MISO 고차 ARX 모델 기반의 MIMO 상태공간 모델의 모델인식: 설계와 적용

원왕연; 윤지은; 이광순; 이봉국; Wangyun Won; Jieun Yoon; Kwang Soon Lee; Bongkook Lee

Korean Chemical Engineering Research, Vol.45, No.1, 67-72, February, 2007

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MISO 고차 ARX 모델 기반의 MIMO 상태공간 모델의 모델인식: 설계와 적용

Identification of MIMO State Space Model based on MISO High-order ARX Model:Design and Application

원왕연, 윤지은, 이광순 ^†, 이봉국¹

서강대학교 화공생명공학과, 121-742 서울시 마포구 신수동 1
¹LS산전 연구소, 431-080 경기도 안양시 동안구 호계동

Wangyun Won, Jieun Yoon, Kwang Soon Lee^†, and Bongkook Lee¹

Department of Chemical and Biomolecular Engineering, Sogang University, 1, Shinsoo-dong, Mapo-gu, Seoul 121-742, Korea
¹LS Industrial System Co., Ltd., Hogye-dong, Dongan-gu, Anyang, Gyeonggi 431-080, Korea

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초록

부분 최소자승회귀, 균형 잡힌 realization, 균형 잡힌 truncation을 결합함으로써, MIMO 상태공간 모델의 모델인식을 위한 효과적인 방법이 개발되었다. 개발된 방법에서 MIMO 시스템은 고차 ARX 모델로 표현되는 다중 MISO 시스템으로 분해된다. 이 때, ARX 모델의 파라미터는 부분 최소자승회귀에 의해 추정된다. 그 후, realization을 통해 각각의 MISO ARX 전달함수에 대한 MISO 상태공간 모델이 만들어지며, MIMO 상태공간 모델로 결합된다. 최종적으로, 균형 잡힌 realization과 균형 잡힌 truncation을 통해 최소의 균형 잡힌 MIMO 상태공간 모델이 얻어진다. 제안된 방법은 고압 CO2 용해도 측정 실험 장치의 온도제어를 위한 모델 예측 제어의 설계에 적용되었다.

An efficient method for identification of MIMO state space model has been developed by combining partial least squares (PLS) regression, balanced realization, and balanced truncation. In the developed method, a MIMO system is decomposed into multiple MISO systems each of which is represented by a high-order ARX model and the parameters of the ARX models are estimated by PLS. Then, MISO state space models for respective MISO ARX transfer function are found through realization and combined to a MIMO state space model. Finally, a minimal balanced MIMO state space model is obtained through balanced realization and truncation. The proposed method was applied to the design of model predictive control for temperature control of a high pressure CO2 solubility measurement system.

Keywords:Identification;PLS;Balanced Realization;Balanced Truncation;Model Predictive Control

[References]

Ljung L, System Identification . Theory for the user, 2nd ed., Prentice-Hall, New Jersey, NJ (1999)
Favoreel W, De Moor B, Van Overschee P, J. Process Control, 10(2-3), 149 (2000)
Vanoverschee P, Demoor B, Automatica, 30(1), 75 (1994)
Qin SJ, Comput. Chem. Eng., 30(10-12), 1502 (2006)
Chiuso A, Picci G, J. Econometrics, 118(1), 257 (2004)
Jia C, Rohani S, Jutan A, Chem. Eng. Process., 42(4), 311 (2003)
Lee KS, Eom Y, Chung JW, Choi J, Yang DY, Comput. Chem. Eng., 24(2-7), 309 (2000)
Sima V, Sima DM, Huffle SV, J. Comp. Appl. Math., 170(2), 371 (2004)
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Astrom KJ, Wittenmark B, Computer-controlled systems theory and design, 3rd ed., Prentice-Hall, New Jersey, NJ (1997)
Won W, Lee KS, Lee B, Lee S, Lee S, “Model Predictive Control of Condensate Recycle Process in a Cogeneration Power Station: I. Controller Design and Numerical Application,” Proceedings of SICE-ICASE International Joint Conference 2006, Busan, Korea, 178 (2006)
Zhou K, Doyle JC, Glover K, Robust and Optimal Control, Prentice-Hall, New Jersey, NJ (1996)

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[1] Ljung L, System Identification . Theory for the user, 2nd ed., Prentice-Hall, New Jersey, NJ (1999)

[2] Favoreel W, De Moor B, Van Overschee P, J. Process Control, 10(2-3), 149 (2000)

[3] Vanoverschee P, Demoor B, Automatica, 30(1), 75 (1994)

[4] Qin SJ, Comput. Chem. Eng., 30(10-12), 1502 (2006)

[5] Chiuso A, Picci G, J. Econometrics, 118(1), 257 (2004)

[6] Jia C, Rohani S, Jutan A, Chem. Eng. Process., 42(4), 311 (2003)

[7] Lee KS, Eom Y, Chung JW, Choi J, Yang DY, Comput. Chem. Eng., 24(2-7), 309 (2000)

[8] Sima V, Sima DM, Huffle SV, J. Comp. Appl. Math., 170(2), 371 (2004)

[9] Abdi H, “Partial Least Squares (PLS) Regression,” Enc. Soc. Sci. Res. Meth., Thousand Oaks (CA), TO (2003)

[10] Helmke U, Huper K, Sys. Cont. Lett., 39, 19 (2000)

[11] Chen CT, Linear System Theory and Design, 3rd ed., OXFORD, New York, NY (1999)

[12] Astrom KJ, Wittenmark B, Computer-controlled systems theory and design, 3rd ed., Prentice-Hall, New Jersey, NJ (1997)

[13] Won W, Lee KS, Lee B, Lee S, Lee S, “Model Predictive Control of Condensate Recycle Process in a Cogeneration Power Station: I. Controller Design and Numerical Application,” Proceedings of SICE-ICASE International Joint Conference 2006, Busan, Korea, 178 (2006)

[14] Zhou K, Doyle JC, Glover K, Robust and Optimal Control, Prentice-Hall, New Jersey, NJ (1996)