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반발력 보상 기구 적용 선형 모터 이송 장치의 입력 성형 기법

황강조1, 정재성2, 안형준3,#

Input-Shaping Methods for a Linear Motor Motion Stage with a Passive RFC(Reaction Force Compensation) Mechanism

Kang Jo Hwang1, Jae Seong Jeong2, Hyeong-Joon Ahn3,#
Journal of the Korean Society for Precision Engineering 2017;34(12):897-902.
Published online: December 1, 2017

1 숭실대학교 대학원 기계공학과

2 숭실대학교 대학원 융합소프트웨어학과

3 숭실대학교 기계공학부

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#E-mail: ahj123@ssu.ac.kr, TEL: +82-2-820-0654
• Received: April 16, 2017   • Revised: October 18, 2017   • Accepted: October 23, 2017

Copyright © The Korean Society for Precision Engineering

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  • The residual vibration during the high acceleration and deceleration of a motion stage degrades the manufacturing-system productivity and lifespan. Although a passive RFC mechanism with a movable magnet track reduces the residual vibration of the system base, a magnet track resonance may occur according to the motion profile, and the mover in-position error increases due to the residual vibration of the magnet track. We investigated input-shaping methods for a linear motor motion stage with a passive RFC mechanism. An air-bearing linear motor motion stage with the passive RFC mechanism is built, and the dynamic characteristic of the passive RFC mechanism is identified using a free-vibration test. Then, mover velocity profiles are generated using various input-shaping methods. Further, the effects of the input-shaping methods on the air-bearing linear motor motion stage are investigated by comparing the magnet track oscillation, settling time, and mover in-position error. Finally, several input-shaping methods are applied to reduce the mover rise-time delay for the proposed linear motor motion stage. A properly shaped input motion profile removes the residual vibration of the passive RFC mechanism without any additional devices, as well as reducing the transmitted reaction force and the in-position error.
  • KEYWORDS: Linear motor motion stage, Residual vibration, Reaction force compensation, Input-shaping method
  • KEYWORDS: 선형 모터 모션 스테이지, 잔류 진동, 반발력 보상, 입력 성형 기법

Ft

Thrust force of mover

Ftran

Transmitted force

mMT

Mover mass

xMT

Displacement of magnet track

kMT

Stiffness of spring

cMT

Damping of magnet track

x˙MT

Velocity of magnet track

x¨MT

Acceleration of magnet track
Moving mass and working area increases associated with enlarged size such as display panel and semiconductor industries require fast response and high precision of a motion stage. In particular, semi-conductor lithography systems require both extreme precision and high speed in very long stroke such as 1 nanometer accuracy and 230 wafers/hour over 2 m stroke.1,2
Residual vibration of the system base due to high speed motion has a negative effect on production quality, manufacturing process time and life of the manufacturing equipment. Rapid acceleration or deceleration motion of a stage induces large reaction force and causes the system base to oscillate either with unacceptable amplitude or in long settling time.3
Base vibration of a linear motor motion stage has been reduced with a passive reaction force compensation (RFC) mechanism.4,5 Although the passive RFC mechanism is compact and cost-effective without any additional external structures or actuator, the passive RFC does not allow in-situ modification of the dynamic characteristic and may have resonance when a motion profile excites natural frequency of the RFC mechanism.4 An active RFC mechanism using an additional coil can tune its stiffness of the magnet track, and minimize the transmitted force under motion profile variations.6 However, the active RFC mechanism results in increasing energy and cost requirements due to extra servo amplifier and motion controller.7 In addition, an eddy-current damper is used to dissipate the residual vibration of the magnet track as an alternative way.8,9
Input-shaping method is widely used to reduce mechanical vibration of a motion control system since it generates a command that cancels its own vibration and does not need an additional sensor for feedback control.10,11 Since the input-shaping method is implemented by convolving a sequence of impulse so that rise time of the motion is delayed proportional to the natural frequency of the vibration. Input-shaping method may resolve residual vibration of the passive RFC mechanism without any additional devices.
This paper presents input-shaping methods for a linear motor motion stage with a passive RFC mechanism. First, an air-bearing linear motor motion stage with the passive RFC mechanism is built for experimental verification and dynamic characteristic of the passive RFC mechanism is identified with free vibration test. Then, velocity profiles of the mover are generated with various input-shaping methods. In addition, we investigate effects of input-shaping methods on the linear motor motion stage with the passive RFC mechanism by comparing the magnet track oscillation, settling time and in-position error of the mover. Finally, special input-shaping methods to reduce the rise time delay of the mover are investigated for the linear motor motion stage with the passive RFC.
Fig. 1 shows the schematics of the passive RFC mechanism. When the mover moves due to thrust force (Ft), its reaction force makes the magnet track with dummy mass (mMT) oscillate and create displacement (xMT) since the magnet track is supported by spring (kMT) and damper (cMT).4,5 The equation of motion of the passive RFC mechanism is given by Eq. (1).
(1)
mMTx¨MT+cMTx˙MT+kMTxMT=Ft
Fig. 1

