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.     

大配平角起始条件下的非线性末制导律研究

针对大配平角误差起始条件下导弹捕获高机动性目标问题，分析了一解非线性末制导运动，得到了稳定性充要条件，基于滑模态控制技术，综合了一种新型的梆－梆末制导律，它是一般非线性末制导运动方程的通解，相对于线性二次型解具有明显的优点：不需目标加速度和剩余时间信息；能够在各种起始大配平角误差条件下收敛。最后给出的仿真算例证明了理论分析的正确性和该制导律的实用价值。     

Lyapunov-based switched-gain impact angle control guidance

To hit stationary ground targets in specified direction, a nonlinear impact angle control guidance law based on Lyapunov stability theory is proposed. The proposed law ensures the convergence of the heading angle and the miss distance to guarantee a successful engagement. The impact angle can be adjusted by varying a single parameter. And the maximum value of acceleration has been analyzed to get the proper range for control parameter. Considering the achievable impact angle set is limited, an additional phase is added to form a two-phase control strategy. The first phase is to establish a proper initial condition for the second phase, and the second phase is to hit the target with a certain impact angle. An analysis of the proper selection of control parameters to expand the achievable impact angle set is presented. The performance of the proposed guidance law is illustrated with simulations.     

二阶弹体特性下带终端角度约束的制导律

针对导弹要求限制终端攻击角度以发挥战斗部的最大效能,提出了一种适用于攻击地面固定目标的具有终端角度约束的最优制导律,并和已有的具有终端角度约束的最优制导律进行了比较。该制导律针对二阶弹体特性,采用最优控制方法,使导弹在命中目标的同时,满足终端角度约束。数字仿真结果表明,所提出的制导律能够实现终端角度约束条件,具有较高的制导精度。     

空地导弹滑模制导方法研究

针对空地导弹的制导规律设计问题,给出了滑模制导方法,建立了纵向平面内的弹-目相对运动方程。基于滑模控制理论,设计了空地导弹的制导规律,以同时保证脱靶量和弹道倾角要求,并针对固定目标,给出了相对距离和相对速度的解算方法,介绍了针对移动目标的相对距离和相对速度估算方法。仿真结果表明,该制导方法具有较高的制导精度,并且满足弹道倾角约束。     

Trajectory reshaping based guidance with impact time and angle constraints

This study presents a novel impact time and angle constrained guidance law for homing missiles. The guidance law is first developed with the prior-assumption of a stationary target, which is followed by the practical extension to a maneuvering target scenario. To derive the closed-form guidance law, the trajectory reshaping technique is utilized and it results in defining a specific poly-nomial function with two unknown coefficients. These coefficients are determined to satisfy the impact time and angle constraints as well as the zero miss distance. Furthermore, the proposed guidance law has three additional guidance gains as design parameters which make it possible to adjust the guided trajectory according to the operational conditions and missile’s capability. Numerical simulations are presented to validate the effectiveness of the proposed guidance law. ? 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).     

一种基于单部雷达的飞行器脱靶量测试方法

对单部雷达测量飞行器脱靶量所涉及到的雷达分辨力和多目标信息获取及处理进行了分析;结合实际靶场应用介绍了脱靶量数据处理方法;分析了脱靶量的测量误差,并给出了分析结果;本方法可最大限度地补偿掉系统误差,脱靶量测量误差主要来源于雷达本身测量精度。     

基于最优控制的落角约束攻击设计

针对导弹落角控制和精度控制的矛盾,运用飞行力学原理和最优控制理论,以落地速度倾角作为终端约束,以脱靶量、最小能量为性能指标,给出了一种适用于攻击地面目标的最优导引律。设计了导弹三通道的PID控制器,最后进行了导弹的6DOF仿真研究,仿真验证了设计方法的有效性。     

带落角约束的虚拟目标实时轨迹生成算法

针对导弹带落角约束条件打击目标的要求,在纵向平面内,根据导弹和目标的实时运动轨迹,提出了一种虚拟目标实时轨迹生成算法,并且给出了该算法中所需要的目标实时位置信息的估算方法.仿真结果表明,以该算法得出的虚拟目标轨迹作为导弹的跟踪对象,采用变结构导引律能满足落角约束条件,并且能够提供很高的命中精度,从而证明了该算法的正确性和有效性,为带落角约束条件打击目标提供了一种新的思路和途径.     

带落角约束的圆弧比例导引律和偏置比例导引律的研究

为了实现导弹以一定落角命中目标,研究了两种带有落角约束的圆弧比例导引律和偏置比例导引律。首先建立弹目相对运动数学模型和框架动力学数学模型,然后阐述了两种导引律的基本原理,接着对导弹在三维空间内攻击静止与运动目标进行数学仿真试验,仿真实验证明两种导引律都能以较小的脱靶量和期望落角命中目标,最后从原理上和仿真实验上对两种导引律进行了对比研究。     

一种基于弹丸激波的矢量脱靶量算法研究

从理论上深入分析了基于弹丸激波的矢量脱靶量测量原理,提出了具有工程实践意义的脱靶量测量方案,研究并建立了该方案的数学模型,提出了一种“动对动”射击时的脱靶量修正算法。     

Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories

The design of a suboptimal terminal guidance system for reentry vehicles with a constraint on the body attitude angle at impact is studied. Permissible range of the miss distance and the body attitude angle at impact is specified. The problem is formulated as a linear quadratic control problem. The Riccati equation is derived to provide time-varying feedback gains. The desired scheme is suboptimal. The region of initial states for which the system meets the specifications becomes smaller as the initial height of the reentry vehicle at initial time is decreased.     

