This paper presents a novel control framework that integrates Physics-Informed Neural Networks (PINNs) with Model Predictive Control (MPC) for nonlinear dynamical systems. Unlike traditional MPC, which requires solving optimization problems in real time, the proposed method trains a single feedforward neural network to serve as an explicit controller that directly maps the current state, set-point, and disturbance signals to optimal control actions. The network is trained using a composite loss function that enforces the governing differential equations while incorporating control-oriented objectives such as set-point tracking, control smoothness, and soft constraints on states, inputs, and outputs. The proposed controller is validated on both single-input single-output (SISO) and multi-input multi-output (MIMO) water-tank benchmark systems, demonstrating accurate set-point tracking, effective measured disturbance rejection, and strong generalization across thousands of randomized test scenarios. A runtime comparison with a nonlinear MPC performing online optimization confirms that the explicit PINN-MPC approach achieves comparable control performance while requiring several orders of magnitude less computation time. These results highlight the scalability and computational efficiency of the proposed framework, positioning it as a novel paradigm for real-time control of nonlinear systems.
{"title":"An explicit model predictive control framework based on physics-informed neural networks","authors":"Argyri Kardamaki , Teo Protoulis , Alex Alexandridis , Haralambos Sarimveis","doi":"10.1016/j.jprocont.2026.103634","DOIUrl":"10.1016/j.jprocont.2026.103634","url":null,"abstract":"<div><div>This paper presents a novel control framework that integrates Physics-Informed Neural Networks (PINNs) with Model Predictive Control (MPC) for nonlinear dynamical systems. Unlike traditional MPC, which requires solving optimization problems in real time, the proposed method trains a single feedforward neural network to serve as an explicit controller that directly maps the current state, set-point, and disturbance signals to optimal control actions. The network is trained using a composite loss function that enforces the governing differential equations while incorporating control-oriented objectives such as set-point tracking, control smoothness, and soft constraints on states, inputs, and outputs. The proposed controller is validated on both single-input single-output (SISO) and multi-input multi-output (MIMO) water-tank benchmark systems, demonstrating accurate set-point tracking, effective measured disturbance rejection, and strong generalization across thousands of randomized test scenarios. A runtime comparison with a nonlinear MPC performing online optimization confirms that the explicit PINN-MPC approach achieves comparable control performance while requiring several orders of magnitude less computation time. These results highlight the scalability and computational efficiency of the proposed framework, positioning it as a novel paradigm for real-time control of nonlinear systems.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103634"},"PeriodicalIF":3.9,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.jprocont.2026.103628
Vikram Singh, Somesh Kumar Sharma
Maintaining quality in the manufacturing system has become a critical challenge in today’s rapidly evolving technological landscape. To overcome this, current research examines the role of Multi-Agent Technology (MAT) in improving the quality of manufacturing processes. For this, a conceptual framework consisting of eight factors and thirty-seven variables of MAT, identified from the literature, was analyzed using the Analytical Hierarchical Process (AHP), Sensitivity Analysis, Decision-Making Trial and Evaluation Laboratory (DEMATEL), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). AHP findings revealed ‘Production Planning’ as the highest-priority factor, followed by ‘Process Monitoring, Control, and Data Acquisition.’ DEMATEL established the interrelationships among variables, ensuring a collaborative approach to maintaining quality. Sensitivity analysis and TOPSIS validated the AHP results for consistency and robustness. The findings also indicated that Virtual Manufacturing, Distributed Digital Manufacturing, and Adaptive Agent-Based Architecture were the globally top ranked variables in the framework that help to ensure the quality of manufacturing processes. These findings contribute to developing autonomous, high-precision manufacturing systems for long-term competitiveness and quality assurance. This study provides valuable insights for researchers and managers, demonstrating that MAT and its parameters can be customized to optimize manufacturing quality.
