Researching | Trajectory planning scheme for ultra-precision system

Optics and Precision Engineering, Volume. 31, Issue 17, 2534(2023)

Trajectory planning scheme for ultra-precision system

Ailin LI^1,2 and Jing LI^1,2、*

Author Affiliations

¹Institute of Microelectronics， Chinese Academy of Sciences， Beijing00029， China

²University of Chinese Academy of Sciences， Beijing100049， China

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Figures&Tables (17)

References (20)

Paper Information

Figures & Tables(17)

Fig. 1. Proposed trajectory planning scheme

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Fig. 2. Individual motion cycle of stage

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Fig. 3. Simplified model of stage's control system

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Fig. 4. Typical fourth-order motion trajectory

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Fig. 5. Tuning feedback controller settings using improved differential evolutionary algorithm^［18］

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Fig. 6. Flow chart trajectory planning algorithm^［4，12］

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Fig. 7. Optimization results of Monte-Carlo algorithm with respect to parameters

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Fig. 8. Distribution of 30 times optimization result by Monte-Carlo algorithm

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Fig. 9. Comparison of tuning efficiency

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Fig. 10. Identification results in x direction of stage

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Fig. 11. Comparison of experiment results

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Table 1. Parameters of stage's model
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Table 1. Parameters of stage's model
Parameters Value
$m_{1} / k g$ 5
$m_{2} / k g$ 20
$h / m m$ 20
$τ / s$ $1 \times 10^{- 4}$
$T_{s} / s$ $2 \times 10^{- 4}$
$ω / H z$ 450
$ζ$ 0.03
$J_{y} / (k g \cdot m)$ 0.10
$J_{z} / (k g \cdot m)$ 0.11

Table 2. Parameters of proposed optimization method
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Table 2. Parameters of proposed optimization method
Parameters Value
NP 50
Q
$k_{P} \in [10^{5}, 10^{7}],$
$k_{I} \in [10^{2}, 10^{4}], k_{D} \in [10, 10^{3}]$
F 0.8
CR 0.6
MC 10
N $10^{4}$
$ρ$ 0.3
MAX_FES 20

Table 3. Parameters of controller

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Table 3. Parameters of controller

Controller parameters	Trial-and-error method	Method in section 4.2
$β_{1}$	25	25
$β_{2}$	$2.50 \times 10^{- 3}$	$2.50 \times 10^{- 3}$
$β_{3}$	$4.94 \times 10^{- 6}$	$4.94 \times 10^{- 6}$
$k_{P}$	$1.38 \times 10^{6}$	$6.43 \times 10^{6}$
$k_{I}$	700	$2.22 \times 10^{3}$
$k_{D}$	$5.70 \times 10^{3}$	$9.25 \times 10^{3}$
PID parameter tuning times	725	50

Table 4. Constraints of trajectory dynamics modified using trial-and-error method

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Table 4. Constraints of trajectory dynamics modified using trial-and-error method

Parameter	1st	2nd	3rd
Iterations	1 800	1 020	5 309
$M A / n m$	1.48	2.91	2.91
Time/s	0.325 0	0.358 6	0.358 6
$s_{m a x} / m$	0.000 3	0.000 32	0.000 32
$v_{m a x} / (m \cdot s^{- 1})$	0.001	0.001	0.001
$a_{m a x} / (m \cdot s^{- 2})$	0.4	0.12	0.1
$j_{m a x} / (m \cdot s^{- 3})$	20	5.5	5.2
$d_{m a x} / (m \cdot s^{- 4})$	2 000	555	575

Table 5. Constraints of trajectory dynanics modified using Monte-Carlo method

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Table 5. Constraints of trajectory dynanics modified using Monte-Carlo method

Parameter	1st	2nd	3rd
Iterations	12	26	25
$M A / n m$	0.134	0.134	0.134
$L / μ m$	277	276.4	280.6
Time/s	0.356 0	0.351 2	0.352 8
$s_{m a x} / m$	$3.278 7 \times 10^{- 4}$	$3.275 9 \times 10^{- 4}$	$3.276 7 \times 10^{- 4}$
$v_{m a x} / (m \cdot s^{- 1})$	0.001	0.001	0.001
$a_{m a x} / (m \cdot s^{- 2})$	0.281 9	0.110 1	0.311 6
$j_{m a x} / (m \cdot s^{- 3})$	6.401 8	13.397 7	9.417 2
$d_{m a x} / (m \cdot s^{- 4})$	2 043	2 408	2 224

Table 6. Comparison of experiment results
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Table 6. Comparison of experiment results
方案 $M A / n m$ $M S D / n m$
本文轨迹规划 1.44 1.25
传统工程调试 1.80 1.55

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Ailin LI, Jing LI. Trajectory planning scheme for ultra-precision system[J]. Optics and Precision Engineering, 2023, 31(17): 2534

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Paper Information

Category: Micro/Nano Technology and Fine Mechanics

Received: Jan. 16, 2023

Accepted: --

Published Online: Oct. 9, 2023

The Author Email: LI Jing (lijing2018@ime.ac.cn)

DOI:10.37188/OPE.20233117.2534

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology