Control of the deployment of an orbital tether system that consists of two small spacecraft

Control of an orbital tether system that consists of two small spacecraft has been considered. The proposed control laws are based on the modification of well-known programs for the deployment of tether system systems under the assumption that the masses of spacecraft and the tether are comparable in magnitude. To construct nominal deployment programs, we have developed a mathematical model of the motion of the given system in an orbital moving coordinate system taking into account the specific features of this problem. The performance of the proposed deployment programs is assessed by a mathematical model of the orbital tether system with distributed parameters written in the geocentric coordinate system. The test calculations involve a linear regulator that implements feedback on the tether length and velocity.     

再论空间系绳在回收容器返回中的应用

在已有的研究结果的基础上，对空间系绳在回收容器回中的应用，作了进一步分析，包括从回收容器离开空间站至回收容器从系绳上脱落的系绳伸展运动，（２）从系绳脱落的回收容器的返回运动，（３）释放容器后的系绳的收回运动。对回收容器的动态释放，除了两阶段指数型伸展程序外，还提出了另外两种导致系绳后摆的方式。对静态释放与动态释放，不仅对系绳长度，而且对系绳张力作了计算与分析。为了系绳收回过程的稳定，不仅要施加张力     

On the deployment dynamics of tether connected two-body systems

A general formulation of the deployment dynamics of tether connected two-body systems taking into account the three dimensional librational motion, longitudinal and transverse vibrations of the continuous tether, eccentricity of the orbit and aerodynamic drag in a rotating, oblate atmosphere, is presented. Three simple deployment procedures (uniform, exponential and their combination) are considered. In the beginning analytical solutions are obtained for the degenerate case of negligible vibrations in a circular orbit, which help in establishing trends for the more general situation. This is followed by the general dynamics of the system investigated through integration of the linearized autonomous equations of motion numerically. Typical plots are presented which describe the effects of various system parameters on the tether dynamics during deployment of a subsatellite from the Space Shuttle.     

YES2 optimal trajectories in presence of eccentricity and aerodynamic drag

YES2 (launching 2007) aims to demonstrate a tether-assisted re-entry concept, whereby payload will be returned to Earth using momentum provided from a swinging tether. Deployment takes place in two phases: (1) deployment of 3.5 km of tether to the local vertical and hold, and (2) deployment to 30 km for a swinging cut. Optimal trajectories are determined for both phases after comparing the effect of different cost functions on the deployment dynamics. Closed-loop control is provided by linearizing the dynamics around the optimal trajectories and solving a receding horizon control problem for a set of linear feedback gains. The controllers are tested in a flexible tether model with large disturbances to the hardware model and environmental variables. Closed-loop simulations show that the system can be controlled quite well using only feedback of length and length rate.     

Optimal control of the Shuttle-Tethered-Subsatellite system

Alternate control laws based on an application of the linear regulator problem are developed for possible use in the operation of the Shuttle-Tethered-Subsatellite system. Control is assumed to be provided only by modulating the tension level in the tether as a function of the difference between actual and commanded tether line length, length rate, in (orbital) plane swing angle and swing angle rate. Necessary and sufficient conditions for stability of the (linear) system motion in the vicinity of its nominal local vertical orientation are developed. By proper selection of the state and control penalty matrices it is possible to obtain faster responses with no increase in maximum power levels for use in station keeping when compared with alternate control strategies. The weighting matrices are adjusted in a piecewise adaptive manner to provide control law gains in order to achieve a smooth deployment history. Successful retrievel is dependent mainly on the initial conditions and the rate at which the commanded length is reduced.     

绳系卫星系统的运动与控制

绳系卫星系统的运动与控制分析,是绳系卫星应用的基础。本文的数学模型考虑了作用在子星、主星及系绳上的空气阻力以及在伸展与收回阶段主星与系绳之间的质量传递,给出了相应的具体的计算式。应用该数学模型,本文对现有的几种主要控制法,进行了模拟计算,作出评审意见。     

柔索驱动式航天员虚拟微重力训练系统控制与实验

针对现有的航天员地面微重力训练设备存在成本高、单次训练时间短、模拟精度低等问题,提出了一种柔索驱动的航天员虚拟微重力训练系统。通过采样航天员对作业对象的操作力,控制柔索驱动虚拟物体(末端执行器)运动,使虚拟物体符合在微重力环境中的运动规律。建立了柔索驱动训练系统的动力学模型,分析了系统的特性。针对传统力伺服系统多余力对控制力精度影响较大且难以克服的问题,提出了一种使用弹簧产生柔索张力的并联柔索全位置型控制方法,并引入力/速局部反馈的控制策略。实验结果表明,系统克服多余力效果明显,可以获得较高的驱动力控制精度;虚拟质量在操作力作用下的运动符合在微重力环境中的运动规律,且有较高的模拟精度;系统稳定性良好,可以实现微重力环境中移动不同质量物体的虚拟作业训练。     