{"title":"Understanding the role of multi-agent technology on quality of manufacturing organizations: A hybrid MCDM analysis","authors":"Vikram Singh, Somesh Kumar Sharma","doi":"10.1016/j.jprocont.2026.103628","DOIUrl":"10.1016/j.jprocont.2026.103628","url":null,"abstract":"<div><div>Maintaining quality in the manufacturing system has become a critical challenge in today’s rapidly evolving technological landscape. To overcome this, current research examines the role of Multi-Agent Technology (MAT) in improving the quality of manufacturing processes. For this, a conceptual framework consisting of eight factors and thirty-seven variables of MAT, identified from the literature, was analyzed using the Analytical Hierarchical Process (AHP), Sensitivity Analysis, Decision-Making Trial and Evaluation Laboratory (DEMATEL), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). AHP findings revealed ‘Production Planning’ as the highest-priority factor, followed by ‘Process Monitoring, Control, and Data Acquisition.’ DEMATEL established the interrelationships among variables, ensuring a collaborative approach to maintaining quality. Sensitivity analysis and TOPSIS validated the AHP results for consistency and robustness. The findings also indicated that <em>Virtual Manufacturing, Distributed Digital Manufacturing,</em> and <em>Adaptive Agent-Based Architecture</em> were the globally top ranked variables in the framework that help to ensure the quality of manufacturing processes. These findings contribute to developing autonomous, high-precision manufacturing systems for long-term competitiveness and quality assurance. This study provides valuable insights for researchers and managers, demonstrating that MAT and its parameters can be customized to optimize manufacturing quality.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103628"},"PeriodicalIF":3.9,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.jprocont.2026.103630
Collin R. Johnson , Kerstin Wohlgemuth , Sergio Lucia
Continuous crystallization processes require advanced control strategies to ensure consistent product quality, yet deploying optimization-based controllers such as model predictive control remains challenging. Combining spatially distributed crystallizer models with detailed particle size distributions leads to computationally demanding problems that are difficult to solve in real-time. This tutorial provides a comprehensive overview of how to address this challenge. Topics include numerical methods for solving population balance equations, modeling of crystallizers, and data-driven surrogate modeling. We show how these elements combine within a model predictive control framework to enable real-time control of particle size distributions. Two case studies illustrate the complete workflow: a well-mixed crystallizer that allows comparison with established methods, and a spatially distributed plug-flow crystallizer that demonstrates application to more complex systems. Readers gain a practical roadmap for implementing model predictive control in continuous crystallization, supported by open-source code and interactive examples. The tutorial concludes by outlining open challenges and emerging opportunities in the field.
{"title":"A tutorial overview of model predictive control for continuous crystallization: Current possibilities and future perspectives","authors":"Collin R. Johnson , Kerstin Wohlgemuth , Sergio Lucia","doi":"10.1016/j.jprocont.2026.103630","DOIUrl":"10.1016/j.jprocont.2026.103630","url":null,"abstract":"<div><div>Continuous crystallization processes require advanced control strategies to ensure consistent product quality, yet deploying optimization-based controllers such as model predictive control remains challenging. Combining spatially distributed crystallizer models with detailed particle size distributions leads to computationally demanding problems that are difficult to solve in real-time. This tutorial provides a comprehensive overview of how to address this challenge. Topics include numerical methods for solving population balance equations, modeling of crystallizers, and data-driven surrogate modeling. We show how these elements combine within a model predictive control framework to enable real-time control of particle size distributions. Two case studies illustrate the complete workflow: a well-mixed crystallizer that allows comparison with established methods, and a spatially distributed plug-flow crystallizer that demonstrates application to more complex systems. Readers gain a practical roadmap for implementing model predictive control in continuous crystallization, supported by open-source code and interactive examples. The tutorial concludes by outlining open challenges and emerging opportunities in the field.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103630"},"PeriodicalIF":3.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.jprocont.2026.103629
Chenlong Wang, Fengying Ma
Microbial fuel cells (MFCs) are novel energy technologies that convert the chemical energy of organic matter in wastewater into electrical energy. However, MFC systems generally require external control to achieve stable voltage output. In this paper, an optimal controller for MFC systems is designed. By adopting the – technique, the intractable Hamilton–Jacobi–Bellman (HJB) equation is transformed into a set of algebraic equations, which enables the solution of the optimal control problem with large initial states. To address parameter uncertainty in the optimal controller, an optimization algorithm is employed to tune its parameters. Furthermore, to overcome the limitations of existing optimization algorithms, including slow convergence speed, low solution accuracy, and premature convergence, an improved reptile search algorithm is proposed by integrating chaotic mechanisms, an elite-guided differential perturbation strategy, and an adaptive crossover probability control mechanism. Simulation results demonstrate that the improved algorithm achieves faster convergence and higher accuracy. Moreover, the designed optimal controller exhibits smaller overshoot and steady-state error in the MFC.
