A Qualitative Study of Proportional Navigation

This paper represents a study of the trajectories of an ideal missile homing on a target according to the proportional navigation law. A qualitative study is performed and conditions are determined which enable one to demonstrate that: 1) the missile always reaches the target regardless of the initial conditions at launch; 2) the rotational rate of the line of sight is decreasing at the pursuit end.     

导弹协同作战飞行时间裕度

 基于导弹协同作战任务规划系统进行合理任务分配的需求,研究了导弹可以修正控制飞行时间的裕度。根据导弹-目标在视线坐标系和角动量坐标系下的运动关系,得出了导弹相对于目标的加速度,并基于此给出了导弹剩余飞行时间的估算方法;当前时刻导弹剩余飞行时间的估算值与已经飞行的时间以及任务规划系统指定的期望到达时间构成时间反馈作用,用于修正控制导弹到达目标的最终飞行时间。由于真比例导引律在工程实现和解析运算中具有一定的优势,选择在真比例制导加速度的视线方向施加时间反馈控制作用,进而得出了基于真比例导引律的导弹协同作战飞行时间控制导引律;最后重点研究了在该时间控制导引律的作用下,存在导弹的飞行速度限制以及弹目相对运动约束时,导弹飞行过程中任一时刻对应解析形式的可控飞行时间的裕度。仿真结果表明,本文的设计合理可行,对于多弹协同作战的实现具有重要意义。     

主动防御协同自适应滑模制导律

飞机相比于攻击导弹,在飞行速度和机动性能等方面存在着劣势.为了提高其生存几率,设计了一种发射防御导弹协同对抗攻击导弹的自适应滑模制导律.该制导律本质是一种视线(Line of Sight,LOS)制导方法,通过对飞机与防御导弹和防御导弹与攻击导弹间的LOS调整以满足特定的几何关系,从而实现对攻击导弹的主动防御.最后,将所设计的制导律与比例导引进行了仿真比较.结果表明,由于与目标间的协同,所设计的制导律在机动性能和拦截性能方面具有明显的优势,且对于三方的飞行速度变化与攻击导弹的机动具有较强的鲁棒性.     

Generalized guidance law for homing missiles

The concept of a generalized guidance law is presented, and the closed-form solution for a homing missile pursuing a maneuvering target according to generalized guidance laws is given. It is shown that the guidance laws appearing in the literature are merely special cases of the one proposed by the authors. The derived generalized forms of capture area, missile acceleration, and homing time duration that are derived provide insight into the performance of the guidance laws being considered and lead to the discovery of new ones. The problem of finding a nonlinear optimal guidance law for a homing missile with controlled acceleration, applied so as to capture a maneuvering target with a predetermined trajectory while minimizing a weighted linear combination of time of capture and energy expenditures, is solved in closed form. The derived optimal control law is equal to the LOS (line of sight) rate multiplied by a trigonometric function of the aspect angle. Numerical simulation shows that the resulting guidance law appears to yield a significant advantage over true proportional navigation     

基于成像跟踪的比例导引律实现

在综述了各种成象跟踪算法的基础上，给出了一种新的适于飞行力学自动目标跟踪算法的基本思想和方法步骤。研究和控制利用成像跟踪算法获取比例导引律中视线角速度和导弹怀目标间相对速度的方法，并结合导弹飞行控制数学模型，提出了一种基于成像跟踪的比例导引律实现方法。     

滚转弹两框架导引头的前馈补偿技术

针对弹体滚转情况下两框架平台式导引头的伺服控制问题,基于导引头运动学和动力学,建立了导引头稳定回路模型。结合弹体滚转条件下的导引头输入指令和输出视线角速率关系,构建了视线闭环回路。针对偏航、俯仰通道间的解耦控制问题,推导出解耦条件,要求两通道由失调角到光轴转动角速度的传递函数相同。仿真分析了该模型在视线角输入以及弹体姿态扰动输入时,弹体滚转对导引头跟踪精度产生的影响,并由此提出了滚转角速度前馈补偿控制方案。结果表明,采用结合滚转角前馈补偿控制的两框架平台式导引头方案可以满足滚转弹的制导精度要求。     

图像导引头最大跟踪角速度的确定

为合理地确定图像导引头的最大跟踪角速度 ,针对坦克和直升机两种目标 ,利用比例导引法中视线角速度和导弹法向过载之间的关系 ,提出了图像导引头最大跟踪角速度指标的确定方法。所确定的指标明显低于常见的空 -空弹点源信号导引头的最大跟踪角速度。该方法既满足了攻击坦克顶部装甲和武装直升机的需要 ,又避免了因指标过高而造成的浪费     

Guidance law with impact time and impact angle constraints

A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile’s normal acceleration (not jerk) as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go (the difference between the designated impact time and the current flight time) for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance (BPNG) law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.     

