Sun–Earth L2 point formation control using polynomial eigenstructure assignment

A nonlinear controller based on polynomial eigenstructure assignment (PEA) is presented for the control of Sun–Earth L₂ point formation flying. The relative motion dynamics is formulated as a nonlinear equation and rewritten as a Quasi-Linear Time-Varying (QLTV) model. Using a coprime factorization of the desired closed-loop transfer function, the PEA controller structure is calculated by representing the controller gains as polynomials. During the implementation of spacecraft formation flying, the PEA method is extended from Linear Time-Invariant (LTI) and Linear Parameter-Varying (LPV) models to a QLTV model to produce a closed-loop system with invariant performance over a wide range of conditions. To ensure system performance, the analytic stability analysis of the closed-loop system is developed and a position keeping controller for MIMO formation flying is designed using a decoupling method to achieve the desired performance. Finally, a simulation is carried out to validate the controller performance for the formation flying.     

基于改进PEA的日地L2平动点编队飞行高精度位置保持

针对日地L2平动点相对运动拟线性变参数(QLPV)动力学模型,提出一种改进的多项式特征结构配置(PEA)方法实现日地L2平动点编队飞行高精度相对位置保持.建立日地L2平动点编队飞行相对运动QLPV动力学模型,将基于线性时不变系统(LTI)的PEA方法进行改进,设计参数/状态变化的控制方法来获取闭环系统设计传递函数,与期望传递函数进行类似于线性系统的条件匹配,获得含时变参数和状态的多项式控制器,确保系统在参数和状态变化时能保持控制系统性能不变.在进行多输入多输出(MIMO)系统的算法设计时,将系统期望传递函数设为解耦形式,实现飞行器三轴位置间的解耦控制,以确保系统的控制精度.考虑到拟线性变参数系统与传统线性系统的不同,对拟线性变参数闭环系统的稳定性进行分析.最后进行了相应的数学仿真验证算法的可行性和有效性.     

基于PEA的椭圆轨道航天器编队飞行高精度位置保持

针对航天器编队飞行时相对位置保持精度要求高的特点,采用基于线性变参数模型的多项式特征结构配置方法设计椭圆轨道航天器间相对位置控制算法。对于线性变参数控制系统,本文将基于线性定常系统的多项式特征结构配置方法推广以确保系统性能与变化参数间的独立性。在特征结构配置时,先设计带参数变化的控制器结构后计算出带未知控制器增益的设计闭环传递函数,接着将其与含有闭环系统性能的期望传递函数在三个条件下进行匹配,进而获得未知控制器增益的表达式。在设计实际控制椭圆轨道编队飞行MIMO相对位置保持算法时,将系统期望传递函数设为解耦形式来实现三轴位置控制间的解耦控制,达到提高系统控制性能的目的。最后进行相应的数学仿真,其结果表明该算法能够保证系统的高精度位置保持要求。     

Spacecraft formation flying: A review and new results on state feedback control

This paper presents a review of previous work within the field of spacecraft formation flying, including modeling approaches and controller design. In addition, five new approaches for tracking control of relative translational motion between two spacecraft in a leader–follower formation are derived. One PD controller with feedback linearisation is derived and shown to result in an exponentially stable equilibrium point of the closed loop system. Four nonlinear controllers are derived and proved by using Lyapunov theory and Matrosov's theorem to leave the closed loop system uniformly globally asymptotically stable. Results from the simulation of the system with the derived controllers are presented, and compared with respect to power consumption and tracking performance.     

