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선형 모터 모션 스테이지의 맞춤형 전류 제어

Customized Current Control of a Linear Motor Motion Stage

Journal of the Korean Society for Precision Engineering 2024;41(11):875-880.
Published online: November 1, 2024

1 숭실대학교 대학원 기계공학과

2 숭실대학교 기계공학부

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#E-mail: ahj123@ssu.ac.kr
• Received: July 16, 2024   • Revised: August 21, 2024   • Accepted: September 2, 2024

Copyright © The Korean Society for Precision Engineering

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • In the 4th Industrial Revolution, advancements in semiconductor technology demand high performance, efficiency, and precision, highlighting the importance of high-speed and ultra-precise motion stages. To improve positioning performance of a motion stage, robust torque generation by current controllers alongside position control is crucial. This paper explored a custom current control for linear motor motion stages. We built a linear motor motion stage with a 560 mm stroke, 5 m/s speed, and 280 N continuous thrust supported by air bearings and equipped with a passive reaction force compensation. Custom user code for position and current controls of PowerPMAC motion controller was developed for the motion stage. The position control code included frequency domain system identification, disturbance observer, and repetitive learning control while the current control code featured vector or d/q-axis current controllers and disturbance observer. We developed a current control tuning GUI to adjust the current control gain by injecting an excitation signal into the motion controller and measuring the frequency response of the open-loop transfer function. Experimental results confirmed the effectiveness of the custom current controller for evaluating static and dynamic performance.

Ci

Current Controller

Cm

Motion Controller

d

Disturbance

d^

Estimated Disturbance

IAct

Actual Current

Ia, Ib, Ic

a,b, and c-Phase Currents

Id, Iq

d and q-axis Currents

IdCmd, IqCmd

d and q-axis Current Commands

Ki

Current Integral Gain

Kpb, Kpf

Current Back and Forward-path Proportional Gains

Ln

Nominal Inductance of Motor

Rn

Nominal Resistance of Motor

s

Continuous Time Domain Variable

Ua, Ub, Uc

a,b, and c-Phase Input Voltages

Ud, Uq

d and q-axis Input Voltages

U *

d and q-axis Input Voltages

z

Discrete Time Domain Variable

ωD

Cutoff Frequency of Current DOB

θp

Phase Angle
21세기 4차 산업혁명 시대에 AI 기술이 발전하면서 반도체 회로의 집적도가 높아지고 수요가 폭발적으로 증가함에 따라 고성능, 고효율, 초정밀 반도체 생산 공정이 요구되고 있다[1]. 예를 들어, 반도체 노광 장비는 고속으로 이동하며 시간당 230장의 웨이퍼를 나노미터 단위의 정밀도로 처리해야 한다[2].
고속 고정밀 반도체 생산 공정 장비의 핵심 요소로서 고성능 모션 스테이지의 중요성이 부각되고 있다. 스테이지의 모션 성능 향상을 위해서는 위치 제어기뿐 아니라 정밀한 추력 생성을 위한 전류 제어기도 중요하다[3]. 간단한 구조로 외란을 추정하고 보상하는 외란 관측기(DOB)를 전류 제어에 적용하여 모델의 불확실성과 역기전력을 보상할 수 있다[4-6]. 하지만 스테이지 최종 성능 향상을 위해서 시스템 주파수 응답을 고려한 체계적인 전류 제어기 설계가 필요하다[7-9].
수동 반발력 보상(Reaction Force Compensation, RFC) 선형 모터 모션 스테이지는 자석 트랙 관성 에너지로 이동자 반발력을 소산하지만 모션 종료 후 자석 트랙 잔류 진동으로 이동자의 정착 시간과 미세 지터(Zitter) 증가 등의 성능 저하가 발생할 수 있다[10]. 모델 기반 외란 관측기를 모션 제어에 적용하여 반발력 보상 스테이지 성능 저하를 줄일 수 있다[11-12].
이 논문에서는 선형 모터 모션 스테이지의 위치 결정 성능 향상을 위한 맞춤형 전류 제어를 연구하였다. 먼저 에어 베어링으로 지지되고 수동 반력 보상 기능을 갖춘 560 mm 스트로크, 5 m/s 속도, 280 N 추력의 선형 모터 모션 스테이지를 구축하였다. Power PMAC 모션 제어기의 맞춤형 전류 제어 유저 코드를 개발하고 이를 선형 모터 모션 스테이지에 적용하였다. 맞춤형 전류 제어에는 d/q축 전류 제어기와 전류 외란 관측기가 포함된다. 모션 제어기에 가진 신호를 주입하고 전체 시스템 주파수 응답을 측정하고 이를 바탕으로 전류 제어기 이득을 조절할 수 있는 튜닝 GUI를 개발하였다. 전류 제어기 이득 조절 전후 Power PMAC 전류 제어기와 정적 및 동적 성능을 비교하여 그 효과성을 검증하였다.
2.1 시스템 구성
수동 반발력 보상 선형 모션 스테이지 모션 제어 시스템은 Fig. 1과 같이 공심형 선형 모터(Justek JTKL-3638), Direct PWM 드라이버(Servotronix CDHD-006), 상용 모션 제어기(PowerPMAC, ACC-24E3)로 구성되어 있다. 모션 스테이지는 최대 스트로크 560 mm, 최대 속도 5 m/s, 연속 추력 280 N, 추력 계수(Km) 34.7 N/A를 가진다. 1 μm 분해능의 아날로그 사인 엔코더(Renishaw)를 측정에 사용한다.
Fig. 1

