分布式卫星轨道构形的大气摄动分析及修正方法

在低轨道运行的分布式卫星受大气摄动的影响,其轨道构形很快遭到破坏,环绕卫星的相对运动轨迹中心不断发生漂移。本研究的目的在于建立一种降低大气摄动对分布式卫星轨道构形影响的补偿方法,以使分布式卫星的轨道构形能够更好地自然维持。研究基于考虑高度变化和太阳周日变化的大气密度模型,得出分布式卫星不同初始相位环绕卫星的长半轴摄动方程。并提出一种补偿大气摄动影响的长半轴修正方法。仿真结果显示,采用此大气摄动补偿方法能够在给定时间内大大降低大气摄动的影响,从而显著提高分布式卫星轨道构形的自然维持能力。     

一种利用面质比调整提高编队构形稳定性的方法

分布式卫星编队构形受大气摄动的影响会产生沿航迹方向的相对漂移。通过合理的面质比调整,可以降低漂移,提高构形稳定性。基于包含周日效应的大气密度模型,研究了编队卫星轨道能量耗散的差异,进而指出大气摄动引起的构形漂移与构形初始相位、以及轨道面和太阳密度周日峰方向夹角之间存在的关系。给出解析形式和数值方式2种面质比调整方法,并对后一种方法进行了仿真。仿真结果显示,利用文中给出的面质比调整方法,能够大大提高构形的稳定性。     

基于近似生成函数迭代的分布式卫星构形最优控制研究

基于考虑地球非球形摄动的分布式卫星相对运动Hamilton力学模型和生成函数方法研究分布式卫星构形最优控制问题,针对生成函数法的高计算开销,提出了生成函数近似迭代方法.先以较低的计算代价,获得最优控制Hamilton系统生成函数的低阶近似,得到近似最优轨线,再将最优控制Hamilton系统相对于近似最优轨线求"相对运动",该"相对运动"仍具有Hamilton性质,利用其生成函数的低阶近似,对近似最优轨线进行迭代修正,从而以计算代价较小的低阶近似逼近计算代价高得多的高阶近似的精度.对圆参考轨道和椭圆参考轨道下的两种分布式卫星构形调整最优控制问题的求解表明,该方法在保持小计算开销情况下达到了高控制精度.     

航天器集群构形控制的虚拟弹簧阻尼网络方法

针对航天器集群质心相对运动构形控制问题,提出了一种基于虚拟弹簧阻尼网络的分布式控制方法。航天器间以虚拟的弹簧阻尼器相互连接,弹簧的原长根据期望的相对运动构形来设定。各航天器的控制输入是与其相连的所有弹簧阻尼器的合力。在线性动力学模型和拓扑结构连通且固定的假设下,基于代数图论的方法推导出了闭环系统稳定性条件。对近地轨道上100个航天器形成格点相对运动构形和20个航天器形成时变距离的椭圆构形的实例进行了仿真,考虑了轨道摄动的影响,结果表明,集群通过虚拟弹簧阻尼网络控制可实现期望构形,并能达到厘米量级的构形保持控制精度。该控制方法不改变集群的质心,只需施加很小的控制加速度;仅基于局部的邻居交互,能够适应大规模集群对分布式控制的要求。     

基于零J_2摄动条件的近圆轨道编队保持双脉冲最优控制方法研究

重点研究了考虑J2摄动作用的近圆轨道编队构形保持双脉冲最优控制策略.利用轨道要素法建立了考虑J2摄动作用影响的相对运动方程,推导了消除相对摄动影响长期项的零J2摄动条件,并利用该条件对C-W方程得到的编队初始条件进行了修正,得到了对J2摄动不太敏感的相对轨道.然后,基于C-W方程建立了编队保持双冲量最优控制模型,并利用非线性规划方法得到了编队保持所需的最优控制脉冲.仿真结果表明,J2项摄动对相对运动的破坏作用明显减小,提出的双脉冲最优控制方法能够有效实现编队保持的高精度控制.     

近地卫星编队构形保持方法

针对J2摄动和大气摄动导致低轨编队卫星构型破坏的情况,基于高斯摄动方程给出了以平均轨道根数为被控制量的脉冲控制模型。利用法向脉冲调整轨道倾角和升交点赤经偏差,在轨道上2个位置施加径向和切向脉冲调整其余轨道根数偏差从而修正卫星编队构形。最后通过数值仿真验证了算法的简单性、有效性。     

基于Lyapunov最小-最大方法的卫星编队飞行队形保持

提出一种卫星编队飞行队形保持的鲁棒控制方法.将环境摄动、推力误差等因素作为干扰项加到相对动力学方程中.然后对于该不确定系统,采用Lyapunov最小一最大方法设计相应的控制律,在存在干扰的情况下,采用该控制律仍然能保证系统渐近稳定.同时针对经典的Lyapunov最小一最大方法导致的控制颤振问题,进行了改进,证明了改进后的控制律能够实现系统的一致终极有界,同时消除颤振.通过仿真,验证了采用Lyapunov最小-最大方法在系统存在干扰的情况下,比一般控制方法具有更强的鲁棒性.     