无阻力双星编队的满系数矩阵MIMO定量反馈控制

研究由两颗无阻力卫星构成的、用于重力场测量的松散式编队相对位置控制方法,主要解决编队控制所产生的非重力加速度在重力场测量频带内的干扰抑制问题。首先,选取双星位置中点作为编队系统质心,建立了考虑J2摄动项的双星相对动力学模型。然后,根据定量反馈理论（QFT）确定系统在频域内的跟踪性能、鲁棒稳定性、输入干扰抑制等约束。与当前常规的对角型QFT控制器设计方法不同,本文针对编队系统的多输入多输出（MIMO）通道强耦合特性,设计了更具一般性的满系数矩阵鲁棒控制器,不但实现了闭环控制回路整定、通道解耦和稳态收敛,还有效抑制了编队控制量功率谱在科学测量频带内的干扰。最后,通过在时域中的数字仿真校验了该方法控制器的有效性和鲁棒性。     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

PRISMA—A formation flying project in implementation phase

The PRISMA project for autonomous formation flying and rendezvous has passed its critical design review in February–March 2007. The project comprises two satellites which are an in-orbit testbed for Guidance, Navigation and Control (GNC) algorithms and sensors for advanced formation flying and rendezvous. Several experiments involving GNC algorithms, sensors and thrusters will be performed during a 10 month mission with launch planned for the second half of 2009.The project is run by the Swedish Space Corporation (SSC) in close cooperation with the German Aerospace Center (DLR), the French Space Agency (CNES) and the Technical University of Denmark (DTU). Additionally, the project also will demonstrate flight worthiness of two novel motor technologies: one that uses environmentally clean and non-hazardous propellant, and one that consists of a microthruster system based on MEMS technology.The project will demonstrate autonomous formation flying and rendezvous based on several sensors—GPS, RF-based and vision based—with different objectives and in different combinations. The GPS-based onboard navigation system, contributed by DLR, offers relative orbit information in real-time in decimetre range. The RF-based navigation instrument intended for DARWIN, under CNES development, will be tested for the first time on PRISMA, both for instrument performance, but also in closed loop as main sensor for formation flying. Several rendezvous and proximity manoeuvre experiments will be demonstrated using only vision based sensor information coming from the modified star camera provided by DTU. Semi-autonomous operations ranging from 200 km to 1 m separation between the satellites will be demonstrated.With the project now in the verification phase particular attention is given to the specific formation flying and rendezvous functionality on instrument, GNC-software and system level.     

TanDEM-X: A radar interferometer with two formation-flying satellites

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurements) is an innovative formation-flying radar mission that opens a new era in spaceborne radar remote sensing. The primary objective is the acquisition of a global digital elevation model (DEM) with unprecedented accuracy (12 m horizontal resolution and 2 m relative height accuracy). This goal is achieved by extending the TerraSAR-X synthetic aperture radar (SAR) mission by a second, TerraSAR-X like satellite (TDX) flying in close formation with TerraSAR-X (TSX). Both satellites form together a large single-pass SAR interferometer with the opportunity for flexible baseline selection. This enables the acquisition of highly accurate cross-track interferograms without the inherent accuracy limitations imposed by repeat-pass interferometry due to temporal decorrelation and atmospheric disturbances. Besides the primary goal of the mission, several secondary mission objectives based on along-track interferometry as well as new bistatic and multistatic SAR techniques have been defined, representing an important and innovative asset of the TanDEM-X mission. TanDEM-X is implemented in the framework of a public–private partnership between the German Aerospace Center (DLR) and EADS Astrium GmbH. The TanDEM-X satellite was successfully launched in June 2010 and the mission started its operational data acquisition in December 2010. This paper provides an overview of the TanDEM-X mission and summarizes its actual status and performance. Furthermore, results from several scientific radar experiments are presented that show the great potential of future formation-flying interferometric SAR missions to serve novel remote sensing applications.     

Multi-objective output-feedback control for microsatellite attitude control: An LMI approach

Mixed H₂/H_∞ output-feedback controller with pole placement constraints against the internal uncertainty of moment-of-inertia variation and space environmental disturbances is proposed for mircosatellite attitude control. The multi-objective controller is designed based on linear model of attitude dynamics. The H_∞ performance takes into account both robustness stability against moments-of-inertia uncertainty and the disturbance rejection aspect. H₂ performance takes into account the LQG aspect which avoids the undesirable wheels’ saturation effect. In addition, the closed-loop poles can be forced into some sector of the stable half-plane to obtain well-damped transient responses. The problem is then reduced to a convex optimization involving linear matrix inequalities (LMIs), so it can be efficiently solved. The simulation results demonstrate that the presented mixed H₂/H_∞ control system is robust stable and optimal in the sense of H₂ norm, and has good steady-state and dynamic performances against the parameter uncertainties and various disturbances for the microsatellite attitude control system.     

