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1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191;
2. 试验物理与计算数学国家级重点实验室, 北京 100076

Predictor-corrector reentry guidance satisfying no-fly zone constraints
ZHAO Jiang1, ZHOU Rui1 , ZHANG Chao2
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. National Key Laboratory of Experimental Physics and Computational Mathematics, Beijing 100076, China
Abstract:To enforce the lateral maneuverability of the reentry gliding flight, a predictor-corrector guidance method satisfying the no-fly zone constraints was proposed for the lifting hypersonic reentry vehicles. First, the longitudinal guidance was developed by the prediction of the landing error and the correction of the guidance command. The downrange was modified in real time by updating the magnitude of the bank angle. Then, a new handoff mechanism for the bank angle reversal logic was designed for the lateral guidance. The maneuver of the lateral motion was performed by employing the heading angle error corridor and the heading angle orienting area. Based on the CAV-H model, the numerical simulations show that the no-fly zone constraints can be satisfied by the predictor-corrector guidance method which is independent of the standard reentry trajectory. The Monte Carlo simulation results of the reentry gliding guidance with random initial dispersions and errors also demonstrate the robustness of the proposed algorithm.
Key words: hypersonic vehicles     reentry guidance     predictor-corrector     no-fly zone     bank angle reversal

1 再入制导问题 1.1 三自由度运动学方程

1.2 再入过程约束

1.3 再入终端约束

1.4 禁飞区约束

2 预测校正制导 2.1 纵向制导律设计

2.2 侧向制导律设计

1) 当再入飞行器远离禁飞区时(这里认为飞行器与禁飞区圆心的水平距离大于其半径2倍的状态为远离禁飞区),采用传统的航向角误差走廊以实现飞行器的侧向运动控制,其具体形式如图 1所示;

 图 1 航向角误差走廊Fig. 1 Heading angle error corridor

2) 当再入飞行器接近禁飞区时,根据禁飞区的位置和半径来确定当前时刻飞行航向角的导向区域,通过倾侧角反转对制导指令进行修正,使航向角位于该导向区域之内,进而完成禁飞区的规避控制.

 图 2 航向角导向区域Fig. 2 Heading angle orienting area

1) 过C点作禁飞圆Z的切线CMCN,记∠MCZ=∠NCZ=δ,则CMCN构成航向角导向区域的内边界.

2) 过C点设计漏斗形的几何区域CACB,使∠ACM=∠BCN=δ,则CACB构成航向角导向区域的外边界.

3) 定义区域Ⅰ和Ⅰ′为航向角的导向区域,定义区域Ⅱ、Ⅱ′、Ⅲ和Ⅲ′为航向角的非导向区域.

1) 当CZ<2rZ时,侧向制导逻辑由传统的航向角误差走廊切换为航向角导向区域.

2) 当目标落点位于CZ延长线的左侧时(例如位于T点),飞行器应紧靠禁飞区的左侧完成规避滑翔；当目标点位于CZ延长线的右侧时(例如位于T′点),飞行器应紧靠禁飞区的右侧完成规避滑翔.

3) 以左侧规避滑翔为例,当飞行航向角(表征速度方向)位于导向区域Ⅰ时,倾侧角的符号保持不变；当飞行航向角越过导向区域的外边界CA时(即位于区域Ⅲ),倾侧角的符号变为正；当飞行航向角越过导向区域的内边界CM时(即位于区域Ⅱ),倾侧角的符号变为负.该制导逻辑的具体计算公式为

4) 当飞行器的当前位置C越过ZS的延长线而位于区域Ⅳ时(S为过T作禁飞圆切线的切点),认为禁飞区规避已经完成,侧向制导逻辑由航向角导向区域切换回航向角误差走廊,以保证滑翔飞行的落点精度,此时制导逻辑计算公式为

