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.     

绳网拖曳带帆板失效卫星的波动控制

针对带有柔性太阳帆板的失效卫星，提出了一种基于波动控制理论的控制方法，同时实现了绳网拖曳过程中稳定碎片姿态与抑制帆板振动两个目标。首先，提出一种新的绳网简化结构，用Kane方法建立了动力学模型，使其能够在保证运算效率的同时具有更高的精度。然后，针对系统特性设计了波动控制策略，仅需要输入系绳张力的大小和方向，便能通过拖船位置的改变来消除失效卫星的自旋和帆板振动。最后，通过数值仿真验证了控制律的有效性。仿真结果表明，在控制律作用下的拖曳过程中，失效卫星的姿态能够快速稳定，同时帆板的振动也得到了良好的抑制。     

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。     

TETHERED SATELLITE SYSTEM ANALYSIS (1) — TWO-DIMENSIONAL CASE AND REGULAR DYNAMICS

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.     

空间碎片绳网捕获拖曳恒张力控制

针对空间绳网系统捕获空间碎片后，在轨道转移过程中的精确控制问题，提出一种使用常值拉力将空间碎片拖曳至坟墓轨道的方法。首先，采用牛顿欧拉法建立绳系组合体动力学模型；其次，通过李雅普诺夫方法证明仅使用恒张力即可实现拖曳过程的稳定控制；再次，提出采用常值拉力切换控制律抑制空间碎片的姿态章动，采用基于相平面控制原理的控制律抑制绳系组合体面内面外摆动，规避在轨道转移过程中系绳松弛造成缠绕、系绳张力过大造成断裂或两星接近发生碰撞等风险。最后，通过拖曳离轨全过程仿真分析，校验了所提出控制方法的有效性。     

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.     

绳系太阳能发电卫星姿态机动的主动振动控制

针对绳系太阳能发电卫星大角度回转机动时太阳能板的振动抑制问题,提出了主姿态控制和基于绳中张力的主动振动控制技术相结合的复合控制方法。建立了绳系太阳能发电卫星系统的动力学方程,并基于任务函数控制算法设计了主控制器保证卫星姿态的渐近稳定和挠性结构振动的衰减性;考虑到绳的非线性特性,基于任务函数控制算法设计了绳系卫星系统的主动振动抑制辅助控制器来抑制挠性结构的振动。设计的同时证明了系统的稳定性。将该方法应用于绳系卫星的大角度单轴回转机动的仿真研究,结果表明:该方法不仅能够使绳系卫星完成姿态机动,而且能够有效地抑制太阳能板的振动。     

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.     

绳系卫星的一种新型高阶滑模控制器设计

针对绳系卫星轨道转移控制问题,给出绳系卫星在轨机动模型并将面内运动处理为典型的欠驱动形式;为实现对面内摆角的跟踪控制,定义滑模面并建立积分链系统,设计一种新型高阶滑模系绳张力控制律,得到无抖振控制量,这种控制律在保证高精度跟踪的前提下,有效避免了控制抖振现象;关于滑模面的高阶滑模运动建立后,在平衡点对闭环系统线性化,根据劳斯判据,闭环系统在平衡点是局部渐近稳定的。最后,通过仿真分析,验证了所提出控制算法的有效性。     

利用姿态机动的绳系卫星编队系统轨道协同控制

为克服绳系卫星编队系统在轨道机动过程中的系绳摆动现象，提出一种通过调整领航星推力方向进而实现编队系统轨道跟踪的控制算法。由于推力方向角与状态量互相耦合且少于系统自由度个数，轨道协同控制属于典型的非仿射欠驱动控制问题。针对此问题，首先采用升阶法将角速度作为虚拟控制输入；然后为各子系统设计子滑模面后加权得到高层滑模面和等效控制输入律，并设计观测器估计系统非线性项；其次基于模型预测控制算法优化得到最高层滑模面的趋近控制律；最后采用MATLAB/Simulink验证了所提控制算法的有效性。     

Study on electrodynamic tether system for space debris removal

As a countermeasure for suppressing space debris growth (P. Eighler, A. Bade, Chain Reaction of Debris Generation by Collisions in Space—A Final Threat to Spaceflight? in: 40th Congress of the International Astronautical Federation, IAA-89-628, October 1989), the National Aerospace Laboratory of Japan is investigating a satellite capture, repair and removal system for non-cooperative satellites, part of which involves assessing the viability of electrodynamic tether (EDT) technology as an orbital transfer system. In this paper, some results concerning the time required to remove existing satellites, the behavior of flexible tethers during the debris separation phase, and orbital transfer strategies of EDT systems during space debris removal operations are described. From numerical simulations, it is found that EDT systems can transfer satellites from LEO to orbits with a short lifetime within a realistic timeframe. It is also found that the stability of EDT systems is compromised when debris separation occurs both while a tether current is running and when the ratio of the end mass to that of the service satellite is high. To ensure stability, the end mass should be selected from the target debris group with due regard for the maximum possible mass that can be maneuvered safely. Moreover, it is also found that orbital elements (a, e, i) can be changed independently with an adequate current control strategy.     