卫星编队飞行相对位置自适应协同控制

针对卫星编队飞行相对位置协同控制问题,基于编队卫星相对运动非线性动力学方程和一致性理论设计了两种自适应协同控制器。首先,在卫星质量不确定和星间信息交互存在通信时延的条件下,设计了一种全状态反馈自适应协同控制器,并证明了该控制策略对空间摄动力的鲁棒性。其次,进一步考虑速度信息不可测的条件下,采用滤波器设计了一种无速度反馈的自适应协同控制器。最后,以编队构型重构为例对两种自适应协同控制器进行了仿真校验。仿真结果表明：两种自适应协同控制器均可有效应用于卫星编队飞行相对位置的协同控制,能够保证编队卫星对各自期望轨迹跟踪的同时暂态保持编队构型的稳定,具有较高的控制精度。     

控制受限的编队航天器鲁棒自适应控制

研究了考虑控制受限的编队航天器鲁棒自适应轨道跟踪控制问题。针对航天器编队飞行系统中控制受限、外部扰动和模型不确定性的情况,利用反步控制方法和指令滤波设计提出了一种鲁棒自适应控制策略。指令滤波器用于补偿控制受限对于控制器的影响,同时设计了自适应律对未知参数进行估计,并且利用Lyapunov稳定性理论分析了闭环系统的渐近稳定性。和滑模控制等传统鲁棒控制不同,所设计的鲁棒自适应控制器是连续的,更便于航天器编队飞行系统的实现。仿真结果表明所设计的控制器既能实现高精度的编队飞行跟踪控制,又能保证控制受限的要求。     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

Combustion chamber pressure control based on mixed H∞-describing function approach

A new single range controller design approach for use with nonlinear liquid propellant engines (LPE) is developed. The approach is based on a describing function model of the nonlinear LPE coupled with the application of the H_∞ control theory. The approach is applicable to nonlinear LPEs of a general nature without any restrictions on nonlinearity type, number of nonlinear terms, nonlinearity arrangement, or system order. The approach is applied to an existing nonlinear LPE, and the results are compared with those obtained with an alternative method that was previously reported in the open literature.     

Controller development of photo bioreactor for closed-loop regulation of O2 production based on ANN model reference control and computer simulation

When Bioregenerative Life Support System (BLSS) is used for long-term deep space exploration in the future, it is possible to perform closed-loop control on growth of microalgae to effectively regulate O₂ production process in emergencies. However, designing controller of microalgae cultivating device (MCD) by means of traditional methods is very difficult or even impossible due to its highly nonlinearity and large operation scope. In our research, the Artificial Neural Network Model Reference Control (ANN-MRC) method was therefore utilized for model identification and controller design for O₂ production process of a specific MCD prototype—photo bioreactor (PBR), based on actual experiment and computer simulation. The results demonstrated that the ANN-MRC servo controller could robustly and self-adaptively control and regulate the light intensity of PBR to make O₂ concentrations in vent pipe be in line with step reference concentrations with prescribed dynamic response performance.     

基于小波降噪的编队卫星相对位置确定

在编队飞行任务中组成编队的卫星之间相对定位非常重要。本文通过分析信号的频谱性质,运用小波阈值去噪法探讨了J2项摄动下的卫星相对位置确定。该方法通过对高频分量的滤波,改善编队卫星相对运动位置确定的精度。仿真验证了处理方法的有效性,表明该方法有利于相对定位精度的提高。     