Fractional order tension control for stable and fast tethered satellite retrieval

The retrieval of a tethered satellite system is intrinsically unstable. This paper develops a new control strategy to retrieve the tethered satellite system stably and quickly using the fractional order control theory. The governing equation of the tethered satellite system and classic linear feedback tension control law were first reviewed and examined as a benchmark. Then, a new fractional order tension control law has been to avoid the tethered satellite winds around the main satellite near the end of retrieval by existing integer order tension control laws. The newly proposed control law has been discretized and implemented by the Laplace transform and Tustin operator. Unlike the existing integer order control laws, which are based on the feedback of current state and memoryless, the fractional order control law has the memory of previous states and thus controls the tether retrieval more smoothly while maintaining the retrieving speed. The effectiveness and advantage of the new fractional order tension control law is demonstrated numerically by comparing with its integer order counterpart. The results show that the new control law not only retrieves the subsatellite without winding around the main satellite, but also provides a better control performance with smaller in-plane libration angles.     

Mechanics of very long tethered systems

A space elevator has been proposed as an alternate method for launching satellites; however, the materials available now are not strong enough to support the stress generated in the structure. On the other hand, with the existing technology, a partial elevator is feasible. In this paper, the mechanics of a very long tethered system that functions as a partial elevator is studied. For such a system, the center of mass, center of gravity, and center of orbit are not coincident; disregarding this distinction can lead to erroneous results. A relation between these three points is presented in this paper. A consistent stress distribution along the tether is obtained by taking into account the distinction between these points. Dynamics of the system consisting of two end bodies, the tether (with mass), and a climber is examined. The equations of motion are derived using the Lagrangian formulation and analyzed numerically.     

Experiments and numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters

The amount of space debris is ever increasing, and pollution of the space environment has become a serious problem that can no longer be ignored. Consequently, the active removal of large space debris from crowded economically useful orbits should begin as soon as possible. The Japan Aerospace Exploration Agency has been investigating an active debris removal system that employs highly efficient electrodynamic tether (EDT) technology for orbital transfer. This study investigates the tether deployment from a spool-type reel using thrusters by means of numerical simulations of an EDT system. The thrusters are used in order to ensure the deployment of a tether with the length of several kilometers. In the simulations using a multiple mass tether model, the key parameters are estimated from various on-ground experiments. By means of the numerical simulations, the dynamics of tether deployment is studied and requirements of thruster needed for the deployment, such as the thrust forces and the periods of thruster activation, are clarified.     

Qualification and in-flight demonstration of a European tether deployment system on YES2

This paper highlights the design, qualification and mission performance of the tether deployer system on the second Young Engineers’ Satellite (YES2), that featured a tethered momentum transfer. The deployer is designed with a broad range of near-term tether applications in mind. The system contains the tether, including features to enhance safety and wound up in controlled manner onto a spool core, optical deployment sensors, a “barberpole” friction brake controlled by a stepper motor and a triple tether cutter system. To initiate the deployment a spring-based ejection system was developed, and to apply accurate momentum transfer a timer and release system is present on the subsatellite side. A small, 6 kg re-entry capsule was developed as subsatellite. On September 25th, 2007, YES2 deployed a 32 km tether in orbit and gathered a wealth of data. Confidence is gained from the mission results for use of the deployer in future missions.     

Tether-platform coupled control

From the control point of view, tethered systems pose several challenges, the major one pertaining to the regulation of the unstable system dynamics during the retrieval phase. On the other hand, the system configuration permits design of controllers using length rate, tension and offset schemes, which are not feasible with other satellites. Here “offset” refers to the time dependent variation of the tether attachment point at the platform end. The present paper studies several applications of the offset scheme in controlling the tethered systems. To that end, planar equations of motion of a space platform based Tethered Satellite System (TSS) are derived by the Lagrangian procedure. This is followed by representative results aimed at the offset control of platform pitch, tether attitude and vibration motions. The offset scheme is used for simultaneous control of platform and tether pitch motion. Finally the attention is directed towards simultaneous regulation of the platform pitch and longitudinal tether vibration. The numerical results clearly show considerable promise for the offset control scheme in regulating tether, platform and combined tether-platform dynamics.     

