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

Abstract

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

CLC Number:

V249.1

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.

Figures/Tables 11

Fig.1

Table 1

Kp fuzzy control rule

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

Table 1

Table 2

Ki fuzzy control rule

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

Table 2

Table 3

Kd fuzzy control rule

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

Table 3

Fig.2

Fig.3

Table 4

Parameters of total energy controller

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

Table 4

Table 5

Fuzzy logic parameters

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

Table 5

Fig.4

Fig.5

Fig.6

References 23

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

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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
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

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