The passive RFC for a linear motion stage

KSPE_2017_v34n12_897_f001.jpg
The transmitted force to the system base through spring and damping is expressed with Eq. (2). The reaction force (Ft) is divided into the inertial force of the magnet track and the force of the spring and the damper transmitted to the system base. The magnet track displacement and the transmitted force can be adjusted by changing the dummy mass and the spring stiffness.
(2)
Ftran=cMTx˙MT+kMTxMT
The passive RFC mechanism may have residual oscillation of the magnet track after a mover motion so that mover jitter may increase, as shown in Fig. 2. Although the magnet track oscillation reduces transmitted force to the system base (Ft → Ftran), the motion jitter after motion may become large when the motion profile excites natural frequency of the magnet track.
Fig. 2

Mover jitter increase due to magnet track oscillation

KSPE_2017_v34n12_897_f002.jpg
3.1 Constitution and Specifications
An air-bearing linear motor motion stage with the passive RFC mechanism is built, as shown in Fig. 3. The specifications of the stage are summarized in Table 1. The stage has in-position error within ± 0.4 μm, straightness with 4.3 μm and flatness within 1.7 μm.
Fig. 3

An air-bearing linear motor motion stage with the passive RFC

KSPE_2017_v34n12_897_f003.jpg
Table 1

Specifications of an air-bearing linear motor motion stage

Table 1
Items Unit Value
Stroke mm 580
Force (Continuous/Peak) N 208/832
Resolution μm 1
Max. speed m/s 5
Max. acc m/s2 50
3.2 System Identification of the Passive RFC Mechanism
Since dynamic characteristic of the passive RFC mechanism is necessary to apply an input-shaping method, modal parameters of the passive RFC mechanism are identified with free vibration test of Fig. 4 and summarized in Table 2.
Fig. 4

System identification of modal parameters of the passive RFC mechanism

KSPE_2017_v34n12_897_f004.jpg
Table 2

Model parameters of the passive RFC mechanism

Table 2
Parameters Unit Value
Mass of magnet track kg 51.67
Stiffness N/m 3820
Damping Ns/m 45
Damped natural frequency Hz 1.37
4.1 ZV and ZVD Methods
Input motion profiles with ZV (zero-velocity) and ZVD (zero-velocity derivative) methods10 are compared with the original motion profile and shown in Fig. 5. The original motion profile has max. 400 mm/s velocity and 450 mm stroke to intentionally excite large residual vibration of the magnet track (or to excite the resonance of the passive RFC).4
Fig. 5

Original and shaped input motion profiles

KSPE_2017_v34n12_897_f005.jpg
Magnet oscillation and the mover in-position errors for three motions profiles are shown in Fig. 6. As shown in Fig. 6(a), magnet track oscillations for the shaped inputs disappear after motion while the original motion profile generates large residual oscillation of the magnet track. In addition, mover in-position errors can be reduced significantly with the shaped motion profiles, as shown in Figs. 6(b) and 6(c). Magnet track oscillations and mover in-position errors are quantitatively summarized during and after motion, as shown in Table 3. Magnet track oscillation and mover in-position errors are reduced even during the motion. In addition, the transmitted force is reduced considerably with the shaped input motion profiles because the transmitted force is proportional to the magnet track oscillation. Fig. 7 show the transmitted force for three motion profiles. The transmitted forces are significantly reduced with the input-shaping methods since the magnet track oscillations decreases.
Fig. 6

Magnet trach oscillations and mover in-position errors for original and shaped input motion profiles

KSPE_2017_v34n12_897_f006.jpg
Table 3

Comparisons of ZV and ZVD methods during and after motion

Table 3
ZV ZVD
During motion Magnet track oscillation 46.3 % 67.1 %
In-position error 3.78 % 29.39 %
After motion Magnet track oscillation 89.9 % 91.4 %
In-position error 94.3 % 93.9 %
Fig. 7

Transmitted force: original and shaped input motion profiles

KSPE_2017_v34n12_897_f007.jpg
4.2 Compensation of Delayed Rise Time of Input-Shaping
Two special input-shaping methods: 5f virtual mode input shaper (5f VMIS)12 and max. speed-up input shaper (MSIS)13 to compensate the delayed rise time of the mover are compared with the original and ZV motion profiles in Fig. 8. ZVD has longer rise time delay than ZV and is not included in comparison. In addition, magnet track oscillations of two motion profiles are compared with those of the original and ZV motion profiles in Fig. 9. Although the magnet track oscillation is larger than ZV input shaper during motions, magnet track oscillations almost disappear after motions. MSIS shows better performance than 5f VMIS in terms of magnet track oscillations.
Fig. 8