改进的绳系卫星系统距离速率控制律

为扩大绳系卫星系统(TSS)控制的稳定域,提出了一种改进距离速率控制算法。根据TSS动力学方程及构造的二阶稳定系统,给出了修正的控制模型。讨论了稳定释放角度和释放/回收速度的影响,并研究了固定绳索长度系留控制方案。算例表明该方法可显著扩大稳定域,提高释放速度。     

一种用于导弹姿态控制系统的直接力非线性控制法

为改善传统导弹姿控系统线性控制法的不足,用相平面法分析了直接力作用下导弹的姿态运动规律和气动力作用对直接力控制的影响,提出了一种综合控制精度、姿控发动机产品特性和推进剂消耗量等指标的直接力非线性控制方法,给出了控制模型。仿真结果表明,该法能在气动力作用或干扰无法忽略的条件下实现导弹姿控发动机的开关工作正常,保证精度及推进剂消耗最省,其控制精度与线性比例微分(PD)控制律相当。     

轨控喷流干扰气动-运动一体化非定常数值模拟

针对运动条件对反作用控制喷流控制气动干扰的影响,基于雷诺平均N-S方程,建立非定常气动--运动一体化方法,通过计算流体力学(CFD)/刚体动力学(RBD)耦合求解,对一种采用轨控喷流直接力控制的锥柱裙外形进行了数值模拟,研究了干扰流场结构、力和力矩与飞行器状态随时间变化特性,分析了运动非定常计算和定常计算的对比结果以及外流参数(马赫数,攻角等)变化对气动运动特性的影响。研究结果表明：轨控喷流使飞行器运动时存在强烈的非定常特性,定常计算的法向力放大系数和干扰俯仰力矩大于运动非定常计算结果。     

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.     

基于最优控制/自抗扰控制的直/气复合控制系统设计研究

为提升控制系统的性能,对直/气复合控制导弹的控制系统设计进行了研究。以俯仰通道为例,用最优控制理论设计了基于状态反馈的导弹俯仰通道控制回路,用线性二次型调节器(LQR)获得控制律。给出了加权矩阵的选取方法:依次调整表征过载偏差、角加速度和角速度的权重,使求出的反馈增益系数满足要求。针对状态反馈控制律无法快速抑制直接力开启带来的干扰问题,用自抗扰控制(ADRC)理论改进了控制器,通过构建状态观测器在线实时估计外界干扰并予以补偿,快速抑制扰动。仿真结果表明:用最优控制/自抗扰控制设计的控制器跟踪速度快,动态过程平稳并具有较强的干扰抑制能力,提高了系统的鲁棒性。     

Results of the parabolic flight tests of the rapunzel deployer

The tether assisted re-entry of small payloads is a highly interesting tool for space transportation especially for the return of small payloads from Space Station ISSA. The small tether mission Rapunzel was initiated in 1991 by the Institute of Astronautics, TU München and the Kayser-Threde Company, to design a low cost and feasible tether experiment for the verification of the tether assisted re-entry. Together with the Samara State Aerospace University, Russia, a mission concept on a Russian Resurs or Photon capsule was developed. Based on this mission a deployer has been designed, mainly based on technology of the textile industry, which insures high reliability at low cost. Recently a similar configuration is being discussed for the ESA-TSE mission.The main work during the recent time was the development and test of the breadboard model of the deployer system. After successfully completing initial ground tests with the deployer, further tests during the ESA Parabolic Flight campaign in November 1995 were conducted. After a short introduction of the overall mission scenario, the planned configuration in orbit, this paper will present the results of the microgravity test campaign onboard the KC-135 aircraft and compare them with the ground test. The deployer showed a good performance during all tests, including ejection of the end-mass, deployment, and braking. Problems that occurred during the tests will be discussed, and solutions for the detected flaws and the results of the redesign now in progress will be presented. These verifications have shown the feasibility of the concept and will lay the base for the planned development of the flight model of the deployer.     

Tethered towing using open-loop input-shaping and discrete thrust levels

Asteroid retrieval, satellite servicing, and debris removal concepts often rely on a thrusting vehicle to redirect and steer a passive object. One effective way to tow the object is through a tether. This study employs a discretized tether model attached to six degree-of-freedom end bodies. To reduce the risk of a post-burn collision between the end bodies, discrete thrust input shaping profiles are considered including a Posicast input and a bang-off-bang thrust profile. These input shaping techniques attain desirable collision avoidance performance by inducing a tumbling or gravity gradient motion of the tethered formation. Their performance is compared to an earlier frequency notched thruster profile.     

辐射开环空间绳系机器人编队动力学及控制

提出了一种新型辐射开环空间绳系机器人编队系统,其在编队稳定性、任务灵活性及燃料消耗等方面具有明显的优势。针对辐射开环空间绳系机器人编队系统自旋运动过程中的构型误差控制问题,首先建立了编队系统的自旋动力学模型;然后分析了空间绳系机器人的绳系拉力和空间平台的自旋扭矩对编队系统自旋运动中出现的构型误差的控制能力;设计了一种依靠空间绳系机器人绳系拉力和空间平台自旋扭矩作为控制量,对构型误差进行控制的协调控制方法;最后通过数字仿真进行了校验和分析。仿真结果表明：设计的协调控制方法能够明显改善编队系统自旋运动中构型误差的控制效果。