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1. 国防科学技术大学 航天科学与工程学院, 长沙 410073;
2. 空间物理重点实验室, 北京 100076

Energy suboptimal flight strategy of bank-to-turn maneuver for lifting vehicle
YANG Ding1,2 , LIU Ming1,2 , YANG Lingxiao2 , YANG Ming1,2 , GE Yajie2
1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China ;
2. Science and Technology on Space Physics Laboratory, Beijing 100076, China
Received: 2016-07-20; Accepted: 2016-08-10; Published online: 2016-08-31
Corresponding author. Tel.:010-88523261,E-mail:liumingbuaa@163.com
Abstract: When lifting vehicle is returning into earth's atmosphere, some path constraints including heating rate, dynamic pressure and overload should be enforced strictly. In order to reduce the energy losing during the performance of bank-to-turn maneuver, it is necessary to develop a suboptimal flight strategy. The main research contents of this paper are as follows. The trajectory characteristic of bank-to-turn maneuver is analyzed via studying the entry dynamics. The analytical solution to terminal velocity at the special terminal heading angle is derived. Furthermore, a suboptimal flight strategy, which considers the path constraints, is proposed based on this analytical solution. In order to verify the optimality of this flight strategy, a trajectory optimization problem is formulated so as to provide optimal energy trajectory. Then, Gauss pseudospectral method is used to solve this problem. The results show that both trajectories are highly consistent, and the flight strategy is more efficient and has greater engineering applicable values.
Key words: lifting vehicle     suboptimal flight strategy     bank-to-turn maneuver     optimal control     Gauss pseudospectral method

1 数学模型 1.1 动力学模型

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1.2 气动模型

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1.3 飞行约束模型

1) 热流峰值约束

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2) 动压约束

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3) 过载约束

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4) 控制量约束

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5) 终端约束

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2 飞行器倾斜转弯基本原理

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 图 1 转弯半径特性曲线 Fig. 1 Characteristic curves of bank-to-turn radius

1) 飞行高度越低，对应飞行器倾斜转弯半径越小。

2) 飞行倾侧角不为0时，飞行攻角越大，对应升力系数越大，则倾斜转弯半径越小。

3) 倾斜转弯机动过程中，飞行倾侧角对应的侧向升力分量越大，则倾斜转弯半径越小。

3 能量近似最优倾斜转弯飞行策略

 图 2 倾斜转弯示意图 Fig. 2 Schematic diagram of bank-to-turn

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 图 3 倾斜转弯终端速度的特性曲线 Fig. 3 Characteristic curves of bank-to-turnterminal velocity

 图 4 高度-速度走廊边界示意图 Fig. 4 Schematic diagram of H-V corridor boundary

1) 基于最优升阻比攻角-速度飞行剖面及飞行过程约束，规划高度-速度飞行走廊。

2) 基于高度-速度飞行走廊下边界获得倾斜机动能量最优高度-速度飞行剖面。

3) 纵向基于高度-速度及攻角-速度剖面、横向通过攻角及高度实时求解倾侧角，获得能量近似最优倾斜转弯轨迹。

 图 5 能量近似最优飞行策略流程图 Fig. 5 Flowchart of energy suboptimal flight strategy
4 最优转弯转弯轨迹优化

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1) 性能指标选取

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2) 控制方程

3) 过程约束

4) 终端约束

5 仿真算例

 初始条件 高度/km 速度/(m·s-1) 弹道倾角/(°) 经度/(°) 纬度/(°) 弹道偏角/(°) 数值 50 6 000 0 0 0 0

 状态 高斯伪谱法算例1 高斯伪谱法算例2 高斯伪谱法算例3 Δψ/(°) 45 90 135

 图 6 攻角随飞行时间变化 Fig. 6 Angle of attack changes with flight time
 图 7 倾侧角随飞行时间变化 Fig. 7 Bank angle changes with flight time
 图 8 高度随速度变化关系 Fig. 8 Altitude changes with velocity
 图 9 地面轨迹 Fig. 9 Ground track
 图 10 热流密度随飞行时间变化 Fig. 10 Heating rate changes with flight time
 图 11 法向过载随飞行时间变化 Fig. 11 Normal load factor changes with flight time

