Control of satellite imaging formations in multi-body regimes

Libration point orbits may be ideal locations for satellite imaging formations. Therefore, control of these arrays in multi-body regimes is critical. A continuous feedback control algorithm is developed that maintains a formation of satellites in motion that is bounded relative to a halo orbit. This algorithm is derived based on the dynamic characteristics of the phase space near periodic orbits in the circular restricted three-body problem (CR3BP). By adjusting parameters of the control algorithm appropriately, satellites in the formation follow trajectories that are particularly advantageous to imaging arrays. Image reconstruction and coverage of the (u, v) plane are simulated for interferometric satellite configurations, demonstrating potential applications of the algorithm and the resulting motion.     

基于T-H方程的卫星轨迹模型参考输出跟踪控制方法

当目标卫星沿椭圆轨道运行时,描述追踪星与目标星相对运动的线性化方程为T-H方程。将描述航天器相对运动的T-H方程变换为周期系统的状态空间形式,并给出卫星轨迹跟踪控制问题的数学描述。基于周期系统的参量Lyapunov方法和模型参考跟踪控制理论,提出了卫星轨迹跟踪控制器的设计方法。利用该方法设计了带有收敛速率保障的反馈镇定控制器和具有自由参数的前馈控制器。对追踪星相对目标星悬停任务进行了数值仿真,仿真结果表明提出的控制方案是有效的。     

Nonlinear feedback control of low-thrust orbital transfer in a central gravitational field

This paper investigates the problem of continuous-thrust orbital transfer using orbital elements feedback from a nonlinear control standpoint, utilizing concepts of controllability, feedback stabilizability and their interaction. Gauss's variational equations (GVEs) are used to model the state-space dynamics of motion under a central gravitational field. First, the notion of accessibility is reviewed. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived which asymptotically steers a spacecraft form an initial elliptic orbit to any given elliptic orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proven, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft onto a parabolic escape trajectory.     

整星零动量小卫星偏置飞行姿态解耦控制

研究了采用反作用飞轮为执行机构的整星零动量卫星绕Ｘ轴大角度偏置飞行模式的姿态解耦控制问题。首先给出卫星姿态运动学和动力学模型，然后在控制作用中引入非线性项对姿态动力学模型线性化，进一步对线性模型进行状态反馈解耦和极点配置。最后，给出了数学仿真算例和仿真结果。     

邻近近圆轨道两个飞行器的最优交会

邻近近圆轨道上两个飞行器的相对运动可以用线性化Ｃ—Ｗ方程描述。本文利用线性化Ｃ—Ｗ方程研究了常推力作用下两个飞行器的固定时间最省燃料交会问题，给出了最优推力作用的开关函数和最优推力方向的计算方法。     

多模切换控制方法及其在分导飞行器姿态机动控制中的应用研究

研究一类离散切换系统的鲁棒保性能状态反馈控制器设计问题。利用切换Lyapunov函数和线性矩阵不等式方法,得到了鲁棒保性能控制器存在的一个充分条件,给出了控制器的参数化表示,并将次优保性能控制器的设计问题转化为基于线性矩阵不等式约束下的凸优化问题。最后将所提理论应用于某飞行器的控制方案设计中,说明了本文所提设计方法的有效性。     

变质心旋转弹头变结构控制研究

针对弹头变质心这种新的控制方式,建立了变质心旋转弹头准弹体下的动力学模型,由于模型是复杂非线性的,通过按线性化族近似化理论对模型进行了合理简化,并用变结构控制理论对系统的姿态控制进行了设计,仿真结果表明,所设计的变质心弹头变结构姿态控制具有很好的快速性、稳定性,而且相对减小了抖震现象,证明这种方法是有效的。     

解析求解非线性相对运动的最优重构问题

椭圆轨道相对运动模型的线性化导致其在大尺度相对运动应用中精度不能满足需求。针对任意椭圆轨道上的大尺度航天器编队最优重构问题,提出一种基于椭圆轨道非线性相对运动模型的近似解析求解方法。首先通过变分法建立了非线性最优重构问题的数学模型;然后采用摄动法,以偏近点角为积分变量求得了不含特殊积分的解析开环最优控制,有效地避免了真近点角域下最优控制解所含有的特殊积分。仿真验证了所求最优控制的有效性和优越性,结果表明在相对运动尺度较大时,相比基于椭圆轨道线性化模型的最优控制,在燃耗保持相近的情况下,所求非线性控制有效地降低了重构误差。     

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。     

Variable structure control for satellite attitude stabilization in elliptic orbits using solar radiation pressure

The paper proposes the use of solar radiation pressure for satellite attitude control in elliptic orbits based on variable structure control. The system comprises of a satellite with two-oppositely placed solar flaps. Sliding mode control and terminal sliding mode control techniques have been adopted to develop nonlinear control laws for suitably rotating the control solar flaps to neutralize the adverse effect of eccentricity normally responsible for a considerable deterioration in the attitude control performance. The detailed numerical simulation of the governing nonlinear equation of the motion including the effects of various system parameters on the controller performance, establishes the feasibility of the proposed control strategy. The proposed controller is found to be robust against parameter uncertainties and external disturbances and thereby, the control strategy presented in the paper may be applicable to future satellite missions.     