分布式卫星编队飞行队形保持协同控制

针对分布式卫星编队飞行队形保持控制问题提出一种分布式协同控制算法,并给出该协同控制算法与编队卫星星间信息传递拓扑结构之间的关系。该协同控制算法以模型预测控制为基础,利用分布式编队卫星的自然特性以及编队卫星之间的信息传递拓扑结构,采用分布式的算法结构,设计分布式的模型预测协同控制算法。该控制算法是一种在线滚动优化控制算法,同时能够较好地解决存在状态约束、控制输入约束等情形下的各种控制问题。最后通过数值仿真验证了结果的有效性。仿真结果表明,当编队卫星星间信息传递拓扑结构中存在生成树时,提出的分布式协同控制算法能够有效地应用到编队卫星队形保持控制问题上来。     

编队构形保持模型预测控制方法研究

针对多星编队构形保持问题,提出了一种基于模型预测控制的编队构形保持协同控制算法。首先,给出了线性化的、基于相对轨道根数的编队相对运动方程,基于此方程,提出了优化确定多星编队系统构形修正相对运动中心和各个卫星目标修正量的线性规划数学模型。然后,在建立离散化状态方程和测量方程的基础上,提出了满足多种约束条件的求解构形保持控制律的混合整数线性规划数学模型。于是,可通过求解上述两个数学规划模型,得到基于模型预测控制的构形保持协同控制算法。最后通过数学仿真验证了算法的有效性和优越性。     

卫星相位保持的多冲量次优控制

在推导了多冲量最优解的必要条件的基础上，给出了一种卫星相位保持的多冲量次优控制方法。由于摄动和截断误差等对控制的影响，在多次冲量的求解时应该使用中间修正。计算表明，加中间修正的多冲量次化控制方法具有很好的鲁棒性。     

Influence of sensor and actuator errors on impulsive satellite formation control methods

This paper investigates how sensor and actuator errors are impacting formation control accuracy and propellant consumption of a two-satellite formation in a low Earth orbit. Realistic relative navigation errors are implemented, based on the results from the PRISMA mission, as well as realistic actuator uncertainty and actuator constraints. Two impulsive control methods are investigated. The first method is based on a controller that is implemented onboard PRISMA and the second method uses linear programming to arrive at a model predictive controller. The control methods are tested in a simulation environment and are subjected to orbital perturbations and realistic sensor errors and actuator errors. Both control methods are able to maintain the desired relative geometry of a projected circular orbit in the presence of the errors. The PRISMA control method demonstrates lower propellant consumption, while the model predictive controller shows better control accuracy. The results show that, based on the used scenario, sensor errors dominate both the formation control accuracy and propellant consumption. The versatility of the model predictive controller is demonstrated in a challenging formation control scenario including formation maintenance and formation reconfiguration tasks.     

Input-to-state stability of model-based spacecraft formation control systems with communication constraints

This paper investigates the formation keeping problem for multiple spacecraft in the framework of networked control systems (NCSs). A continuous-time representation of the NCS is considered for the tracking control of relative translational motion between two spacecraft in a leader–follower formation in the presence of communication constraints and system uncertainties. Model-based control schemes are presented, which employ state feedback (when the relative position and velocity vectors are directly measurable) and output feedback (when velocity measurements are not available), respectively, to guarantee input-to-state stability (ISS) of the system. The stability conditions on network transfer intervals are derived as simple eigenvalue tests of a well-structured test matrix. The results are then extended to include network communication delay. Numerical simulations are presented to demonstrate the effectiveness of the control scheme ensuring high formation keeping precision and robustness to nonlinearities and system uncertainties. The proposed controllers are robust not only to structured uncertainties such as system parameter perturbations but also to unstructured uncertainties such as external disturbances and measurement noises.     

Modal control of the planar motion of a long flexible beam in orbit

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems are investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit is analyzed. In this study, first order effects of gravity-gradient are included, whereas external perturbations and related orbital station keeping maneuvers are neglected. A mathematical model which describes the system deflections within the orbital plane has been developed by treating the beam as having a maximum of three discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of this system are simulated and, in addition, the effects of the control devices are considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, is examined. The effect of varying the number of modes in the model as well as the number and location of the control devices are also considered.     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

基于有向图的航天器编队鲁棒自适应姿态协同跟踪控制

针对一组有向通讯拓扑关系的编队航天器的协同控制问题,考虑航天器的模型不确定性(指惯量不确定性)以及受到的外部干扰的影响,设计了分布式自适应协同姿态跟踪控制器,使得各航天器姿态协同的同时跟踪时变的期望姿态。首先,针对由MRP参数描述的航天器误差动力学方程,选取了包含相对误差项以及绝对误差项的滑模面,将模型不确定项和外界干扰项作为整体处理,基于Lyapunov稳定性理论给出了非回归项的自适应算法和分布式协同跟踪控制律的设计方法,以使得各航天器协同收敛到期望的姿态,最后通过仿真验证了该算法的有效性、可行性。