 状态 终端弹道偏角/(°) 终端速度Vf/(m·s-1) 终端高度Hf/km 近似最优倾斜转弯飞行策略 高斯伪谱法 近似最优转弯飞行策略 高斯伪谱法 算例1 45 4 702 4 720 32.3 32.1 算例2 90 3 712 3 726 28.8 28.9 算例3 135 2 917 2 926 25.3 25.7

 s 状态 近似最优倾斜转弯飞行策略计算时间 高斯伪谱法计算时间 算例1 ＜1 630 算例2 ＜1 972 算例3 ＜1 1 316

6 结 论

 [1] 童雄辉. 美国未来全球快速精确打击体系预测分析[J]. 导弹与航天运载技术, 2008 (5) : 57 –61. TONG X H. Forecast and analysis of USA's future conventional prompt global strike system[J]. Missile and Space Vehicle, 2008 (5) : 57 –61. (in Chinese) [2] 康开华, 才满瑞, 伍赣湘, 等. 美国高超声速技术飞行器[J]. 航天制造技术, 2010 (5) : 7 –11. KANG K H, CAI M R, WU G X, et al. U.S.hypersonic technology vehicle[J]. Aerospace Manufacturing Technology, 2010 (5) : 7 –11. (in Chinese) [3] 李广华, 张洪波, 汤国建. 高超声速滑翔飞行器典型弹道特性分析[J]. 宇航学报, 2015, 36 (4) : 397 –403. LI G H, ZHANG H B, TANG G J. Typical trajectory characteristics of hypersonic glide vehicle[J]. Journal of Astronautics, 2015, 36 (4) : 397 –403. (in Chinese) [4] 陈小庆, 侯中喜, 刘建霞. 高超声速滑翔飞行器倾斜转弯分析及控制系统设计[J]. 国防科技大学学报, 2012, 34 (3) : 17 –23. CHEN X Q, HOU Z X, LIU J X. Analysis and controller design of bank-to-turn system for hypersonic gliding vehicle[J]. Journal of National University of Defense Technology, 2012, 34 (3) : 17 –23. (in Chinese) [5] 张忠峰, 高云峰, 宝音贺西. 高超声速飞行器机动航迹优化[J]. 弹箭与制导学报, 2009, 29 (3) : 164 –172. ZHANG Z F, GAO Y F, BAOYIN H X. Optimization of maneuvering flight path of hypersonic vehicle[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2009, 29 (3) : 164 –172. (in Chinese) [6] 黄育秋, 何麟书. 升力式再入飞行器多约束多阶段弹道优化设计[J]. 哈尔滨工业大学学报, 2011, 43 (7) : 144 –148. HUANG Y Q, HE L S. Multi-constraints and multi-phases trajectory optimization of lift reentry vehicle[J]. Journal of Harbin Institute of Technology, 2011, 43 (7) : 144 –148. (in Chinese) [7] 周文雅, 杨涤, 李顺利. 利用高斯伪谱法求解升力航天器最优再入轨迹[J]. 南京理工大学学报, 2010, 34 (1) : 85 –90. ZHOU W Y, YANG D, LI S L. Using Gauss pseudospectral method to solve optimal reentry trajectory for lifting vehicle[J]. Journal of Nanjing University of Science and Technology, 2010, 34 (1) : 85 –90. (in Chinese) [8] 周浩, 陈万春. 基于拟平衡滑翔的横程最大轨迹研[J]. 飞行力学, 2010, 28 (3) : 64 –68. ZHOU H, CHEN W C. Maximum cross range trajectory optimization based on quasi-equilibrium glide conditions[J]. Flight Dynamics, 2010, 28 (3) : 64 –68. (in Chinese) [9] 张红文, 张科南, 陈万春. 带静态参数的高超声速飞行器轨迹优化算法[J]. 北京航空航天大学学报, 2014, 40 (2) : 141 –147. ZHANG H W, ZHANG K N, CHEN W C. Indirect method for trajectory optimization of hypersonic vehicle with static parameters[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40 (2) : 141 –147. (in Chinese) [10] 李瑜, 杨志红, 崔乃刚. 助推-滑翔导弹最大射程优化[J]. 弹道学报, 2008, 20 (4) : 53 –56. LI Y, YANG Z H, CUI N G. Optimization of maximum range for boost-glide missile[J]. Journal of Ballistics, 2008, 20 (4) : 53 –56. (in Chinese) [11] ZHANG K N,CHEN W C.Reentry vehicle constrained trajectory optimization[C]//17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference 2011.Reston:AIAA,2011. [12] ZHAO Z G.A rapid reentry trajectory planning method for CAV[C]//2010 3rd International Symposium on Systems and Control in Aeronautics and Astronautics.Piscataway NJ:IEEE Press,2010:1255-1260. [13] VINH N X. Flight mechanics of high-performance aircraft[M]. Cambridge: Cambridge University Press, 1993 : 374 . [14] TERRY H P.A common aero vehicle model,description,and employment guidance[R].Arlington:Schafer Corporation for AFRL and AFSPC,2003. [15] 汪朝群. 航天飞机的再入飞行走廊及再入飞行轨迹[J]. 航天控制, 1990 (1) : 1 –10. WANG C Q. On entry flight corridor and entry trajectory for space shuttle reentry[J]. Aerospace Control, 1990 (1) : 1 –10. (in Chinese)

#### 文章信息

YANG Ding, LIU Ming, YANG Lingxiao, YANG Ming, GE Yajie

Energy suboptimal flight strategy of bank-to-turn maneuver for lifting vehicle

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(11): 2540-2547
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0613