree per second. Gravitational and restoring aerodynamic moments were taken into account in the equations of satellite’s motion, as well as a dissipative moment from eddy currents induced in the shell of the satellite by the Earth’s magnetic field. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape and nongravitational external moments are introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasistationary rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. We propose to consider such quasistationary rotations as unperturbed motions of the satellite in the spin-up mode.     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.     

Influence of disturbances on the angular motion of a spacecraft in the powered section of its descent

The motion of a variable-mass spacecraft is considered in the powered section of a descending trajectory. Approximate analytical solutions are obtained for the angles of spatial orientation of the spacecraft, which allows one to analyze the nutation motion and to develop recommendations on the spacecraft’s mass configuration, providing the smallest possible deviations of the longitudinal axis and thrust vector from specified directions. The errors of stabilization of the spacecraft’s longitudinal axis are calculated by means of numerical integration of complete models and using the obtained analytical solutions, the results being in good agreement.     

Spin-stabilized satellite magnetic attitude control scheme without initial detumbling

The angular motion of an axisymmetrical satellite equipped with an active magnetic attitude control system is considered. The dynamics of the satellite are analytically studied on the whole control loop. The control loop is as follows: preliminary reorientation along with nutation damping, spinning about the axis of symmetry, then precise reorientation of the axis of symmetry in inertial space. Reorientation starts right after separation from the launch vehicle. Active magnetic attitude control system time-response with respect to its parameters is analyzed. It is proven that low-inclined orbit forces low control system time-response. Comparison with the common control scheme shows the time-response gain. Numerical analysis of the disturbances effect is carried out and good pointing accuracy is proved.     

卫星液体晃动气浮台仿真试验系统的运动分析

本文通过边界元数值法求解了部分充液自旋球腔内的液体晃动问题。以流体运动的基本方程和系统运动的Ｅｕｌｅｒ动力学方程为基础，考虑了贮箱偏置、涡旋、重力及Ｃｏｒｉｏｌｉｓ力等因素对流体晃动和系统运动状态的影响，求解出液体的速度场，并在此基础上估算液体的能量耗散率和系统的章动时间常数     

The Solution of Some Problems of Optimizing the Processes of a Flexible Correction of Motion of Satellite Systems: II.

In a previous paper [1], as a result of group-theoretic decomposition, one of the problems of the optimization of the flexible correction process was reduced to a series of subproblems. In this paper, the analytical solutions to these subproblems are obtained by the sweep method. A series of other similar problems with different variants of flexibility is also considered; the decomposition of these problems is performed, and their analytical solutions are presented. It is shown for some numerical examples that flexible corrections require essentially lower fuel consumption than the rigid correction, where all parameters characterizing the absolute motion of a satellite system are corrected to their nominal values.     

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。     

Model development and adaptive imbalance vibration control of magnetic suspended system

A system model is developed to describe the translational and rotational motion of an active-magnetic-bearing-suspended rigid rotor of a single-gimbal control moment gyro (SCMG) onboard a rigid satellite. This model closely reflects the motion characteristics of the rotor by considering the dynamic and static imbalance as well as the coupling between the gimbal's and the rotor's motion on a satellite platform. Adaptive autocentering control is strictly constructed for the preceding rotor with unknown dynamic imbalance. The rotor achieves its rotation about the principal axis of inertia by identifying the little rotational angles from the geometric axis to the principal axis and then using the results to tune a stabilizing controller, which is composed of a decentralized PD controller with cross-axis proportional gains and high-pass and low-pass filters. The main disturbance in the wheel spinning can thereby be completely removed and the vibration acting on the satellite can be attenuated.     

The Motion of Coaxial Bodies of Varying Composition on the Active Leg of Descent

The motion of a spacecraft (SC) with double rotation and variable mass on the active leg of its descent is considered. The SC consists of two coaxial bodies. The coaxial scheme is used for gyroscopic stabilization of the SC longitudinal axis by the method of partial spin-up. The equations of spatial motion of coaxial bodies of varying composition are derived and approximate solutions for the angles of spatial orientation are found. The condition of decreasing amplitude of nutation oscillations is obtained, which allows the estimation of efficiency of the stabilization by partial spin-up. The errors in the magnitude and direction of the vector of braking thrust are also determined.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 224–232.Original Russian Text Copyright © 2005 by Aslanov, Doroshin, Kruglov.     

Optimal control of a spinning double-pyramid Earth-pointing tethered formation

The dynamics and control of a tethered satellite formation for Earth-pointing observation missions is considered. For most practical applications in Earth orbit, a tether formation must be spinning in order to maintain tension in the tethers. It is possible to obtain periodic spinning solutions for a triangular formation whose initial conditions are close to the orbit normal. However, these solutions contain significant deviations of the satellites on a sphere relative to the desired Earth-pointing configuration. To maintain a plane of satellites spinning normal to the orbit plane, it is necessary to utilize “anchors”. Such a configuration resembles a double-pyramid. In this paper, control of a double-pyramid tethered formation is studied. The equations of motion are derived in a floating orbital coordinate system for the general case of an elliptic reference orbit. The motion of the satellites is derived assuming inelastic tethers that can vary in length in a controlled manner. Cartesian coordinates in a rotating reference frame attached to the desired spin frame provide a simple means of expressing the equations of motion, together with a set of constraint equations for the tether tensions. Periodic optimal control theory is applied to the system to determine sets of controlled periodic trajectories by varying the lengths of all interconnecting tethers (nine in total), as well as retrieval and simple reconfiguration trajectories. A modal analysis of the system is also performed using a lumped mass representation of the tethers.     

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.     

Analysis of a double gimbaled reaction wheel spacecraft attitude stabilization system

Three axis attitude stabilization of a satellite using a single spinning reaction wheel mounted on a two degree-of-freedom passively and actively torqued gimbal system is investigated. The passive control is assumed to be provided by a spring-loaded damper mounted on each of the gimbal axes, while active control results from both the wheel acceleration and the torque applied about the gimbal axes. The stability of the uncontrolled and passively controlled systems is investigated analytically. For constant wheel speed the pitch motion is decoupled from the roll-yaw and gimbal motions. Control laws for the roll-yaw motion are developed based on pole clustering and linear optimal control theory. For the pitch motion control laws are obtained based on classical second order system theory. Estimation techniques are applied to the roll-yaw system for the case when the complete state may not be directly observable (in the absence of a fine yaw position sensor).     

双自旋同步气象卫星的姿态稳定度分析

本文在一般双自旋卫星动力学模型线性分析的基础上,给出了双自旋同步气象卫星姿态稳定度的数学描述和不规律姿态运动(摆动运动、章动运动)对姿态稳定度影响的解析表达式,并与非线性模型数学仿真结果进行对比,表明仿真结果与线性分析结果相当一致。