Robust eigenstructure assignment based on μ-analysis applied to flight control law design

针对特征结构配置应用于飞行控制律设计鲁棒性较差的问题,提出了一种新的鲁棒特征结构配置方法.该方法结合参数化特征结构配置与μ分析,把鲁棒特征结构配置问题转化为包含系统全部自由参数的带约束条件的非线性优化问题.根据飞行控制律特点,提出分步优化策略解决鲁棒特征结构配置多变量优化问题,以降低问题复杂度,同时采用等值分布曲线直观描述优化指标随设计参数变化规律.该方法利用系统全部自由度提高系统鲁棒性,并对自由参数施加约束条件以保证标称闭环系统性能.仿真表明该方法能满足一级飞行品质要求,提高系统鲁棒性,减小保守性.     

四阶微分方程两点边值问题解的存在唯一性

讨论了非线性四阶常微分方程y（4）=f（x,y,y’,y”,y”’）在混合两点边值条件y’（a）=0,y”（a）＋y”（6）=0,y（b）=0,y”’（b）=0或y’（a）=0,y”＇（a）＋y＇”（b）=0,y（b）=0,y”（6）=0下,解的存在唯一性。其中f在[a,b]×R4上连续且满足Lipschitz条件。并在推广后的Lipschitz条件与Banach压缩映射原理基础上,得到一些新的存在唯一性结果。     

On the possibility of existence of an additional source of anomalous cosmic rays outside the solar system

On the basis of experimental data obtained at exposure of solid-state track detectors in the magnetosphere of the Earth during solar flares and in quiet Sun periods, an estimate of possible contribution of singly charged oxygen ions to the flare particle fluxes is made. A possibility is considered of the appearance in the vicinity of the solar system of singly ionized oxygen ions generated on stars.     

ZrO2陶瓷切向超声辅助磨削表面及亚表面损伤机制

为进一步揭示切向超声辅助磨削过程中硬脆材料的表面及亚表面损伤机理,基于应变率模型对其磨削过程中材料的动态力学性能进行分析,并在此基础上建立了硬脆材料的脆-塑转变临界切削深度模型与微裂纹损伤深度模型。研究发现,脆-塑转变临界切削深度和微裂纹损伤深度均与应变率有关,其中临界切削深度随着应变率的增加而增加,而横向裂纹损伤深度与中位裂纹损伤深度均随应变率的增加而减小。通过ZrO₂陶瓷切向超声辅助磨削试验进行验证。试验结果表明：由于切向超声振动的引入提高了材料应变率,进而提高了材料的动态断裂应力以及动态断裂韧性,从而扩大了ZrO₂陶瓷的塑性域去除范围,降低了加工表面的横向裂纹与中位裂纹损伤深度,使得ZrO₂陶瓷的表面及亚表面质量得到明显改善。试验结果与理论分析相一致,为进一步揭示切向超声辅助磨削过程中硬脆材料的表面及亚表面微观损伤机理提供了理论参考。     

Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV$\mathrm{\Delta }V$ required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto–Ganymede–Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton–Raphson method, time of flight iteration solution to the _V∞$V_{\infty }$-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto–Ganymede transfer, the Ganymede flyby, and the Ganymede–Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

On Lambert’s problem and the elliptic time of flight equation: A simple semi-analytical inversion method

In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180°$180°$ transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

归一化参数蠕变模型的程序实现与验证

为了准确模拟实际构件的蠕变行为和应力松弛效应,在通用有限元程序环境下,利用其提供的用户可编程特性工具,将所发展的一种能完整描述蠕变3个阶段变形特征的归一化参数模型编制成用户子程序.考查了子程序计算结果与试验数据的差异、时间步长对计算结果的影响,并对不同规模有限元模型的计算耗时作了对比分析.针对变载(应力、温度)情形,在子程序中实现了时间硬化理论和应变硬化理论,并提出的介于两者之间的相对时间硬化理论.对带孔平板进行了实例计算,表明所发展的模型能够与有限元结果对实际结构进行蠕变模拟,计算结果的规律说明所发展的方法可较好地模拟实际构件的蠕变行为和应力松弛效应,验证了子程序的有效性.