飞行器制导控制一体化编队控制器设计

针对主从式结构飞行器协同编队控制问题，以侧滑转弯飞行器为研究对象，采用制导控制一体化(Integrated guidance and control, IGC)方法设计编队控制器。首先在惯性坐标系中定义相对运动坐标系，建立相对运动模型，结合飞行器动力学模型，得到全状态制导控制一体化模型；然后采用反演方法，结合滑模变结构与神经网络自适应理论设计了编队控制器，并证明了控制系统稳定性；最后在高速情况下进行了六自由度数值仿真，对比了IGC设计方法与分离设计方法的控制性能。仿真结果表明所设计的IGC控制器能够快速精确地对期望编队队形进行构建与保持，并且较分离设计方法具有优越性。     

主从式编队航天器连通性保持与碰撞规避

针对主从式航天器编队过程中存在的通信距离约束、航天器之间的碰撞以及空间干扰等问题，提出一种基于非线性干扰观测器和人工势函数的分布性协同控制方法。当初始通信网络连通时，通过在分布式协同控制器中引入吸引势函数，保证整个编队过程中通信网络始终是连通的。针对主航天器速度仅有部分从航天器直接可知的情况，为每一个从航天器设计分布式的速度观测器估计主航天器的速度，从而实现航天器之间的速度协同。此外，通过在控制器中引入非线性干扰观测器对外界干扰进行观测，显著增强了航天器编队的精度。仿真结果表明，本文提出的分布式协同控制方法不但能够实现对主航天器的速度跟踪以及航天器之间的队形保持，而且能够在编队过程中实现通信网络的连通性保持和航天器之间的碰撞规避。     

航天器编队飞行及其关键技术的开发

简要论述由分布式航天器系统构成的空间编队飞行的概念 ,扼要介绍 NASA为未来航天器编队飞行项目开发的几项关键技术 ,着重阐明基于 GPS的分散式编队飞行控制和相对导航技术能充当未来多星编队飞行任务的导航系统 ,从而使未来的空间科学研究发生深刻变化     

考虑状态约束的二体旋转库仑卫星系统重构控制

研究考虑控制输入饱和与状态约束的深空旋转二体库仑卫星构型控制问题,只采用卫星之间的库仑力作为控制力,提出一种基于反步法的非线性控制方法。首先推导了二体库仑卫星在地-月系平动点附近的相对运动方程,利用旋转二体库仑卫星的特性,对方程进行了简化。为了完成禁止相对运动区域的回避,设计了新的状态限制辅助函数,结合抗饱和方法与反步法得到了二体库仑卫星的构型控制器。接着证明了由于状态限制辅助函数的加入,所设计的控制器可以保证卫星相对运动不超出限制范围。进一步应用Lyapunov稳定性定理证明了其闭环系统的一致最终有界性。最后在Matlab/Simulink平台上进行了仿真校验,结果表明了方法的有效性。     

Lorentz-force-perturbed orbits with application to J2-invariant formation

The Lorentz force acting on an electrostatically charged spacecraft in the Earth's magnetic field provides a new propellantless means for controlling a spacecraft's orbit. Assuming that the Lorentz force is much smaller than the gravitational force, the perturbation of a charged spacecraft's orbit by the Lorentz force in the Earth's magnetic field, which is simplified as a titled rotating dipole, is studied in this article. Our research starts with the derivation of the equations of motion in geocentric equatorial inertial Cartesian coordinates using Lagrange mechanics, and then derives the Gauss variational equations involving Lorentz-force perturbation using a set of nodal inertial coordinates as an intermediate step. Subsequently, the approximate averaged changes in classical orbital elements, including single-orbit-averaged and one-day-averaged changes, are obtained by employing orbital averaging. We have found that the approximate analytic one-day-averaged changes in semi-major axis, eccentricity, and inclination are nearly zero, and those in the other three angular orbital elements are affected by J₂ and Lorentz-force perturbations. This characteristic is applied to model bounded relative orbital motion in the presence of the Lorentz force, which is termed Lorentz-augmented J₂-invariant formation. The necessary condition for J₂-invariant formation is derived when the chief spacecraft's reference orbit is either circular or elliptical. It is shown that J₂-invariant formation is easier to implement if the deputy spacecraft is capable of establishing electric charge. All conclusions drawn from the approximate analytic solutions are verified by numerical simulation.