Korean Chemical Engineering Research

  • 제46권3호
  • /
  • Pages.486-491
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  • 2008
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  • 0304-128X(pISSN)
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  • 2233-9558(eISSN)
한국화학공학회 (The Korean Institute of Chemical Engineers)
권호 표지

상업용 12인치 급속가열장치의 제어계 설계를 위한 모델인식

Model Identification for Control System Design of a Commercial 12-inch Rapid Thermal Processor

  • Yun, Woohyun (Department of Chemical and Biomolecular Engineering, Sogang University) ;
  • Ji, Sang Hyun (KORNIC Systems Co., Ltd.) ;
  • Na, Byung-Cheol (KORNIC Systems Co., Ltd.) ;
  • Won, Wangyun (Department of Chemical and Biomolecular Engineering, Sogang University) ;
  • Lee, Kwang Soon (Department of Chemical and Biomolecular Engineering, Sogang University)
  • 투고 : 2007.12.15
  • 심사 : 2008.01.24
  • 발행 : 2008.06.30
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초록

상업용 12인치 급속가열장치(RTP)의 다변수 고급제어기를 개발하기 위하여 열전대가 부착된 웨이퍼를 대상으로 다변수 모델인식을 수행하였다. 웨이퍼에는 7개의 열전대가 설치되어 있으며 10개의 텅스텐-할로겐 램프 그룹으로 가열을 할 수 있다. 모델인식 실험과정에서 웨이퍼의 휨을 최소화하며 최종적으로 10-입력 7-출력의 균형 잡힌 상태공간 모델을 얻기 위한 모델인식방법을 제안하였다. 또한 넓은 온도영역에서 복사에 의한 비선형성을 가장 효과적으로 상쇄시킬 수 있는 출력변수 정의방법을 제안하였다. 600, 700, $800^{\circ}C$ 부근의 정상상태에서 실험을 수행하여 모델을 추정한 결과 상태의 차수는 80~100, 모델출력은 $y=T(K)^2$으로 결정하는 것이 바람직하며, 이때 one-step-ahead 온도예측 오차의 제곱평균은 0.125~0.135 K 정도로 나타났다.

This paper describes a model identification method that has been applied to a commercial 12-inch RTP (rapid thermal processing) equipment with an ultimate aim to develop a high-performance advanced controller. Seven thermocouples are attached on the wafer surface and twelve tungsten-halogen lamp groups are used to heat up the wafer. To obtain a MIMO balanced state space model, multiple SIMO (single-input multiple-output) identification with highorder ARX models have been conducted and the resulting models have been combined, transformed and reduced to a MIMO balanced state space model through a balanced truncation technique. The identification experiments were designed to minimize the wafer warpage and an output linearization block has been proposed for compensation of the nonlinearity from the radiation-dominant heat transfer. As a result from the identification at around 600, 700, and $800^{\circ}C$, respectively, it was found that $y=T(K)^2$ and the state dimension of 80-100 are most desirable. With this choice the root-mean-square value of the one-step-ahead temperature prediction error was found to be in the range of 0.125-0.135 K.

키워드

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