Two special shaped motion profiles to compensate delayed rise time

KSPE_2017_v34n12_897_f008.jpg
Fig. 9

Magnet track oscillations of two special shaped motion profiles

KSPE_2017_v34n12_897_f009.jpg
Mover in-position errors of two motion profiles are compared with those of the original and ZV motion profiles in Fig. 10. In addition magnet track oscillations and mover in-position errors of two input-shaping methods are quantitatively summarized during and after motion, as shown in Table 4. Mover following error of MSIS is smaller than ZV and 5f VMIS both during and after motions. In particular, MSIS shows much better performance than ZV and 5f VMIS in terms of in-position errors.
Fig. 10

Mover in-position errors of two special shaped motion profiles

KSPE_2017_v34n12_897_f010.jpg
Table 4

Comparisons of ZV, 5f VMIS and MSIS methods during and after motion

Table 4
ZV 5fVMIS MSIS
During motion Magnet track oscillation 46.3 % 16.8 % 67.1 %
In-position error 3.78 % 3.0 % 29.39 %
After motion Magnet track oscillation 89.9 % 92.2 % 91.4 %
In-position error 94.3 % 91.2 % 93.9 %
This paper presents input-shaping methods for a linear motor motion stage with a passive RFC mechanism. We built an air-bearing linear motor motion stage with the passive RFC mechanism and investigated effect of input-shaping methods on the linear motor motion stage with passive RFC mechanism by comparing the magnet oscillation and in-position error of the mover. In addition, special input-shaping methods to reduce the rise time delay of the mover are investigated for the linear motor motion stage with the passive RFC. Properly shaped input motion profile such as ZVD or MSIS not only removes residual vibration of the passive RFC mechanism without any additional devices but also reduce transmitted reaction force and in-position error.
This work was by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2013R1A1A2010764).
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Input-Shaping Methods for a Linear Motor Motion Stage with a Passive RFC(Reaction Force Compensation) Mechanism
J. Korean Soc. Precis. Eng.. 2017;34(12):897-902.   Published online December 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.12.897
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Input-Shaping Methods for a Linear Motor Motion Stage with a Passive RFC(Reaction Force Compensation) Mechanism
J. Korean Soc. Precis. Eng.. 2017;34(12):897-902.   Published online December 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.12.897
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Input-Shaping Methods for a Linear Motor Motion Stage with a Passive RFC(Reaction Force Compensation) Mechanism
Image Image Image Image Image Image Image Image Image Image
Fig. 1 The passive RFC for a linear motion stage
Fig. 2 Mover jitter increase due to magnet track oscillation
Fig. 3 An air-bearing linear motor motion stage with the passive RFC
Fig. 4 System identification of modal parameters of the passive RFC mechanism
Fig. 5 Original and shaped input motion profiles
Fig. 6 Magnet trach oscillations and mover in-position errors for original and shaped input motion profiles
Fig. 7 Transmitted force: original and shaped input motion profiles
Fig. 8 Two special shaped motion profiles to compensate delayed rise time
Fig. 9 Magnet track oscillations of two special shaped motion profiles
Fig. 10 Mover in-position errors of two special shaped motion profiles

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Input-Shaping Methods for a Linear Motor Motion Stage with a Passive RFC(Reaction Force Compensation) Mechanism

Specifications of an air-bearing linear motor motion stage

Items Unit Value
Stroke mm 580
Force (Continuous/Peak) N 208/832
Resolution μm 1
Max. speed m/s 5
Max. acc m/s2 50

Model parameters of the passive RFC mechanism

Parameters Unit Value
Mass of magnet track kg 51.67
Stiffness N/m 3820
Damping Ns/m 45
Damped natural frequency Hz 1.37

Comparisons of ZV and ZVD methods during and after motion

ZV ZVD
During motion Magnet track oscillation 46.3 % 67.1 %
In-position error 3.78 % 29.39 %
After motion Magnet track oscillation 89.9 % 91.4 %
In-position error 94.3 % 93.9 %

Comparisons of ZV, 5f VMIS and MSIS methods during and after motion

ZV 5fVMIS MSIS
During motion Magnet track oscillation 46.3 % 16.8 % 67.1 %
In-position error 3.78 % 3.0 % 29.39 %
After motion Magnet track oscillation 89.9 % 92.2 % 91.4 %
In-position error 94.3 % 91.2 % 93.9 %
Table 1 Specifications of an air-bearing linear motor motion stage
Table 2 Model parameters of the passive RFC mechanism
Table 3 Comparisons of ZV and ZVD methods during and after motion
Table 4 Comparisons of ZV, 5f VMIS and MSIS methods during and after motion

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Table 2

Table 3

Table 4

JKSPE : Journal of the Korean Society for Precision Engineering

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