Small tracking error correction for moving targets of intelligent electro-optical detection systems

doi:10.1007/s11465-024-0782-6

Frontiers of Mechanical Engineering

2024, Vol. 19

Issue (2): 11 https://doi.org/10.1007/s11465-024-0782-6

本期目录

Small tracking error correction for moving targets of intelligent electro-optical detection systems

Cheng SHEN, Zhijie WEN(

), Wenliang ZHU, Dapeng FAN, Mingyuan LING

College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

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Abstract：

Small tracking error correction for electro-optical systems is essential to improve the tracking precision of future mechanical and defense technology. Aerial threats, such as “low, slow, and small (LSS)” moving targets, pose increasing challenges to society. The core goal of this work is to address the issues, such as small tracking error correction and aiming control, of electro-optical detection systems by using mechatronics drive modeling, composite velocity–image stability control, and improved interpolation filter design. A tracking controller delay prediction method for moving targets is proposed based on the Euler transformation model of a two-axis, two-gimbal cantilever beam coaxial configuration. Small tracking error formation is analyzed in detail to reveal the scientific mechanism of composite control between the tracking controller’s feedback and the motor’s velocity–stability loop. An improved segmental interpolation filtering algorithm is established by combining line of sight (LOS) position correction and multivariable typical tracking fault diagnosis. Then, a platform with 2 degrees of freedom is used to test the system. An LSS moving target shooting object with a tracking distance of S = 100 m, target board area of A = 1 m², and target linear velocity of v = 5 m/s is simulated. Results show that the optimal method’s distribution probability of the tracking error in a circle with a radius of 1 mrad is 66.7%, and that of the traditional method is 41.6%. Compared with the LOS shooting accuracy of the traditional method, the LOS shooting accuracy of the optimized method is improved by 37.6%.

Key words： electro-optical detection system small tracking error moving target visual servo aiming control

收稿日期: 2023-09-10 出版日期: 2024-05-30

Corresponding Author(s): Zhijie WEN

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2024, 19(2): 11.
Cheng SHEN, Zhijie WEN, Wenliang ZHU, Dapeng FAN, Mingyuan LING. Small tracking error correction for moving targets of intelligent electro-optical detection systems. Front. Mech. Eng., 2024, 19(2): 11.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-024-0782-6
https://academic.hep.com.cn/fme/CN/Y2024/V19/I2/11

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Tab.1

Parameter	Value
Velocity-loop proportional coefficient k_P	0.700
Velocity-loop integration coefficient k_I	0.045
Velocity-loop differential coefficient k_D	0
Position-loop proportional coefficient $k p a$	19.500
Position-loop integration coefficient $k i a$	0
Unit step signal starting time t	0.050 s
Unit step signal duration T₁	0.500 s
Sinusoidal response signal frequency f	1 Hz
Sinusoidal response signal amplitude	2°
Sinusoidal response signal duration T₂	3 s

Tab.2

Fig.11

Tab.3

Fig.12

Tab.4

Fig.13

Parameter	Value
EODS resolution	1280 × 720
EODS FOV angle	3.6125° × 2.034°
Target manipulator angular velocity ω	−30 °/s to 30 °/s
Target manipulator rod length $L o$	1.6 m
Target manipulator deceleration ratio $K k$	30
Tracking distance S	100 m

Tab.5

Fig.14

Fig.15

Abbreviations
BLDC	Brushless direct-current motor
DOF	Degree of freedom
EODS	Electro-optical detection system
FOV	Field of view
LOS	Line of sight
LSS	Low, slow, and small
MD	Miss distance
PID	Proportional–integral–differential
Variables
A	Target board area
B	Viscous friction coefficient of the motor
E	Counter-electromotive force
E_a	Material elastic modulus
e	Counter-electromotive force
e_a, e_b, e_c	Counter-electromotive force of each phase winding
F	Constant force
f	Sinusoidal response signal frequency
G (t)	Intermediate function
$G q s (s)$	Current-loop delay
$G f e (s)$	Delay compensator
$G k a (s)$	Position-loop delay
G_Lag (s)	Improved Lagrange interpolation compensator
G_o (z)	Compensate function
G_oc (s), G_cc (s)	Transfer functions of the open and closed loops
G_op (s)	Open-loop transfer function of the position-loop
$G op e (s)$	Open-loop transfer function of the current-loop
$G PI a (s)$	Position-loop controller
G_ov (s)	Open-loop transfer function of the velocity-loop
$G PI b (s)$	Velocity-loop controller
$G PI e (s)$	Current-loop controller
G_pr (s)	Closed-loop transfer function of the position-loop
G_s (s)	Transfer function
$G s b (s)$	Velocity-loop delay
$G s e (s)$	Current-loop controlled object
G_Track	Image tracker
G_T (s)	Electromagnetic torque
$G ZOH a (s)$	Zero-order hold
G_θ (s)	Controller of the position loop
G_ω (s), G_FF (s), G_I (s)	Controllers of the velocity loop
I	Material cross-sectional moment of inertia
I (s)	Current function
i_a, i_b, i_c	Current of each phase winding
i_d, i_q	Current of the d–q axis
i_f	Current
J	Moment of inertia
K	Free quantity
K_e	Coefficient of counter-electromotive force
K_k	Target manipulator deceleration ratio
K_o, K_δ, K_w	Conversion coefficient
K_N	Coefficient of pulse conversion
K_V, K_I, K_ω, K_θ	Coefficients of visual servo
k_P, k_I, k_D	Coefficients of the velocity-loop controller
k_p, k_i, k_d	Coefficients of the current-loop controller
$k p a, k i a, k q a$	Coefficients of the position-loop controller
L	Stator inductance
L (x)	Interpolation function
L_d, L_q	Inductance of the d–q axis
L_n (x)	Lagrange interpolation polynomial
L_o	Target manipulator rod length
l	Length of the beam
l_i	Length of the ith structure
L_k (x)	Interpolation basis function
M	Coil mutual inductance of each phase winding
M (x)	The function of bending moment
M_a	Bending moment
M × N	Resolution
{m_n, m_n+1, ..., m_n+4}	Dataset of miss distance
N	Interpolation step size
n	Stepper motor speed
n₀	Speed output of the decelerator
O_A	Line of sight line
O_B	Fire line
O_a, O_b	Reference axis of the calibration tool
P	The stress on the beam
P_n	Number of motor poles
q	Uniformly distributed load
R	Stator resistance
s	Differential module
S	Tracking distance
ds	Differential arc of a cantilever beam
T	Sampling time
T₁	Unit step signal duration
T₂	Sinusoidal response signal duration
T_d, T_f, T_k, T_b	Constant of delay time
T_e, T_L	Electromagnetic torque and load torque
T_s	Sampling period of the encoder
t	Unit step signal starting time
U (s)	Voltage function
u	Voltage
u_a, u_b, u_c	Voltage of each phase winding
u_d, u_q	Voltage of the d–q axis
v	Linear velocity
w	Deflection curve
w_max	Maximum deflection
X (t)	Sampling value
x	Displacement
x₀, x₁, ..., x_n	Independent variables
Y	Feedback coordinate
y₀, y₁, ..., y_n	Function values
y_a1	Section deflection
y_α1, y_α2, y_α3, y_α4	Deflection distance
y_β1, y_β2, y_β3, y_β4	Total deflection distance
z	A variable after the difference transformation
α	Adjustment coefficient
β1, β2	Orthogonal decomposition distances
ψ	Total flux of each phase winding
ψ_a, ψ_b, ψ_c	Flux linkage of each phase winding
ψ_f	Magnetic linkage of the permanent magnet
ψ_m	Rotor permanent magnet flux
$ψ s e j θ s$	Flux components of each phase winding
θ	Offset angle
θ^*	Output control instruction
θ_α1(l − x)	Offset angle of section A
θ_e	Relative angle
θ_max	Maximum offset angle
ρ	Curvature radius
δ1, δ3	Calibration deviation
δ2	Vertical distance
δ_max	Calibration error
\|δ\|, δ_x, δ_y	Shooting accuracy judgment threshold
\|δ\|	Tracking error
ε	Stability coefficient of the closed loop
τ_I	Integral time constant of the velocity loop
τ_i	Integral time constant of the current loop
ω	Target manipulator angular velocity
ω_e	Electrical angular velocity
ω_r	Angular velocity
(x, y)	Target pixel coordinate
(Δx, Δy)	Pixel distance
(θ_M, θ_N)	Angle of the lens
(θ_x, θ_y)	Miss distance
(α, β)	Output pulse of the motor
$(w / 2, h / 2)$	Center of the lens

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