Design of a Neural Network Acceleration Autopilot for Spinning Projectile Based on Adaptive Disturbance Observer

doi:10.12382/bgxb.2023.1085

Abstract

Abstract:

The spinning projectiles are influenced by various disturbances during flight, includingthe model uncertainties due to the drastic variations in aerodynamic parameters during cross-domain flight, as well as the external perturbations caused by external forces and moments. The research aims to address the robust control challenges of dual-channel spinning projectiles in high-dynamic flight environments. A pseudo-inverse feedback controller is designed based on the trajectory linearization control method, and an adaptive feedforward compensation controller is developed using radial basis function neural networks to accurately approximate the model uncertainties. Finally, an adaptive disturbance observer is designedby treating the neural network approximation errors and external disturbances as total disturbance based on the fixed-time stability theory, which is used to accurately estimate and compensate for total disturbance. The ultimate uniform boundness (UUB) of the closed-loop system is rigorously proven through Lyapunov theory. The effectiveness of the proposed methodology is illustrated through numerical simulations.

Key words: spinning projectile, dual-channel control, radial basis function neural network, adaptive disturbance observer, fixed-time stability theory

CLC Number:

WANG Wei, YANG Jing, NAN Yuxiang, LI Junhui, WANG Yuchen. Design of a Neural Network Acceleration Autopilot for Spinning Projectile Based on Adaptive Disturbance Observer[J]. Acta Armamentarii, 2024, 45(11): 3841-3855.

Figures/Tables 20

Fig.1 Schematic diagram of RBFNN

Fig.2 Schematic diagram of spinning projectile

Fig.3 Frame work of acceleration autopilot

Table 1 Parameters of observer

观测器类别	观测器形式	参数取值
FTDO	$z · 0$ =v₀-f₁-b₁u,v₀=-λ₂L¹^/³\|z₀-x\|²^/³sgn(z₀-x)+z₁ $z · 1$ =v₁,v₁=-λ₁L¹^/²\|z₁-v₀\|¹^/²sgn(z₁-v₀)+z₂ $z · 2$ =-λ₀Lsgn(z₂-v₁)	z_i(0),i=1,2 λ₀=1.1,λ₁=1.5,λ₂=2 L=50
FxTESO	$z · 1$ =f₁+b₁u+α₁si $g o 1$ (x₁-z₁)+β₁si $g θ 1$ (x₁-z₁) $z · 2$ =α₂si $g o 2$ (x₁-z₁)+β₂si $g θ 2$ (x₁-z₁)+γsign(x₁-z₁)	z_i(0)=0,i=1,2,α₁=3,β₁=15 α₂=1.5,β₂=7.5,o₁=0.9,θ₁=1.01 o₂=2o₁-1,θ₂=2θ₁-1,γ=50
AFxTSMDO	$z ˜$ =z-x, $z ·$ =-f₁-b₁u-κ(sig^p( $z ˜$ )+sig^q( $z ˜$ ))+v_d σ= $z ˜ ·$ +κ(sig^p( $z ˜$ )+sig^q( $z ˜$ )) $v · d$ =-κ(sig^p(σ)+sig^q(σ))-K(t)sgn(σ) $K ·$ (t)= $K ¯ σ \|, \| σ \| > ε 0, 其他$	z(0)=0,v_d(0)=0,κ=2,p=0.5 q=1.5,K(t)=0, $K ¯$ =10,ε=0.1

Table 1 Parameters of observer

观测器类别	观测器形式	参数取值
FTDO	$z · 0$ =v₀-f₁-b₁u,v₀=-λ₂L¹^/³\|z₀-x\|²^/³sgn(z₀-x)+z₁ $z · 1$ =v₁,v₁=-λ₁L¹^/²\|z₁-v₀\|¹^/²sgn(z₁-v₀)+z₂ $z · 2$ =-λ₀Lsgn(z₂-v₁)	z_i(0),i=1,2 λ₀=1.1,λ₁=1.5,λ₂=2 L=50
FxTESO	$z · 1$ =f₁+b₁u+α₁si $g o 1$ (x₁-z₁)+β₁si $g θ 1$ (x₁-z₁) $z · 2$ =α₂si $g o 2$ (x₁-z₁)+β₂si $g θ 2$ (x₁-z₁)+γsign(x₁-z₁)	z_i(0)=0,i=1,2,α₁=3,β₁=15 α₂=1.5,β₂=7.5,o₁=0.9,θ₁=1.01 o₂=2o₁-1,θ₂=2θ₁-1,γ=50
AFxTSMDO	$z ˜$ =z-x, $z ·$ =-f₁-b₁u-κ(sig^p( $z ˜$ )+sig^q( $z ˜$ ))+v_d σ= $z ˜ ·$ +κ(sig^p( $z ˜$ )+sig^q( $z ˜$ )) $v · d$ =-κ(sig^p(σ)+sig^q(σ))-K(t)sgn(σ) $K ·$ (t)= $K ¯ σ \|, \| σ \| > ε 0, 其他$	z(0)=0,v_d(0)=0,κ=2,p=0.5 q=1.5,K(t)=0, $K ¯$ =10,ε=0.1

Fig.4 State estimationand tracking error bound for Case 1

Fig.5 Disturbance estimation and tracking error bound for Case 1

Fig.6 Adaptive gain for Case 1

Fig.7 State estimationand tracking error bound for Case 2

Fig.8 Disturbance estimation and tracking error bound for Case 2

Fig.9 Adaptive gain K(t) for Case 2

Table 2 Aerodynamic parameters of spinning projectile

参数	取值	参数	取值
b_L	1.1240	a_G	0.0791
b_M	7.667×10^-4	v/(m·s^-1)	1200
a_L	140.6137	k_s	10
a_M	-7.1831	μ_s	0.5
a_ω	2.4018	T_s/s	0.016
a_δ	-11.6520	τ/s	0.015

Fig.10 Scheme of dual-channel controlled PI acceleration autopilot

Fig.11 Tracking result of acceleration

Fig.12 Accelerations tracking error

Fig.13 Tracking result of accelerations

Fig.14 Actuator deflection commands

Fig.15 Disturbance estimation of acceleration loop

Fig.16 Disturbance estimation of attitude loop

Fig.17 Weights updating of the NN of acceleration loop

Fig.18 Weights updating of the NN of attitude loop

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