间歇蒸煮过程的降阶模型与蒸煮终点卡伯值预测控制研究

刘守元; 魏代兴; 刘聪汉; 宋晓轩; 辛丽平; 江才嘉; 吴永玲; 范锐; 孙荣荣

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Reduced-order Modeling and Predictive Control of Kappa Number at Cooking Endpoint in Batch Digestion Processes

Received:January 14, 2025 Revised:March 24, 2025

DOI：10.11981/j.issn.1000-6842.2025.02.164

Key Words:batch cooking process;Kappa number;extended Purdue model;model order reduction;model-predictive control

Fund Project:山东省自然科学基金（ZR2021MF076、ZR2016FB04）；山东省重点研发项目（2018GHY115025）；中国博士后面上项目（2018M642611）；国家自然科学基金（201606141、62303258）。

Author Name	Affiliation	Postcode
LIU Shouyuan^*	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
WEI Daixing	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
LIU Conghan	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
SONG Xiaoxuan	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
XIN Liping^*	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
JIANG Caijia	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
WU Yongling	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
FAN Rui	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500
SUN Rongrong	School of Information and Control Engineering， Qingdao University of Technology， Qingdao， Shandong Province， 266500	266500

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Abstract:

This study proposed a model predictive control （MPC） algorithm based on subspace identification. By extending the Purdue model， it simulated and modeled the changes in component concentrations of the solid phase， free liquid phase， and retained liquid phase during the batch cooking process. The numerical algorithm （N4SID） for subspace system identification was used to reduce the order of the nonlinear batch cooking process’s kinetic model， establishing a low-dimensional reduced-order state space model. A Lombard observer was introduced to perform online estimation of the state variables. Combined with the MPC strategy， precise control of the intermittent cooking process was achieved. MATLAB simulation results showed that under the developed MPC algorithm， the system could suppress fluctuations in the cooking process’s Kappa number， ensuring that the pulp Kappa number at the end of cooking reached the preset value with an error of ≤2%. The established fourth-order state-space model of the intermittent cooking process and the extended Purdue model achieved a fitting degree of 99.80%， demonstrating good agreement with the actual system and effectively reducing the computational complexity of the predictive control algorithm.

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