Prescribed Performance-based Lateral Channel Control Method of Underactuated Hypersonic Vehicle

doi:10.12382/bgxb.2023.0544

Abstract

Abstract:

A control method combining the prescribed performance function and dynamic surface control is designed for the underactuated problem caused by the lateral channel of hypersonic vehicle only through aileron control. The lateral underactuated system is transformed into a roll-yaw cascade control system. For the rolling rotor circuit, the limiting of sideslip angle command is regarded as the saturation problem of control input. A prescribed performance function is designed, and a control strategy is proposed based on the dynamic surface control theory, which realizes the active control of the tracking speed, transient tracking error and stable tracking accuracy of a bank angle. Then, aiming at the requirement that the sideslip angle needs to be stabilized in a given range, based on the limiting sideslip angle instruction, a prescribed performance function of yaw sub-loop is designed, which theoretically ensures that the sideslip angle meets the stabilization range requirements and can achieve the specified tracking accuracy at the required tracking speed. Finally, the stability of the lateral attitude controller is proved based on the Lyapunov stability principle. The simulated results show that the proposed control method can be used to make the bank angle reach the specified tracking accuracy at the required tracking speed and the transient tracking error satisfies the given boundary; the sideslip angle satisfies the given limited range; and the controller has good robustness.

Key words: hypersonic vehicle, underactuation, lateral, prescribed performance, dynamic surface control

CLC Number:

TJ765.2

WANG Xiaofang, XU Jiaqi. Prescribed Performance-based Lateral Channel Control Method of Underactuated Hypersonic Vehicle[J]. Acta Armamentarii, 2024, 45(8): 2749-2760.

Figures/Tables 20

Fig.1 Relationship diagram of bank angle tracking error and performance function

Table 1 Structure and aerodynamic parameters of hypersonic vehicle

参数	数值	参数	数值
m/kg	310	S/m	0.4
L/m	1.8	I_x/(kg·m²)	23
I_y/(kg·m²)	120	I_z/(kg·m²)	120
$m x ω x$	-35	$m x δ x$	-0.002
$m y δ x$	-0.002	$m y β$	0.027
$m x β$	-0.3	$C z β$	-2.1
$m y ω y$	-110

Table 1 Structure and aerodynamic parameters of hypersonic vehicle

参数	数值	参数	数值
m/kg	310	S/m	0.4
L/m	1.8	I_x/(kg·m²)	23
I_y/(kg·m²)	120	I_z/(kg·m²)	120
$m x ω x$	-35	$m x δ x$	-0.002
$m y δ x$	-0.002	$m y β$	0.027
$m x β$	-0.3	$C z β$	-2.1
$m y ω y$	-110

Table 2 The parameters of controller

参数	数值	参数	数值
$k γ v$	0.1	$k ω x$	7
$τ ω x$	0.1	$β γ v 1$	3
$β γ v 2$	0.8	$β ω x 1$	5
$β ω x 2$	5	$h γ v$	3
$h ω x$	3	h	0.01
k_β	0.0025	$k ω y$	12
$τ ω y$	0.1	$β β 1$	4.7
$β β 2$	2.2	$β ω y 1$	13
$β ω y 2$	18	h_β	4
$h ω y$	4	$α γ v 1$ = $α γ v 2$	0.5
$α ω x 1$ = $α ω x 2$	0.5	α_β₁=α_β₂	0.5
$α ω y 1$ = $α ω y 2$	0.5

Table 2 The parameters of controller

参数	数值	参数	数值
$k γ v$	0.1	$k ω x$	7
$τ ω x$	0.1	$β γ v 1$	3
$β γ v 2$	0.8	$β ω x 1$	5
$β ω x 2$	5	$h γ v$	3
$h ω x$	3	h	0.01
k_β	0.0025	$k ω y$	12
$τ ω y$	0.1	$β β 1$	4.7
$β β 2$	2.2	$β ω y 1$	13
$β ω y 2$	18	h_β	4
$h ω y$	4	$α γ v 1$ = $α γ v 2$	0.5
$α ω x 1$ = $α ω x 2$	0.5	α_β₁=α_β₂	0.5
$α ω y 1$ = $α ω y 2$	0.5

Table 3 The parameters of ADRC controller

参数	数值	参数	数值
$ω 0 γ v$	0.9	$k γ v$	100
$ω 0 ω x$	15	$k ω x$	5
ω₀_β	50	k_β	5
$ω 0 ω y$	8	$k ω y$	0.8

Table 3 The parameters of ADRC controller

参数	数值	参数	数值
$ω 0 γ v$	0.9	$k γ v$	100
$ω 0 ω x$	15	$k ω x$	5
ω₀_β	50	k_β	5
$ω 0 ω y$	8	$k ω y$	0.8

Fig.2 Tracking curves of bank angle under the control of two controllers

Fig.3 Tracking error curves of bank angle under the control of two controllers

Fig.4 Change curves of sideslip angle under the control of two controllers

Fig.5 Change curves of sideslip angle error under the control of two controllers

Fig.6 Tracking curve of rolling angular velocity

Fig.7 Tracking curve of yawing angular velocity

Fig.8 Aileron variation curve

Fig.9 Observed results of composite disturbance f γ v

Fig.10 Observed results of composite disturbance f ω x

Fig.11 Observed results of composite disturbance fβ

Fig.12 Observed results of composite disturbance f ω y

Fig.13 Response curve of bank angle under tension deviation

Fig.14 Response curve of bank angle error under tension deviation

Fig.15 Response curve of sideslip angle under tension deviation

Fig.16 Response curve of sideslip angle error under tension deviation

Fig.17 Aileron response curve under the condition of deflection

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