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Guidance law with impact angle constraints based on extended disturbance observer
ZHANG Jiao , YANG Xu, LIU Yuanxiang
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract: Aimed at the requirement for intercepting maneuvering targets with impact angle constraint, based on the technology of extended disturbance observer (EDO), a novel finite-time convergence guidance law was presented. Considering the relative motion between missile and target, the time-varying uncertainty of missile velocity and the unknown target acceleration were regarded as the disturbance, which is estimated and compensated by EDO. The fast tracking differentiator was introduced to solve the immeasurability problem of the desired line of sight angle rate. Moreover, the domain of sliding mode capturability was introduced to the performance evaluation of guidance law. The simulation experiments of different interception scenarios and different forms of maneuvering target were carried out. The simulation results show that the proposed guidance law has good interception performance and robustness, and it is of less missile acceleration and higher guidance accuracy, which is more helpful for the realization in engineering.
Key words: terminal guidance law     impact angle constraint     finite time convergence     extended disturbance observer     tracking differentiator
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1 导弹拦截模型

 图 1 导弹-目标平面拦截几何 Fig. 1 Missile-target engagement geometry

atλ=atcos($\phi$tq),atλ为目标法向加速度沿垂直视线方向的分量.在实际工程应用中,目标的法向加速度at是未知的,因此如何实时准确快速估算出at的值是制导律设计的关键.

 图 2 导弹和目标碰撞航迹 Fig. 2 Missile and target on collision course

2 复合制导律设计

 图 3 复合制导律结构框图 Fig. 3 Structure block diagram of compound guidance law
2.1 扩张干扰观测器

i=1时,系统的总干扰d(t)的估计误差为

2.2 有限时间收敛制导律设计

2.3 快速跟踪微分器

3 稳定性分析

β－(ε/|x2|γsgn(x2))>0时,式(38)仍保持非奇异终端滑模面的形式,且x2的收敛区域为

4 仿真结果分析

4.1 打击场景分析

1) 当导弹采用垂直拦截时,所对应的攻击角为:θimp1=π/2 rad,由式(8)可得初始的期望视线角为qF0=3.201 rad.根据式(5)的约束条件则有qF0－$\phi$m0=2.416 rad>π/2 rad,使得目标不在导引头的视场范围内.因此,需将式(8)修改为

3) 上述给出了在两种特殊攻击角约束的情况下,期望视线角的计算.当选取其他任意攻击角约束时可以参考上述方法计算期望的视线角.

4.2 滑模捕获能力分析

4.3 仿真算例对比及分析

 图 4 算例1中弹目相对运动轨迹(θimp1=π/2) Fig. 4 Curves of relative motion between missile and target in case 1(θimp1=π/2)

 图 5 恒值机动目标的仿真结果(θimp1=π/2) Fig. 5 Simulation results of constant maneuver target (θimp1=π/2)

 图 6 算例1中弹目相对运动在(υR,υq)空间内的 轨迹(θimp1=π/2) Fig. 6 Trajectory of relative motion between missile and target in (υR,υq) space in case 1 (θimp1=π/2)

 图 7 算例1中弹目相对运动轨迹(θimp2=0) Fig. 7 Curves of relative motion between missile and target in case 1 (θimp2=0)

 图 8 恒值机动目标的仿真结果(θimp2=0) Fig. 8 Simulation results of constant maneuver target (θimp2=0)

 图 9 算例1中弹目相对运动在(υR,υq)空间内的 轨迹(θimp2=0) Fig. 9 Trajectory of relative motion between missile and target in (υR,υq) space in case 1 (θimp2=0)

 图 10 算例1中不同扩张阶数时的估计误差 Fig. 10 Estimation error with different extended orders in case 1

 图 11 算例2中蛇行机动目标的仿真结果(θimp1=π/2) Fig. 11 Simulation results of weaving maneuver target in case 2 (θimp1=π/2)

 图 12 算例2中蛇形机动目标的仿真结果(θimp2=0) Fig. 12 Simulation results of waving maneuver target in case 2 (θimp2=0)

 图 13 目标加速度幅值不同时的仿真结果 Fig. 13 Simulation results of weaving target with different amplitudes of weave maneuver

 图 14 不同攻击角时拦截蛇行机动目标的仿真结果 Fig. 14 Simulation results of interception of a weaving maneuver target with various impact angles

 图 15 算例2中不同扩张阶数时的估计误差 Fig. 15 Estimation error with different extended order in case 2

 图 16 跟踪微分器仿真结果 Fig. 16 Simulation results of tracking differentiator

 图 17 不同制导律拦截蛇形机动目标的仿真结果(θimp1=π/2) Fig. 17 Simulation results of interception of weaving maneuver target with different guidance law(θimp1=π/2)

 图 18 不同制导律拦截蛇形机动目标的仿真结果(θimp2=0) Fig. 18 Simulation results of interception of weaving maneuver target with different guidance laws (θimp2=0)
5 结 论

1) 借鉴干扰观测器的设计思想,设计了扩张干扰观测器,并给出其稳定性证明及误差收敛域,同时,给出了基于带宽的调参方法,便于工程应用及推广.

2) 在制导律设计过程中,引入快速跟踪微分器解决了制导律中所需的期望视线角速率无法直接给出的问题.同时,推导了该复合制导律的收敛时间及收敛域,为参数的整定提供指导.

3) 将该复合制导律应用于不同攻击场景、目标不同的机动形式的仿真,引入滑模捕捉能力的概念.对比仿真结果表明,导弹在垂直攻击场景中拦截快速高机动目标时,本文提出的制导律能够保证导弹以更短的时间、更小的需用过载和更精确的攻击角度实现对目标的精度打击.

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#### 文章信息

ZHANG Jiao, YANG Xu, LIU Yuanxiang

Guidance law with impact angle constraints based on extended disturbance observer

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(12): 2256-2268.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0013