Korean Chemical Engineering Research, Vol.46, No.3, 486-491, June, 2008
상업용 12인치 급속가열장치의 제어계 설계를 위한 모델인식
Model Identification for Control System Design of a Commercial 12-inch Rapid Thermal Processor
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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 ℃ 부근의 정상상태에서 실험을 수행하여 모델을 추정한 결과 상태의 차수는 80~100, 모델출력은 y=T(K)2으로 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 ℃, respectively, it was found that y=T(K)2 and the state dimension of 80-100 are most desirable. With this choice the rootmean-square value of the one-step-ahead temperature prediction error was found to be in the range of 0.125-0.135 K.
Keywords:Identification;High-Order ARX Model;Balanced Realization;Balanced Truncation;Rapid Thermal Processing
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