高阶线性比例制导系统脱靶量幂级数解

脱靶量是导弹制导系统设计和评估的重要指标,对于一阶环节线性比例制导系统,可以得到脱靶量的解析解,而对于更接近实际的高阶制导系统一般得不到解析解,通常由直接仿真或伴随仿真获得;研究了高阶线性比例制导系统脱靶量的幂级数解,为脱靶量的解算提供一种新的手段。首先,构造伴随系统,假设伴随系统的解为幂级数与指数函数乘积的形式;然后,利用幂级数法给出了脱靶量的幂级数解的系数递推关系;进一步严格证明了脱靶量幂级数解的收敛性;最后针对一阶环节和高阶二项式环节等特殊制导系统,通过选取适当的指数衰减参数,得到了幂级数解系数简化的递推关系,并且一阶环节制导系统的幂级数解和解析解是一致的。在计算脱靶量时,实际用到的是脱靶量幂级数部分和,而部分和项数的确定依赖于指数衰减参数。因此,还分析了指数衰减参数对幂级数解部分和的收敛速度的影响,并给出了指数衰减参数与部分和项数的选取方法,为幂级数解的应用奠定了基础。     

固定时间拦截变轨段制导的摄动修正方法

采用航迹角迭代法,讨论了固定时间拦截有限推力初始变轨段的制导问题。通过引入虚拟拦截点,将实际存在各种摄动因素的固定时间拦截初始变轨问题转化到二体理论下讨论。在远距离拦截中,当初始变轨段较短、制导精度又较高时,可大大减小Lambert制导中由于忽略近地轨道的各种摄动因素而引起的等时脱靶量。     

基于多项式函数求解的落角约束制导律

在攻击坦克、舰艇等特定目标时,需要对导弹的终端落角进行约束,进一步提高战斗部的毁伤效能。针对这一问题,设计了基于多项式函数推导的落角约束制导律。首先在纵向对称平面内建立弹目相对运动学的小扰动线性化模型,利用落角和脱靶量的始端和终端约束条件,推导得到了满足落角约束的制导律的解析表达式。对该制导律进行仿真,仿真结果表明该制导律可以使导弹按照期望落角命中目标。     

基于Lyapunov稳定性的扩展比例导引律研究

利用虚拟目标概念和三维空间追逃模型,提出了一种基于Lyapunov稳定性的扩展比例导引律。该导引律能同时满足脱靶量要求和末端落角要求,保证了大空域变轨弹道的各段弹道平滑衔接。利用该导引律引导反舰导弹实现了各种形式的大空域变轨弹道。采用大空域变轨弹道有利于提高反舰导弹的机动能力和突防能力。仿真结果证明了所提出的基于Lyapunov稳定性的扩展比例导引律是很有效的。     

基于预测脱靶量的远程拦截速度增益导引

 针对拦截器使用耗尽关机固体燃料发动机的情况,设计了大气层外目标拦截的速度增益导引方法。导引律中根据Lambert导引确定指令推力方向初值,利用剩余速度增量信息,计算惯性速度增益下的预测脱靶量,使用Kepler轨道摄动方程计算消除脱靶量所需的速度增益修正,根据惯性速度增益和速度增益修正之和确定指令推力方向。给出了一种计及J2项引力摄动影响的滑行段弹道预测半解析方法,减少导引律运算量,降低导引方法误差;导引律中引入了剩余速度增量测量环节,增强了导引精度对推进系统参数的鲁棒性。与传统的通用能量管理（GEM）导引相比,采用该导引律拦截远程目标时指令推力方向平稳、变化范围小,脱靶量降低了两个数量级。     

变质心再入弹头螺旋机动突防弹道设计

为提高高超声速变质心再入弹头的突防能力,设计了一种基于主动螺旋机动的突防弹道。在建立变质心弹头动力学模型和弹目运动学模型的基础上,引入新的控制变量,通过控制质量块的偏移位置,将速度矢量和弹目连线的夹角控制在固定值并且使速度矢量绕弹目连线以一定转速旋转来实现螺旋机动。在实现螺旋机动的基础上,推导了弹体处于螺旋机动状态下的螺旋机动半径和稳态脱靶量均方根的解析解。六自由度弹道仿真表明,所设计的突防方案使再入弹头能够进行有效的螺旋机动,通过合理控制机动幅度大小,可以在实现螺旋机动突防的同时保证较高的命中精度。     

基于零控脱靶量的大气层外拦截中制导研究

针对大气层外拦截中段采用耗尽关机固体燃料发动机的情况,设计了基于零控脱靶量的鲁棒中制导律。推导了系统状态转移矩阵,通过数值方法求解得到考虑地球扁率J2摄动项的拦截器零控脱靶状态,在此基础上将推力分解到视线方向和垂直视线方向,并根据垂直视线方向需要速度增量大小设计了推力分配比例系数,使得推力方向平稳变化且能快速减小系统的零控脱靶量。仿真表明,所设计的中制导律简单、可靠,便于工程实现,能有效提高拦截精度,并对发动机工作参数具有较强的鲁棒性。     

Method for Optical-Flow-Based Precision Missile Guidance

A new precision guidance law is presented for three-dimensional intercepts against a moving target. In contrast to previously published guidance laws, it does not require knowledge of the range to the target. This makes it appropriate for use on platforms which have an imaging device, such as a video camera, as a primary sensor. We prove that with idealized dynamic model, the guidance law results in zero miss distance, and a formula is given for impact angle error which tends to zero as does target speed, making this method particularly suitable against slow moving targets. Computer simulations are used to test the law with a more realistic model, with a video camera and optical-flow algorithm providing target information. It is shown to perform well compared with another law from the literature, despite requiring less information.