一种用于空间系绳卷取的自适应机构

针对空间绳网系统的缆绳收口要求,介绍了一种由双转子电机、双卷筒和自由导绳套筒组成的自适应缆绳卷取机构,给出了机构的设计思路。通过建立其系统动力学方程,据此得到系统各状态变量的稳态解,理论和实验分析缆绳卷取过程的特性,证实此卷取机构的有效性和一定的适应性,为类似空间绳系的卷取机构设计提供参考。     

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。     

SST-LL重力测量卫星轨道分析

论述了SST-LL重力测量卫星科学任务对轨道寿命、地面覆盖性能、轨道高度单圈波动、星间距离变化范围的需求。根据需求,计算了轨道的自然衰减情况,得出轨道初始高度为500km;综合考虑地面覆盖要求及运载火箭能力,得出了最佳轨道倾角为89°;得出了0.002 0偏心率下轨道高度波动范围不超过50km;分析得出星间距离的长周期变化主要受大气阻力影响,初步确定了轨道控制方案,即定期对受大气阻力较大的卫星进行轨道机动。     

含不确定性的绳系卫星姿态的鲁棒最优控制

针对绳长变化的旋转二体绳系卫星姿态跟踪控制问题,提出了一种分布式鲁棒最优控制方法。首先针对单体绳系卫星姿态模型,在假设模型精确和不存在干扰的条件下,设计基于HamiltonJacobiBellman方程的最优控制器;进一步考虑到实际系统存在参数不确定性和干扰,采用自适应方法和鲁棒误差积分方法隐式学习参数不确定性和有界干扰,与最优控制器结合设计鲁棒最优控制器,并应用Lyapunov稳定性定理证明其闭环系统的渐近稳定性。其次,根据绳系卫星系统的运动同步性,将单体绳系卫星姿态控制器设计扩展至二体绳系卫星系统,设计二体绳系卫星姿态系统的分布式鲁棒最优控制器。最后在Matlab/Simulink平台上进行仿真验证,结果表明了所设计控制器的可行性与有效性。     

Orbital and relative motion of a tethered satellite system

A simplified model for the orbital and relative motion of a tethered satellite system is presented. The tether acts as a light elastic string with small structural damping but without bending stiffness. Its mass is taken into account in the calculation of the total kinetic and potential energies of the tethered system. This formulation allows the inclusion of the complete gravity gradient influence on the dynamics of the system. The resulting three-dimensional motion is separated in the centre of mass orbital motion on the one hand and the relative motion of the end-bodies on the other. No restrictions on length of the tether or on mass ratio of the end-masses are imposed. It is found that the frequencies and amplitudes of the longitudinal tether oscillations are realistic as long as the tether mass is less than that of the subsatellite.     

绳系卫星系统中的周期运动

在椭圆轨道上飞行的绳系卫星系统的重要特征是系绳的方向角具有周期性运动，称为驻环。不稳定的驻环导致全系统的不稳定性。本文给出系统运动的数学模型、距离速率控制方法、求解驻环的数值迭代算法、驻环的稳定性和吸引域以及控制参数平面上驻环存在的区界和计算机仿真结果     

Satellite pitch and roll attitude maneuvers through very short tethers

Explored here is the feasibility of achieving satellite pitch and roll attitude maneuvers through tethers. The proposed tethered satellite system (TSS) comprises of four identical tethers connecting the auxiliary mass to the satellite at its four distinct off-centered and equiangularly spaced points. The open-loop tether length control laws have been developed in order to achieve arbitrary pitch and roll attitude slewing maneuvers. Numerical simulation of the nonlinear governing equations of motion for these tether length variations establishes the feasibility of executing fixed as well as chase-slewing maneuvers. Nearly passive nature of the proposed mechanism using very short tethers along with small auxiliary mass needed makes the concept particularly attractive for future space missions.     

Electrodynamic Tethered Deorbit System Dynamics and Performance Analysis

Electrodynamic tethered deorbit technology is a novel way to remove abandoned spacecrafts like upper stages or unusable satellites. This paper investigates and analyses the deorbit performance and mission applicability of the electrodynamic tethered system. To do so, the electrodynamic tethered deorbit dynamics with multi-perturbation is firstly formulated, where the Earth magnetic field, the atmospheric drag, and the Earth oblateness effect are considered. Then, the key system parameters, including payload mass, tether length and tether type, are analyzed by numerical simulations to investigate their influences on the deorbit performance and to give the setting principles for choosing system parameters. Based on this and given an appropriate group of system parameters, numerical simulations are undertaken to study the impact of the mission parameters, including orbit height and orbit inclination, and thus to investigate the mission applicability of the electrodynamic tethered deorbit technology.     

绳系卫星安全捕获策略下的释放最优控制

安全捕获是绳系卫星系统空间应用的一个重要拓展。考虑系绳质量、系统质心变化及状态、控制约束,采用基于Lagrange方程的圆轨道条件下空间绳系网捕系统三维动力学模型。建立了安全捕获模型,推导得到零相对速度条件下的安全捕获末端条件。为保证方法的适用性,将基于Legendre伪谱法的连续时间最优控制问题离散为标准的非线性动态规划问题。最后在考虑释放控制前初始面外角偏差为5°的情况下,通过数值仿真验证了方法的有效性。仿真结果表明：对于远距离释放条件下的安全捕获,系统质心变化不容忽视;最小能量与绳长加速度约束下的控制响应相比最小时间与面内角约束要更平滑。