基于总能量方法的空中加油自适应编队会合控制

doi:10.7527/S1000-6893.2025.32997

集群智能与协同控制

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基于总能量方法的空中加油自适应编队会合控制

张宇含¹, 徐骋¹^,²(), 冀华², 尉明军²

^1.复杂系统控制与智能协同全国重点实验室，北京 100074
^2.北京机电工程研究所，北京 100074

收稿日期:2025-10-30 修回日期:2025-12-04 接受日期:2025-12-31 出版日期:2026-01-16 发布日期:2026-01-15
通讯作者: 徐骋 E-mail:xch2000_1980@sina.com.cn

Adaptive formation rendezvous control for aerial refueling based on total energy method

Yuhan ZHANG¹, Cheng XU¹^,²(), Hua JI², Mingjun WEI²

^1.National Key Laboratory of Complex System Control and Intelligent Agent Cooperation，Beijing 100074，China
^2.Beijing Electro-Mechanical Engineering Institude，Beijing 100074，China

Received:2025-10-30 Revised:2025-12-04 Accepted:2025-12-31 Online:2026-01-16 Published:2026-01-15
Contact: Cheng XU E-mail:xch2000_1980@sina.com.cn

摘要/Abstract

摘要：

针对空中加油场景中受油机与加油机的编队会合问题，提出了一种基于总能量的自适应控制方法。将高度与速度指令转换为动能与势能关系，通过对能量的协调分配实现对高度与速度的控制，避免在快速爬升过程中的速度损失和攻角过大，进而有效防止失速现象的发生，提升了控制过程的平稳性。为增强系统鲁棒性，引入模糊逻辑对控制系统的关键参数进行实时自适应调整。仿真结果表明，所设计的控制器能够完成受油机与加油机的编队会合任务，避免了速度损失和攻角过大，系统稳定性好，为空中加油的受油机自适应编队会合提供了一种稳定性强、鲁棒性好的解决方案。

关键词: 空中加油, 总能量, 模糊逻辑, 自适应控制, 编队会合

Abstract:

An adaptive control method based on total energy is proposed to address the formation rendezvous problem of the receiver and tanker aircraft in the aerial refueling scenario. The altitude and velocity instructions are transformed into the a relationship between kinetic and potential energy. Through the coordinated distribution of energy， the altitude and velocity are controlled， and the velocity loss and excessive angle of attack in the process of rapid climbing are avoided， which effectively prevents the occurrence of stall phenomenon and improves the stability of the tracking process. To enhance the robustness of the system， fuzzy logic is introduced to adjust the key parameters of the control system in real time. The simulation results show that the designed controller achieves the formation rendezvous of the receiver and tanker aircraft， avoids the velocity loss and excessive angle of attack， and has good system stability， which provides a stable and robust solution for the adaptive formation rendezvous of the receiver aircraft for aerial refueling.

Key words: aerial refueling, total energy, fuzzy logic, adaptive control, formation rendezvous

中图分类号:

V249.1

张宇含, 徐骋, 冀华, 尉明军. 基于总能量方法的空中加油自适应编队会合控制[J]. 航空学报, 2026, 47(S1): 732997.

Yuhan ZHANG, Cheng XU, Hua JI, Mingjun WEI. Adaptive formation rendezvous control for aerial refueling based on total energy method[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(S1): 732997.

图/表 11

图1

表1

Kp模糊控制规则

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PB	PB	PM	PS	ZO
NM	PB	PB	PB	PB	PM	ZO	ZO
NS	PM	PM	PM	PM	ZO	PS	NS
ZO	PM	PM	PS	ZO	NS	NS	NM
PS	PS	PS	ZO	NS	NM	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

表1

表2

Ki模糊控制规则

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	NB	NB	NM	NM	NS	ZO	ZO
NM	NB	NB	NM	NS	NS	ZO	ZO
NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
PS	NM	NS	ZO	PS	PS	PM	PB
PM	ZO	ZO	PS	PM	PM	PB	PB
PB	ZO	ZO	PS	PM	PM	PB	PB

表2

表3

Kd模糊控制规则

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	PS	NS	NB	NB	NB	NM	PS
NM	PS	NS	NB	NM	NM	NS	ZO
NS	ZO	NS	NM	NM	NS	NS	ZO
ZO	ZO	NS	NS	NS	NS	NS	ZO
PS	ZO	ZO	ZO	ZO	ZO	ZO	ZO
PM	PB	PS	PS	PS	PS	PS	PB
PB	PB	PM	PM	PM	PS	PS	PB

表3

图 2

图 3

表4

总能量控制器参数

参数	数值	参数	数值
$K v p$	1	$K v t$	2
$K v i$	0.005	$K v ϑ$	1.5
$K h p$	1	$K h t$	2
$K h i$	0.001	$K h ϑ$	3

表4

表5

模糊逻辑参数

参数	俯仰通道	速度通道
$E$	$- 5,5$	$- 5,5$
$E c$	$- 5,5$	$- 5,5$
$K p$	$- 0.05,0.05$	$- 1,1$
$K i$	$- 0.005,0.005$	$- 0.001,0.001$
$K d$	$- 0.1,0.1$	$- 1,1$

表5

图 4

图 5

图 6

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于总能量方法的空中加油自适应编队会合控制

Adaptive formation rendezvous control for aerial refueling based on total energy method

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图/表 11

参考文献 23

相关文章 15

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E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PB	PB	PM	PS	ZO
NM	PB	PB	PB	PB	PM	ZO	ZO
NS	PM	PM	PM	PM	ZO	PS	NS
ZO	PM	PM	PS	ZO	NS	NS	NM
PS	PS	PS	ZO	NS	NM	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	NB	NB	NM	NM	NS	ZO	ZO
NM	NB	NB	NM	NS	NS	ZO	ZO
NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
PS	NM	NS	ZO	PS	PS	PM	PB
PM	ZO	ZO	PS	PM	PM	PB	PB
PB	ZO	ZO	PS	PM	PM	PB	PB

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	PS	NS	NB	NB	NB	NM	PS
NM	PS	NS	NB	NM	NM	NS	ZO
NS	ZO	NS	NM	NM	NS	NS	ZO
ZO	ZO	NS	NS	NS	NS	NS	ZO
PS	ZO	ZO	ZO	ZO	ZO	ZO	ZO
PM	PB	PS	PS	PS	PS	PS	PB
PB	PB	PM	PM	PM	PS	PS	PB

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E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PB	PB	PM	PS	ZO
NM	PB	PB	PB	PB	PM	ZO	ZO
NS	PM	PM	PM	PM	ZO	PS	NS
ZO	PM	PM	PS	ZO	NS	NS	NM
PS	PS	PS	ZO	NS	NM	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
NB	NB	NB	NM	NM	NS	ZO	ZO
NM	NB	NB	NM	NS	NS	ZO	ZO
NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
PS	NM	NS	ZO	PS	PS	PM	PB
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E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
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NS	ZO	NS	NM	NM	NS	NS	ZO
ZO	ZO	NS	NS	NS	NS	NS	ZO
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E	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PB	PB	PM	PS	ZO
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ZO	PM	PM	PS	ZO	NS	NS	NM
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NB	NB	NB	NM	NM	NS	ZO	ZO
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NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
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PM	ZO	ZO	PS	PM	PM	PB	PB
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E	$E c$
E	NB	NM	NS	ZO	PS	PM	PB
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