三维制导的几何方法与鲁棒控制方法

 在考虑导弹速度和目标速度均为时变的情况下,将微分几何方法与李雅普诺夫稳定理论结合起来,提出了一种导弹三维导引规律设计新方法。对机动目标,PPNG方法的主要问题是在导引末段,它要求导弹在俯仰和偏航通道上具有较大的加速度,为了解决这一问题,本文应用基于李雅普诺夫稳定理论的鲁棒控制方法,提出了一种三维鲁棒制导算法。这种方法在导引末段不需要过大的加速度命令,不需要知道目标精确的加速度和速度方位信息。     

非合作目标动态RCS仿真方法

针对非合作目标难以开展动态测量的问题,根据空气动力学原理提出了一种非合作目标动态雷达散射截面（RCS）仿真方法。该方法首先建立测量背景下典型飞行航路模型,然后计算雷达视线在机体坐标系上的时变姿态角。根据姿态角开展电磁计算,获得F-117A隐身攻击机在侧站平飞、背站拉起、对站俯冲、侧站盘旋4种航路下的动态RCS数据。着重分析了动、静态RCS特性在起伏目标检测性能评估上的差异。结果表明：静态RCS特性难以反映目标运动时真实的雷达特性,利用静态数据描述目标特性可能导致错误结论,而文中方法获取的动态RCS数据可以提高结论的完整性和可信度。     

用于被动寻的导弹的带末端落角约束的变结构导引律

使被动寻的导弹在较低的平飞弹道情况下，以较小的俯冲过载和最佳攻击姿态精确命中目标；采用带落角约束的变结构导引律，对弹目距离及距离变化率进行估计，克服被动寻的导弹不能测距的约束，同时使切换开关增益随时间自适应变化以减小俯冲过载；利用某型在研被动寻的导弹的气动参数，对此变结构导引律进行了数学仿真，仿真结果表明，在较低的平飞弹道约束条件下及过载要求范围内，该导引律能以期望落角命中静止与机动的坦克目标，对弹目距离变化率及距离的较大估计误差具有较强的鲁棒性。     

Direct Intercept Guidance using Differential Geometry Concepts

This paper examines the application of differential geometry to the engagement of both nonmanoeuvring and manoeuvring targets. The kinematics of the engagement for both manoeuvring and nonmanoeuvring target are developed and expressed in differential geometric terms. Two-dimensional geometry is then used to determine the intercept conditions for a straight line target and a constant manoeuvre target. The intercept conditions for both targets are developed for the case when the interceptor missile guides onto a straight line interception. These two cases are shown to have a common set of core conditions such that it enables a unified guidance law to be developed. The guidance law is shown to be globally stable using Lyapunov theory, so that guidance capture is assured for any initial condition. The analysis and guidance law design does not rely on local linearisation and can be shown to produce guidance trajectories that mirror proportional navigation for the straight line interception of a nonmanoeuvring target for which proportional navigation was originally developed. The paper finishes with simulation in two dimensions, illustrating the convergence and solution properties of the approach.     

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three-dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.     

被动式寻的导弹的运动跟踪变结构制导

应用运动跟踪变结构控制理论设计被动式寻的导弹的制导律。这种运动跟踪变结构制导律（ＭＴＶＳＧ）可以令导弹－目标相对视线角速度按照给定的运动规律变化,从而增强被动跟踪问题（等价于一个非线性系统）的可观性,同时保证导弹有很高的命中精度。仿真研究表明,在ＭＴＶＳＧ下,系统的可观性明显增强,因此系统状态的估计精度较高。进一步的研究表明,ＭＴＶＳＧ对系统状态估计误差有很强的鲁棒性。ＭＴＶＳＧ的上述各种优点使得导弹有很高的命中精度。     

Capturability of the 3-dimensional pure PNG law

Although a lot of effort has been recently devoted to the capturability analysis of the pure proportional navigation guidance (PPNG) law, there are still significant discrepancies between the analysis results and the actual capturability of the PPNG law. In this paper, a Lyapunov-like approach along with a vector analysis method based on the so-called LOS (line of sight) plane is introduced to analyze the capturability of the 3-dimensional PPNG law against a target maneuvering arbitrarily with time-varying normal acceleration. Thereby, our analysis result can explain the high capturability of the PPNG law theoretically much better than those presented in the prior literature. In our capturability analysis, the nonlinear dynamics of 3-dimensional pursuit situations have been taken into full account. Our approach is also expected to be useful for the design and analysis of other PPNG-like missile guidance laws     

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.     

考虑导弹自动驾驶仪二阶动态特性的三维导引律

基于三维(3D)空间坐标系下目标-导弹相对运动方程,考虑导弹自动驾驶仪的二阶动态特性,应用动态面控制方法设计了一种新的三维空间导引律.在设计过程中,通过引入一阶低通滤波器,使得导引律的最终表达式中不含有视线角速率的高阶导数,更易于实际应用.该导引律有效地克服了导弹控制系统的动态延迟对制导精度的影响.将该导引律与未考虑导...     

基于分数阶微积分理论的最优导引律设计

随着技术的发展及战场环境的日益复杂化,拦截机动目标的需求越来越大。然而传统制导律在拦截机动目标时存在制导精度差、末端过载突变的问题,故提出了一种基于分数阶微积分理论的最优导引律。首先,介绍了分数阶微积分的定义、性质及其数字实现方法;然后,分析了弹目相对运动关系,通过分数阶变阶次建模和最优控制理论推导出了分数阶导引律;最后,仿真结果表明：与传统比例导引法相比,所设计的分数阶最优导引律能够保持比例导引法良好的追踪性能且拦截时间能够缩短2s,末端过载值趋近于0。该方法解决了传统比例导引法在末端由视线角速率发散而导致的末端过载突变问题。     

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.     

防空导弹任务规划与协同控制技术研究

针对防空导弹拦截群目标的任务需求，提出了多弹协同作战框架。考虑到实际拦截过程中弹目相对速度和角度较大的问题，建立了导弹拦截目标的能力预测模型，以确保分配结果处于导弹攻击能力范围内，并采用了改进的粒子群优化算法进行任务分配。然后为了兼顾协同制导和命中精度的要求，基于弹道成型和偏置比例导引的思想，结合一致性理论，设计了多弹时间/角度协同制导律。最后通过4枚导弹拦截3个目标的典型场景仿真，证明了方案的有效性。