3 仿真分析

 参数 高度/ km 速度/ (m·s-1) 经度/ (°) 纬度/ (°) 航迹角/ (°) 航向角/ (°) 数值 80.0 7 100.0 10.0 -20.0 -1.0 45.0

3.1 标准条件下制导方法仿真分析

 禁飞区约束 中心位置 半径/km 算例2 (N10°,E60°) 700 算例3 (N10°,E60°) 1 000

 图 3 标准条件下制导仿真结果Fig. 3 Results of reentry guidance in standard condition

1) 两种制导方法都能够满足预定航程要求,落点的经纬度误差均小于0.1°,与目标点的距离不超过10 km,符合再入制导的精度要求.

2) 与算例1相比,本文提出的制导算法能够导引飞行器躲避半径不同的禁飞区约束,验证了该方法的可行性.

3) 算例2和算例3表明,考虑禁飞区规避的制导算法能够根据禁飞区的位置和半径自适应地修正制导指令,提高了再入滑翔飞行的机动性.

3.2 扰动条件下制导方法仿真分析

 禁飞区约束 中心位置 半径/km 禁飞区1 (N1°,E45°) 700 禁飞区2 (N25°,E58°) 700

 偏差项 分布类型 偏差限 高度偏差Δh/km 均匀分布 ±2.0 经度偏差Δθ/(°) 均匀分布 ±0.2 纬度偏差Δφ/(°) 均匀分布 ±0.2 速度偏差ΔV/(m·s-1) 高斯分布 ±100 航迹角偏差Δγ/(°) 高斯分布 ±0.3 航向角偏差Δψ/(°) 均匀分布 ±1.0 升力系数误差ΔCL/% 高斯分布 ±10 阻力系数误差ΔCD/% 高斯分布 ±10

 图 4 扰动条件下制导仿真结果Fig. 4 Results of reentry guidance with random dispersions

1) Monte Carlo仿真实验表明,考虑禁飞区规避的预测校正制导可以满足预定航程要求,其终端经纬度误差均小于0.1°,符合再入制导的精度要求.

2) 经纬度扰动散布偏差表明,再入落点受到禁飞区约束的影响,主要集中在目标点的东南方,与目标点距离不超过10 km.

3) 在再入点初始散布误差存在的情况下,滑翔飞行轨迹能够满足路径约束、终端约束和禁飞区约束的要求,然而,初始航向角偏差过大会对制导精度产生影响,因此应该尽量减小再入滑翔飞行的初始航向角偏差.

4) 仿真结果表明,在飞行过程中引入升力系数误差和阻力系数误差,会在一定程度上影响纵向制导的精度,但预测校正制导仍然满足给定的精度需求,且没有对禁飞区规避产生影响,说明本文提出的算法具备可行性和鲁棒性.

5) 对于传统的再入预测校正制导方法,倾侧角指令往往进行2~3次反转以实现航向控制.为了提升飞行器的横向机动性能,本文引入了禁飞区规避机制,且每添加一个禁飞区约束,倾侧角指令都需要增加2次反转.从Monte Carlo仿真结果可以发现,每一次制导指令反转时刻对应的飞行航程间隔均在200 km以上,因而不会超过飞行器的机动能力限制,进而保证了制导精度要求.

4 结 论

1) 本文提出的制导方法易于实现,且不改变传统预测校正制导的表达形式,不依赖于标准再入轨迹.

2) 改进的侧向制导逻辑可以进行航向角误差走廊和航向角导向区域的切换,提高了倾侧角反转策略的灵活性.

3) 标准条件下的仿真结果表明,与传统的预测校正制导相比,本文提出的制导方法能够有效地规避禁飞区约束.

4) 扰动条件下的Monte Carlo仿真结果表明,本文提出的制导方法具有良好的鲁棒性.

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#### 文章信息

ZHAO Jiang, ZHOU Rui, ZHANG Chao

Predictor-corrector reentry guidance satisfying no-fly zone constraints

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(5): 864-870.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0488