Control system of the RFC linear motor motion stage

KSPE_2024_v41n11_875_f001.jpg
2.2 전류 제어 알고리즘
Power PMAC 제어기의 전류 제어 알고리즘은 Fig. 2와 같이 d/q축 PI 제어와 후진 경로 비례 이득(Kpb)을 포함한다. d축 전류 명령(IdCmd)은 0이고, q축 전류 명령(IqCmd)은 위치 제어 추력 명령이다. 각 제어기 출력은 식(1)과 같이 역 Park and Clarke 변환을 거쳐 3상으로 PWM 드라이버에 입력된다. 측정된 실제 3상 전류는 다시 식(2)와 같이 Park and Clarke 변환을 거쳐 d/q축 전류 제어기로 궤환된다. Power PMAC 전류 제어기를 분석해 동일한 구조를 갖는 전류 제어기 유저 코드를 C언어로 작성하여 구현하였다.
Fig. 2

Block diagram of PMAC current controller

KSPE_2024_v41n11_875_f002.jpg
(1)
UaUbUc=sinθpcosθpsinθp+23πcosθp+23πsinθp-23πcosθp-23πUdUq
(2)
IdIq=cosθp+π2cosθp+7π6cosθp-π6sinθp+π2sinθp+7π6sinθp-π6IaIbIc
2.3 전류 제어 실험

2.3.1 주파수 응답 비교

상용 제어기와 유저코드 전류 제어기 성능을 비교하기 위해 위치 제어기 서보 출력단에 1-1 kHz의 다중 주파수 정현파 신호를 주입하고 주파수 응답을 측정하여 Fig. 3에 나타냈다. 상용제어기와 유저 코드 전류 제어기는 동일한 주파수 응답을 가진다. d축 전류 명령과 제어 출력은 거의 0에 가깝기 때문에 전류 명령으로 충분한 가진이 어려워 측정 주파수 응답에 잡음이 포함되어 있다.
Fig. 3

FRF of current controllers

KSPE_2024_v41n11_875_f003.jpg

2.3.2 시간 영역 성능 비교

Fig. 4와 같이 이동 거리 200 mm, 최대 속도 250 mm/s, 최대 가속도 2,500 mm/s²의 모션 프로파일에 대한 d/q축 전류 명령, 실제 전류, 그리고 전류 오차를 Fig. 5에 나타냈다. 그리고 각 제어기 위치 명령 추종오차를 Fig. 6에 나타냈다. 유저 코드로 구현된 전류 제어기 추종 성능이 기존 PowerPMAC 전류 제어기와 동일하였다.
Fig. 4

