有界控制导弹攻击防御性飞机的制导律

为提高攻击导弹同时面对目标飞机及其防御导弹情况下的命中概率,基于微分对策理论,对攻击导弹的制导律进行了设计。应对独立控制的多对象博弈问题,微分对策理论具有天然的优势,且相比于最优制导律,微分对策制导律对于目标机动估计误差和机动策略具有更强的鲁棒性。所推导的微分对策制导律进一步考虑了攻击导弹的控制有界性,且适用于攻击导弹、目标飞机和防御导弹具有高阶线性控制系统动态的情形。为验证制导律性能,进行了非线性系统仿真,结果表明该制导律在成功归避防御导弹的同时可实现趋于零脱靶量的目标拦截。攻击导弹为实现规避和攻击的双重任务,仅需要保持相比于防御导弹两倍左右的机动优势。     

基于状态相关黎卡提方程的非线性协同制导律

针对小角度假设或其他线性化条件不满足时的协同拦截问题,提出了一种适用于非线性模型的协同微分对策制导律。考虑两枚拦截弹协同拦截单个机动目标,以微分对策理论为基础,以实现碰撞拦截为目的,将两枚拦截弹的视线角速度作为状态变量,结合状态相关黎卡提方程方法,把复杂的求解偏微分方程问题转化为容易求解的次优化问题,最后得出了可在线应用的解析形式闭环解。这种闭环解在形式上具有耦合性,体现了一种显式的协同关系,且不依赖于剩余时间,从而避免了对剩余时间估计精度问题的考虑。通过非线性仿真验证了所设计制导律的性能,拦截弹采用所提协同制导方法时侧向加速度要求得到了降低,与线性方法相比所消耗的控制能量减少了约25%。     

考虑输入受限和自动驾驶仪延迟的自适应滑模制导律

在输入受限的情况下,为了满足导弹拦截机动目标时高精度制导的需求,首先建立了满足输入受限和考虑导弹自动驾驶仪一阶动态特性的制导模型,其把目标加速度视为未知有界的外界干扰,通过设计自适应控制估计干扰的上界来避免对干扰上界的先验要求,同时结合滑模控制,设计了一种考虑输入受限和自动驾驶仪延迟的自适应滑模制导律,并且基于Lyapunov稳定性理论证明了制导系统状态渐进收敛到零。最后,在所设计的制导律下,对目标余弦机动和阶跃机动两种情况进行了仿真,得到的脱靶量分别为0.040 m和0.036 m,拦截时间分别为6.460 s和7.833 s。仿真结果表明所设计的制导律不仅保证导弹有效击中目标,并且具有较高的制导精度。     

带落角约束的多导弹分布式协同制导律

为实现多枚导弹协同攻击机动目标,基于具有推力可控能力的导弹,提出了一种带落角约束的多导弹分布式协同制导律。将制导律的设计分离为视线方向和视线法向上两个部分:视线方向上基于多智能体协同控制理论和超螺旋控制算法,设计制导律控制导弹剩余时间在有限时间内趋于一致;视线法向上运用零化视线角速率思想和有限时间滑模控制理论,设计制导律控制导弹击中目标的同时满足落角约束。并针对两部分制导律中存在的目标机动信息,分别设计非齐次干扰观测器进行估计。仿真结果表明,提出的制导律能够有效完成协同攻击任务,脱靶量和落角误差分别控制在0.13 m和0.02°以内,并且有效抑制了抖振现象,有利于提高导弹自动驾驶仪的跟踪精度。     

多导弹攻击时间协同的滑模制导律

针对多导弹攻击时间协同的高价值或大型目标攻击问题,基于滑模控制方法,提出了一种非奇异的滑模制导律,并设计了一种适用于机动目标的导弹剩余飞行时间估计方法。通过对滑模制导律切换控制部分的合理设计,保证了系统的Lyapunov稳定性,且避免了滑模面的收敛和保持受到弹道收敛的影响总是可达的。适用于机动目标的剩余飞行时间估计方法采用虚拟目标的设计思路,将目标加速度和速度对弹目相对运动关系的影响投影到弹目视线方向上,从而实现目标的虚拟静止。针对目标固定、非机动和机动三种情况,进行了多枚导弹飞行时间协同攻击的数字仿真。仿真结果表明所估计的剩余飞行时间可以快速收敛到真值,且误差趋近于零。所设计的多导弹攻击时间协同滑模制导律在完成目标攻击的同时,实现了导弹间在攻击时间上的协同。     

