On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T  . Therefore, for a pre-fixed minimum contribution, for instance 1×10^-8$1\times {10}^{-8}$ m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500 km of altitude (like the GRACE satellites at the beginning of their mission) we found 35?M?198$35?M?198$ for T=1$T=1$ day. We analyzed the individual contribution of the second order harmonic (_J2$J_2$) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.     

Maneuver planning of a rigid spacecraft with two skew control moment gyros

The attitude maneuver planning of a rigid spacecraft using two skew single-gimbal control moment gyros (CMGs) is investigated. First, two types of restrictions are enforced on the gimbal motions of two skew CMGs, with each restriction yielding continuous control torque along a principal axis of the spacecraft. Then, it is proved that any axis fixed to the spacecraft can be pointed along an arbitrary inertial direction by at most two sequent rotations around the two actuated axes. Given this fact, a two-step eigenaxis rotation strategy, executing by the two single-axis torques respectively, is designed to point a given body-fixed axis along a desired direction. Furthermore, a three-step eigenaxis rotation strategy is constructed to achieve an arbitrary rest-to-rest attitude maneuver. The rotation angles required for the single-axis pointing and arbitrary attitude maneuver schemes are all analytically solved. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.     

刚体航天器大角度姿态机动控制算法

针对刚体航天器在参数不确定及环境扰动情况下的大角度姿态机动问题,提出一种自适应离散变结构姿态控制算法.建立包含航天器姿态运动学及动力学的仿射模型,并精确反馈线性化解耦;对得到的各线性动态方程离散化处理,由离散指数趋近律推导了参数化的离散变结构姿态控制律.最后基于Lyapunov稳定性理论设计了控制参数的自适应更新律,有效克服了模型中的各时变项及干扰项影响.仿真结果表明,该算法可有效减小干扰引起的姿态指令角跟踪偏差,确保了大角度姿态机动控制的精确性与鲁棒性,并且消除了常规变结构控制的抖振现象.     

含热诱发扰动的挠性卫星L_1自适应控制

为了揭示挠性帆板的热诱发运动机理及其对卫星本体姿态机动的影响,采用拉格朗日能量法建立了主刚体带挠性梁模型受到突加热流时系统的动力学模型,分析了帆板热诱发运动的特性。假设系统的模型参数未知,设计了L1自适应控制器,仅卫星的姿态角和姿态角速度作为反馈量,将帆板热致振动和变形作为未建模动力学特性,实现卫星考虑帆板热扰动力矩的快速姿态机动控制。数值仿真结果表明,环境温度突然变化引起的帆板运动包括准静态变形和振动两部分,同时引起的姿态误差也包括常值偏差和姿态振动,所设计的控制器在系统考虑热引起的扰动时仍可以有效地实现卫星的快速姿态机动,且系统各阶挠性模态稳定,参数估计收敛。     

非线性相对运动方程的分析解

阐述追踪航天器相对目标航天器的运动方程的建立,以线性相对运动方程分析解为基础,推导出非线性相对运动方程分析解,这里目标航天器沿一般椭圆轨道（包括圆）运动,追踪航天顺受常值推力作用或在自由状态下运动。     

飞行器轨道交会的H_∞次优控制问题

研究了近圆轨道上两个飞行器轨道交会的控制问题。通过对最优控制理论设计最优交会轨线的研究 ,提出了利用 H∞控制理论设计实际控制器的方法 ,给出了仿真结果 ,验证了这种方法的正确性。说明了该方法具有鲁棒的控制效果以及次优的轨道特性。     

一种轮控卫星姿态机动变结构控制器

针对小卫星3轴反作用轮姿态控制系统的非线性特性,应用误差四元数来描述姿态运动,将星体大角度姿态机动问题转化为误差四元数的调节问题.利用误差四元数和误差角速度建立滑动模态,并基于Lyapunov定理推导出一种姿态机动的引入角加速度负反馈的变结构控制律.仿真结果表明,该控制律能够提高收敛速度,降低机动过程中角速度的超调量和对起始力矩的要求.同时,在模型参数不确定和有外干扰的情况下该控制律也具有全局稳定性和鲁棒性.      

GNSS广域差分改正数估计方法研究

随着我国北斗三号基本系统的正式运行,基于地面监测站的广域差分增强系统成为进一步提升卫星导航定位精度的手段之一。在码噪声多径误差修正(CNMC)的基础上,使用等效钟差方法实现GNSS卫星轨道与钟差误差的解耦,并依据卫星轨道运动的动力学特性,引入希尔差分方程描述卫星轨道误差变化,实现对轨道误差的实时卡尔曼滤波估计。基于GPS实测数据,对改正前后的用户等效测距误差(UERE)和定位精度进行了对比研究。实验结果表明,采用该方法,UERE标准差由改正前的0.456 m减小至0.227 m,降幅达到50.22%;整体水平定位误差(95%置信区间)由0.981 m减小至0.782 m,垂直定位误差(95%置信区间)由1.991 m减小至1.131 m,分别提升了20.29%和43.19%,差分改正效果明显。     

一种顾及轨道误差的实时GPS钟差估计方法

为了提高实时卫星钟差估计的精度和稳定性,提出了一种顾及轨道误差的实时GPS钟差估计方法。基于超快速轨道产品,分析了轨道标准差与绝对轨道误差的相关性。通过线性插值获得实时轨道误差信息,以优化先验残差的随机模型。基于先验轨道标准差阈值,采用分段方式剔除实时轨道异常卫星对应的观测值。实验结果表明：轨道标准差和轨道误差的相关性高达0.82。与常用的高度角相关的随机模型相比,GPS卫星钟差估计精度最大提高了15.2%,平均提高了8.1%,钟差误差的时间序列更加平稳,所有GPS卫星的平均钟差STD均在0.15ns以内。因此,超快速轨道产品中提供的轨道标准差与绝对轨道误差表现出较强相关。采用顾及轨道误差的实时钟差估计方法可提高GPS卫星钟差估计精度,准确识别并剔除GPS实时轨道异常的卫星,从而提高GPS实时钟差估计的稳定性。     

地球同步卫星的发射轨道的选择

本文对地球同步卫星的发射轨道作了一些分析。讨论了有关发射点纬度、停泊轨道、非共面发射轨道对发射轨道选择的影响。