Motion profiles

KSPE_2024_v41n11_875_f004.jpg
Fig. 5

Current and current errors

KSPE_2024_v41n11_875_f005.jpg
Fig. 6

Position errors

KSPE_2024_v41n11_875_f006.jpg
2.4 전류 외란 관측기(DOB)
반발력 보상 선형 모터 모션 스테이지 고속 운전으로 발생하는 역기전력과 같은 외란을 보상하기 위해 d/q축 전류 제어기에 외란 관측기를 적용하였다. 전류 외란 관측기의 구조는 Fig. 7와 같고 공칭 인덕턴스(Ln), 공칭 저항(Rn), 절점주파수(ωD)를 가지는 1차 Q 필터로 구성된다. 식(3)과 같이 선형 모터 실제 전류(IACT), 전류 제어기 출력(U*) 그리고 1차 Q필터로 외란을 추정하여 보상할 수 있다.
Fig. 7

Block diagram of Current DOB

KSPE_2024_v41n11_875_f007.jpg
(3)
d^=ωDs+ωDU*+LnωDIAct+RnIAct-LnωDIAct=ωDs+ωDU*+-ss+ωDLnωDIAct-ωDs+ωDRnIAct=ωDs+ωDU*-ωDs+ωDIActLns+Rn=ωDs+ωDU*-ωDs+ωDU*-dLns-RnLns+Rn=ωDs+ωDd
3.1 주파수 응답 측정
Fig. 8과 같이 1-1 kHz 다중 정현파 신호를 주입하여 전기 시스템(Pi)과 기계 시스템(Pm)을 포함한 선형 모터 모션 스테이지(P), 위치 제어(Cm) 그리고 전류 제어(Ci)로 구성된 전체 시스템 주파수 응답을 측정하였다. 가진 신호 주입 전후의 위치 제어기 출력을 이용하여 개루프 주파수 응답을 측정하였다.
Fig. 8

Schematic of frequency response measurement

KSPE_2024_v41n11_875_f008.jpg
3.2 주파수 응답 기반 전류 제어기 설계
전류 제어가 포함된 모션 제어 시스템의 안정성과 성능을 예측하고 평가하기 위해 Fig. 9와 같은 주파수 응답 기반 전류 제어 튜닝 GUI를 개발하였다. 기존 전류 제어 이득, 외란 관측기가 포함된 전류 제어기 전달함수 식(4)와 3.1에서 측정한 개루프 전달함수 주파수 응답을 이용해 제어 이득 변화에 따른 개루프 전달함수, 폐루프 민감도 함수, 대역폭, 이득 및 위상 여유변화를 예측할 수 있다. 특히, Fig. 9 오른쪽 폐루프 민감도 함수에서 기계 모드에 의한 최댓값이 크기 때문에 전체 주파수 응답을 고려한 제어 이득 조절이 필요하다. Table 1에 튜닝 전후의 전류 제어기 이득을 표시하였다.
Fig. 9

Frequency response based Current control tuning GUI

KSPE_2024_v41n11_875_f009.jpg
Table 1

Current controller tuning

Table 1
Gains Before After Gains Before After
Kpf 0.566 0 Kpb 0 2.4
Ki 0.037 0.4 ωD 0 150
(4)
Cis=Kpf+Kisss+ωD+PisLns+RnωDs+ωD+Kpb
4.1 주파수 영역 전류 제어기 설계 결과
전류 제어 이득 조절 전후 이론 및 실험 개루프 전달 함수 주파수 응답을 Fig. 10에 나타냈다. 이득 조절 후 대역폭과 이득 및 위상 여유 변화를 각각 Figs. 10(a)10(b)에 나타냈다. 전류제어 튜닝 GUI 예측 정확도는 Table 2와 같이 대역폭이 99.87%, 위상 여유가 97.22%, 이득 여유가 98.92%이다.
Fig. 10

FRF of the open-loop transfer function

KSPE_2024_v41n11_875_f010.jpg
Table 2

Accuracy of the current control tuning GUI

Table 2
Performance Theory Experiment Accuracy
Bandwidth 62.26 Hz 62.18 Hz 99.87%
Phase margin 29.74º 30.59º 97.22%
Gain margin 6.03 dB 6.09 dB 98.92%
4.2 시간 영역 성능 평가