High-precision single-input control of relative motion in spacecraft formation

A Newton-type method is proposed to improve the accuracy of control for relative motion of two satellites in close formation. We assume that the deputy satellite is equipped with a passive attitude control system that provides one-axis stabilization, and one or two orbit control thrusters are installed along the stabilized axis. Previous studies show that it is possible to construct periodic relative trajectories both in case of passive magnetic and spin stabilization. However, the accuracy of the numerically obtained control is quite low due to modeling errors caused by linearization of the equations of relative motion. Therefore, a correction procedure is required to compensate for nonlinear effects. To this end we suggest a recently developed algorithm based on the Newton method for solving nonlinear systems with geometric constraints. Being implemented, this algorithm allows decreasing the modeling error by up to ten times. The previously found control and trajectory of the linearized system are used as initial approximations.     

登月舱软着陆的非线性神经元控制

本文针对登月舱软着陆过程的控制问题，提出了一种非线性动态逆与状态反馈控制相结合的神经元控制系统设计方案。该方案包含两分：（１）借助前馈神经元网络通过学习逼近任意非线性映射的能力，建立被控系统的非线性动态逆神经元模型，用神经元网络实现被控非线性系统的线性化；（２）在线性化模型的基础上构造系统的神经元最优状态反馈控制器。本文给出的仿真结果显示出神经计算学在航天飞行器控制问题中所具有的潜在能力。     

Formation design in elliptical orbit using relative orbit elements

A new set of relative orbit elements is strictly defined through spherical geometry. The exact transformation equations between the new relative orbit elements and classical-orbital elements are derived. A new relative motion model with no singularity problem is derived based on the relative orbit elements, which are suitable for both elliptical and circular reference orbits. The in-plane and out-of-plane relative motion can be completely decoupled based on the new model. The inverse transformation of state transfer matrix is obtained to analyze perturbation effects and control strategy. The geometric characteristics of relative motion can be easily described using the relative eccentricity/inclination vector method. The proposed method and conclusions are validated by simulation through some typical examples. This paper improves the basic theory of relative orbit elements and unifies the expressions of the elliptical and near-circular close relative motion.     

卫星轨道保持的非线性鲁棒自适应变结构控制

应用反馈线性化方法，对卫星轨道保持的非线性动力学进行线性化，考虑线性化模型的范数有界不确定性，设计变结构各棒控制器，得到卫星轨道保持的非线性鲁棒控制律。在此基础上，利用自适应控制方法，得到一种具有不确定性范数上界估计能力的鲁棒自适应变结构控制器。进行数值仿真研究，验证了所提出控制器设计方法的有效性和适应性。     

非线性条件下编队卫星周期性相对运动条件

利用编队卫星机械能守恒原理，提出了非线性条件下求解编队卫星周期性相对运动条件的新方法，给出了非线性周期相对运动的初始条件。编队卫星相对距离较近时，利用非线性周期运动条件，可修正Hill方程的初始条件，抑制编队卫星的长期漂移。编队卫星相对距离较大，非线性因素不可忽略时，利用非线性周期运动条件，可找到不需消耗任何燃料的周期性相对运动轨道。最后的数值仿真结果验证了该方法的正确性。     

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.     

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。     

Revisiting the general periodic relative motion in elliptic reference orbits

A general periodicity condition is presented by analyzing the relative motion between two spacecraft performing formation flight in Keplerian elliptic orbits. The Tschauner–Hempel equation is used to describe the relative motion, and the general periodicity condition is derived through a state transition matrix with a true anomaly as a free variable. The general periodicity condition is also derived by using the energy matching condition, and the resulting periodic conditions by two approaches are compared to each other. Moreover, the zero offset condition is presented to locate the leader spacecraft at the center of the formation geometry. Then, the periodic relative motion in the elliptic reference orbit is expressed using the periodicity condition and the zero offset condition. Numerical simulations demonstrate the periodic relative motion in the elliptic reference orbit, and the results show that the general periodicity condition guarantees the bounded periodic relative motion in arbitrary elliptic orbits, and the zero offset condition makes the formation center coincide with the leader spacecraft.     

第三体引力摄动的近地轨道卫星相对运动方程

针对受第三体引力摄动的近地轨道卫星,推导了基于参考卫星轨道要素RSV的卫星运动方程、以及卫星的相对运动方程。两组方程均以显式给出,形式简洁且较为精确。基于这两组方程,本文还定性地分析了第三体摄动对卫星（相对）运动的影响。