拦截机动目标的多约束下协同制导律

为使多空空导弹以不同的落角同时命中机动目标的不同关键部位,提出一带有落角约束和视场角约束的三维协同制导律。首先在导弹的偏航和俯仰平面分别运用二次型最优控制的黎卡提方程推导了带有落角约束的加速度指令,以确保导弹按期望的落向和落角打击目标。其次采用可控开关反向原加速度指令的方法,对视场角进行修正,确保目标始终在导弹视场内。然后基于有限时间一致性理论,在落角约束与视场角约束的基础上设计了具有时变导引系数的协同制导律,使各导弹同时击中机动目标。最后通过仿真验证了所设计的多约束条件协同制导律的有效性与正确性,相比于比例导引可以实现对目标不同方位的协同打击,脱靶量小于0.41 m,落角落向误差均小于0.23°,时间误差在0.1 s以内,并有效避免了机动指令的抖振现象。     

带有攻击角约束的多导弹协同制导律

针对带有攻击角约束的多导弹同时攻击机动目标问题,提出了一种带有攻击角约束的协同制导律。首先基于平面内的导弹-目标相对运动方程,建立了带有攻击角约束的协同制导模型;其次,把协同制导律的设计过程分离为两个部分:一是基于图论的有关内容,运用有限时间一致性理论设计沿着视线方向上的加速度指令来保证所有导弹与目标的相对距离在有限时间内到达一致,进而保证所有的导弹同时击中机动目标;二是利用非齐次干扰观测器对机动目标的加速度进行估计,并运用滑模控制设计视线法向上的加速度指令来保证每枚导弹与目标间的视线角速率收敛到零和视线角收敛到期望的终端视线角,即每枚导弹以期望的终端视线角成功击中目标;最后,对三枚导弹同时打击同一机动目标的情况进行仿真,仿真结果表明本文设计的带有攻击角约束的协同制导律的有效性和正确性。     

考虑自动驾驶仪二阶动态与输入受限的制导律设计

在输入受限情形下,为了提高导弹拦截机动目标的拦截概率和毁伤效果,首先,建立了同时考虑攻击角约束、输入受限和导弹自动驾驶仪二阶动态特性的制导系统模型。其次,基于动态面技术、低通滤波器和自适应技术,设计了满足攻击角约束、输入受限和自动驾驶动态特性的自适应动态面制导律,通过引入辅助系统和新型自适应算法,不仅满足执行器物理受限的要求,同时也保证了自适应参数在系统动态过程中的有界性。最后,利用李雅普诺夫理论对整个闭环系统的稳定性给出了严格的理论证明,仿真获得的脱靶量和拦截时间分别为0.831 m和16.375 s,仿真结果表明所提出制导策略的有效性。     

拦截高超声速飞行器的三维有限时间制导律设计

由于高超声速飞行器具有飞行速度快、机动能力强等特点,因此,传统的制导方式难以保证拦截弹拦截高超声速飞行器时的制导精度。为了减小弹目相对速度,降低对拦截弹的过载能力要求,按照前向制导方式,设计了有限时间收敛的三维前向滑模制导律。该制导律采用了连续的快速双幂次趋近律,不仅保证收敛速度快,同时削弱了传统制导律中存在的抖振现象。在此基础上为了处理系统扰动的上界未知的问题,又设计了自适应滑模制导律,该制导律既可以处理未知上界的外部扰动又可以保证第一种制导律所具有的良好特性。运用李雅普诺夫稳定性理论对所设计的滑模制导律进行了理论证明,最后,通过数值仿真验证了所设计制导律的有效性及优越性。     

一种带有末端弹体姿态角约束的非线性制导律

针对带有末端多约束的三维非线性制导问题,设计了一种通用模型预测静态规划制导算法。该制导算法通过向后迭代求解权矩阵微分方程对控制量进行更新,将动态优化问题转化为静态优化问题,计算效率得以提高。阐述了通用模型预测静态规划制导算法的基本原理,详细给出了基于通用模型预测静态规划算法的制导律设计过程。所设计的制导律满足末端法向加速度约束,因此,间接满足末端弹体姿态角约束。仿真时考虑目标的机动方式和落角约束,仿真结果表明,末端位移偏差小于0.5 m,末端落角可控制在0.01°范围内,末端法向加速度小于0.01 m/s2,该制导律能够很好地满足末端位移、落角和法向加速度约束。     

Distributed group cooperative guidance for multiple missiles with fixed and switching directed communication topologies

Distributed group cooperative guidance (DGCG) problems for multiple missiles with fixed and switching directed communication topologies are dealt with. In contrast to traditional cooperative guidance utilized to intercept one single target, the group cooperative guidance is applicable to multiple targets. In the group cooperative attack, multi-missile system is classified into multiple subgroups, and each subgroup attacks its respective target. Missiles in the same subgroup are required to reach the target simultaneously, while different subgroups may cooperate successively in terms of the impact time. To realize the group cooperative attack, a two-step guidance strategy is developed. The first step adopts a DGCG law based on local neighboring information for multiple missiles to realize group consensus on range-to-go and leading angle. The second step begins when the group consensus of missiles is achieved. During this step, each missile attacks the target under the proportional navigation guidance law. Derived from feedback linearization and convergence analysis, sufficient conditions for multiple missiles to realize the group cooperative attack with fixed and switching directed communication topologies are proposed, respectively. Finally, numerical examples with two subgroups are given to show the effectiveness of the two-step guidance strategy.     