4.2.1 모션 스테이지 위치 결정 성능 평가

Fig. 4의 모션 프로파일을 사용하여 전류 제어 이득 조절 전후 모션 스테이지 위치 결정 성능, 즉, 추종 오차와 지터를 Fig. 11에 나타냈다. 동일한 위치 제어 이득에서 전류 제어 이득 조절만으로 지터의 평균 제곱근 오차가 12.19% 감소했다. 0.2 mm 저주파 지터는 반발력 보상 선형 모터 모션 스테이지의 자석 트랙 잔류 진동으로 발생하며 위치 제어 외란 관측기로 지터 크기가 크게 감소했지만 추가 보상을 위한 연구가 진행 중이다[11-12].
Fig. 11

Following errors

KSPE_2024_v41n11_875_f011.jpg
4.3 외란 제거 성능 평가
전류 외란 관측기의 외란 제거 성능을 평가하기 위해 크기 4 V 계단 외란을 d/q축 제어기 출력단에 입력하였다. 외란을 입력한 추종 오차를 Fig. 12(a)에, 입력한 외란과 추정 외란을 Fig. 12(b)에 나타내었다. 외란 관측기 적용후 전압 외란에 의한 추종 오차가 82.41% 감소했다.
Fig. 12

Current DOB experiment

KSPE_2024_v41n11_875_f012.jpg
이 연구에서는 반발력 보상 선형 모터 모션 스테이지의 위치 결정 성능을 향상시키기 위해 맞춤형 전류 제어 방법을 개발하고 이를 실험적으로 검증하였다. 먼저 상용 Power PMAC 모션 제어기의 전류 제어기와 동일한 구조를 갖는 유저 코드를 개발했다. 전류 외란 관측기가 포함된 전류 제어기 주파수 영역 설계를 위해 개루프 전달함수의 주파수 응답을 측정하여 전류 제어기 이득을 조절할 수 있는 전류 제어 튜닝 GUI를 개발하였다. 전류 제어 튜닝 GUI는 전류 제어 이득 조절 전후 대역폭을 99.87%, 위상 여유를 97.22%, 이득 여유를 98.92%의 정확도로 예측하였다. 주파수 영역 기반 전류 제어기 이득 조절 후 지터의 평균 제곱근 오차가 12.19% 감소했다. 전류 제어기 출력단 4 V계단 외란의 제거 성능을 비교한 결과 외란에 의한 추종 오차가 82.41% 감소하여 맞춤형 전류 제어기의 효과를 실험적으로 검증했다.
이 연구는 산업통상자원부(한국산업기술평가관리원) 산업기술혁신사업(2021년도 소재부품기술개발사업)의 지원으로 수행되었음(20017202).
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Kyung Ho Yang
KSPE_2024_v41n11_875_bf001.jpg
M.Sc. candidate in the Department of Mechanical Engineering, Soongsil University. His research interest is linear motor control.
Hyeong-Joon Ahn
KSPE_2024_v41n11_875_bf002.jpg
Received B.Sc., M.Sc., Ph.D. degrees from the Department of Mechanical Design & Production Engineering, Seoul National University. His research interest is the area of mechatronics, sensors, actuators, control and precision machine design.

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Customized Current Control of a Linear Motor Motion Stage
J. Korean Soc. Precis. Eng.. 2024;41(11):875-880.   Published online November 1, 2024
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Customized Current Control of a Linear Motor Motion Stage
J. Korean Soc. Precis. Eng.. 2024;41(11):875-880.   Published online November 1, 2024
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Customized Current Control of a Linear Motor Motion Stage
Image Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 Control system of the RFC linear motor motion stage
Fig. 2 Block diagram of PMAC current controller
Fig. 3 FRF of current controllers
Fig. 4 Motion profiles
Fig. 5 Current and current errors
Fig. 6 Position errors
Fig. 7 Block diagram of Current DOB
Fig. 8 Schematic of frequency response measurement
Fig. 9 Frequency response based Current control tuning GUI
Fig. 10 FRF of the open-loop transfer function
Fig. 11 Following errors
Fig. 12 Current DOB experiment
Customized Current Control of a Linear Motor Motion Stage
Gains Before After Gains Before After
Kpf 0.566 0 Kpb 0 2.4
Ki 0.037 0.4 ωD 0 150
Performance Theory Experiment Accuracy
Bandwidth 62.26 Hz 62.18 Hz 99.87%
Phase margin 29.74º 30.59º 97.22%
Gain margin 6.03 dB 6.09 dB 98.92%
Table 1 Current controller tuning
Table 2 Accuracy of the current control tuning GUI