采用捷联惯导系统的反辐射导弹抗关机制导方案研究

本文提出了一种基于被动雷达导引头＋捷联惯导系统的空地反辐射导弹复合制导方案。在此主制导方案的基础上，设计了“目标视线角优化估计”抗关机制导方案，建立了反辐射导弹抗关机性能评估准则，最后通过数学仿真，验证了本文所述方案的有效性。关键词     

基于反演高阶滑模的飞行器最优末制导律

针对传统最优末制导律鲁棒性能较弱,且对参数摄动及外扰敏感的不足,而滑模控制对扰动具有较强鲁棒性的优点,提出一种新的基于反演准连续高阶滑模的最优末制导律,其中反演控制能够有效保证系统全局稳定性,而准连续高阶滑模控制则用于消除扰动影响。为了去除抖振效果,引入自适应超螺旋算法在线更新控制参数以消除符号函数导致的高频抖振影响。仿真结果表明:飞行器在该末制导律导引下,弹目视线角速率快速收敛,从而保证飞行器有很高的命中精度;鲁棒性较强;能够较好的满足约束条件要求。     

Study of the open and closed loop characteristics of a tractor and a single axle towed implement system

Accurate automatic guidance of towed implements is important for performing agricultural field operations and for gaining the ultimate benefit from such systems. The study of open and closed loop system responses of a vehicle-implement system can be helpful in the design of practical guidance controllers. Open loop analysis of the kinematic and dynamic models revealed that the higher order dynamics captured by the tractor and implement dynamic model had an impact on simulated responses at higher operating velocities and on higher input frequencies. In addition, a dynamic model with tire relaxation length dynamics was also studied. The various model responses were compared with the experimental responses. Closed loop system characteristics were studied by using a linear quadratic regulator (LQR) controller. The tractor position and heading and implement heading states along with respective rate states were fed back to close the loop. Steering dynamics were also added to the dynamic model closed loop analysis, which helped to achieve a realistic closed loop steering angle history. The closed loop system dynamics became faster as the forward velocity was increased. The open and closed loop response analysis performed in this work provided an understanding about the system at various forward velocities, which will help to design and develop efficient and robust tractor and towed implement guidance controller.     

基于BDS的导弹脱靶量数据处理方法

研究利用导弹过靶前的测量数据解算脱靶量参数。针对导弹过靶时刻BDS(北斗系统)不能定位和测量数据丢失等问题,采用最优滤波平滑处理技术,建立过靶瞬间弹道外推数学模型,对导弹飞行轨迹外推,获得过靶时的完整弹道参数。为解决靶船上合作目标部位不一致问题,利用导弹射向、弹道偏角、靶船航向信息和靶船上BDS天线相位中心相对于角反射体中心的位置,对合作目标部位进行修正,解算相对于角反射体中心的脱靶量参数。通过建立过靶痕迹方向判别坐标系,利用脱靶量参数,判别导弹过靶痕迹方向性。测试数据处理结果表明该方法精度高,脱靶量精度达到0.5 m。     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.     

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.     

Two approximate analytical solutions for the kinematically determined velocity equations for granular solids

For axially symmetric flows of dilatant granular materials, the velocity equations uncouple from the stress equations in certain plastic regimes, and assuming dilatant double shearing a closed set of three first-order partial differential equations are obtained. These supposedly simple equations are deceptive, because although they are simple in appearance, the determination of exact solutions is non-trivial. For one of the known families of solutions which has not been studied previously, the authors present the non-linear ordinary differential equation for the stress angle ψ and determine two small ψ approximations. Furthermore, the stream function and streamlines are obtained for ψ determined numerically and from the two small ψ approximations. For purposes of comparison, the streamlines for three further known exact solutions are also presented. In addition, we briefly examine the circumstances for which solutions of the velocity equations satisfy the principle of non-negative plastic work. For example, we are able to establish that in the case when the velocity equations are derived from a plastic potential, the solutions always satisfy the principle when the material has no cohesion.     

多束破片聚焦式杀伤战斗部毁伤目标的仿真

论述了多束破片聚焦式杀伤战斗部毁伤目标的特点 ,提出了破片聚焦式杀伤战斗部毁伤目标取决于导弹的制导误差和引战配合效率。给出了一种典型多束破片聚焦式杀伤战斗部毁伤某歼击机目标时 ,单发杀伤概率的计算实例。