{"title":"A microbial fuel cell with an optimal controller based on improved reptile search algorithm","authors":"Chenlong Wang, Fengying Ma","doi":"10.1016/j.jprocont.2026.103629","DOIUrl":"10.1016/j.jprocont.2026.103629","url":null,"abstract":"<div><div>Microbial fuel cells (MFCs) are novel energy technologies that convert the chemical energy of organic matter in wastewater into electrical energy. However, MFC systems generally require external control to achieve stable voltage output. In this paper, an optimal controller for MFC systems is designed. By adopting the <span><math><mi>θ</mi></math></span>–<span><math><mi>D</mi></math></span> technique, the intractable Hamilton–Jacobi–Bellman (HJB) equation is transformed into a set of algebraic equations, which enables the solution of the optimal control problem with large initial states. To address parameter uncertainty in the optimal controller, an optimization algorithm is employed to tune its parameters. Furthermore, to overcome the limitations of existing optimization algorithms, including slow convergence speed, low solution accuracy, and premature convergence, an improved reptile search algorithm is proposed by integrating chaotic mechanisms, an elite-guided differential perturbation strategy, and an adaptive crossover probability control mechanism. Simulation results demonstrate that the improved algorithm achieves faster convergence and higher accuracy. Moreover, the designed optimal controller exhibits smaller overshoot and steady-state error in the MFC.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103629"},"PeriodicalIF":3.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-13DOI: 10.1016/j.jprocont.2026.103627
Shuai Tan , Shuxuan Zeng , Jijie Han , Qingchao Jiang , Weimin Zhong , Jiayi Wang
Multi-source domain adaptation poses more complex challenges compared to traditional single source domain adaptation. While constrained target domain labeling and limited information from a single source can be mitigated, the inherent discrepancies among multiple domains exacerbate the difficulty of fault diagnosis under varying operating conditions, particularly in real industrial systems with diverse and intricate environments. To tackle these issues, a novel Multi-source Inter-domain Feature Discrepancy (MIFD) model is proposed in this paper, which differs from existing multi-source adaptation methods by explicitly modeling inter-domain feature discrepancies instead of solely enforcing a unified shared feature space through global or marginal distribution alignment. In the proposed framework, a three-scale alignment mechanism is introduced to jointly align feature representations, class semantics, and domain distributions, thereby constraining domain shifts at multiple semantic levels while preserving domain-pair-specific characteristics. A discrepancy-aware feature matching module is developed to enable the extraction of reliable and transferable features tailored to specific source–target domain pairs. Furthermore, a class-center and domain alignment strategy is designed to constrain conditional distributions and alleviate pseudo-label bias. In addition, a dual-level weighting scheme is proposed, by which domain contributions are adaptively quantified and irrelevant classes are automatically filtered. Experimental results on two benchmark fault diagnosis scenarios under partial label space settings demonstrate that the proposed MIFD model outperforms state-of-the-art multi-source domain adaptation methods by up to 5.13% on the CWRU dataset and achieves an improvement of 2.16% on the TEP dataset, effectively reducing negative transfer and domain conflicts while enhancing diagnostic robustness under label space inconsistency.
{"title":"An inter-domain feature discrepancy method for multi-source partial domain fault diagnosis","authors":"Shuai Tan , Shuxuan Zeng , Jijie Han , Qingchao Jiang , Weimin Zhong , Jiayi Wang","doi":"10.1016/j.jprocont.2026.103627","DOIUrl":"10.1016/j.jprocont.2026.103627","url":null,"abstract":"<div><div>Multi-source domain adaptation poses more complex challenges compared to traditional single source domain adaptation. While constrained target domain labeling and limited information from a single source can be mitigated, the inherent discrepancies among multiple domains exacerbate the difficulty of fault diagnosis under varying operating conditions, particularly in real industrial systems with diverse and intricate environments. To tackle these issues, a novel Multi-source Inter-domain Feature Discrepancy (MIFD) model is proposed in this paper, which differs from existing multi-source adaptation methods by explicitly modeling inter-domain feature discrepancies instead of solely enforcing a unified shared feature space through global or marginal distribution alignment. In the proposed framework, a three-scale alignment mechanism is introduced to jointly align feature representations, class semantics, and domain distributions, thereby constraining domain shifts at multiple semantic levels while preserving domain-pair-specific characteristics. A discrepancy-aware feature matching module is developed to enable the extraction of reliable and transferable features tailored to specific source–target domain pairs. Furthermore, a class-center and domain alignment strategy is designed to constrain conditional distributions and alleviate pseudo-label bias. In addition, a dual-level weighting scheme is proposed, by which domain contributions are adaptively quantified and irrelevant classes are automatically filtered. Experimental results on two benchmark fault diagnosis scenarios under partial label space settings demonstrate that the proposed MIFD model outperforms state-of-the-art multi-source domain adaptation methods by up to 5.13% on the CWRU dataset and achieves an improvement of 2.16% on the TEP dataset, effectively reducing negative transfer and domain conflicts while enhancing diagnostic robustness under label space inconsistency.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103627"},"PeriodicalIF":3.9,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-06DOI: 10.1016/j.jprocont.2025.103611
Yun Li , Neil Yorke-Smith , Tamas Keviczky
Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate research questions. The first concerns the computational challenge in applying these uncertainty sets in RO-based predictive control. To address this, a monolithic mixed-integer representation of the uncertainty set is proposed to uniformly describe the union of multiple subsets, enabling the computation of the worst-case uncertainty scenario across all subsets within a single mixed-integer linear programming (MILP) problem. The second research question focuses on mitigating the conservatism of conventional RO formulations by leveraging the structure of the uncertainty set. To achieve this, a novel objective function is proposed to exploit the uncertainty set structure and integrate the existing RO and distributionally robust optimization (DRO) formulations, yielding less conservative solutions than conventional RO formulations, while avoiding the high-dimensional continuous uncertainty distributions and the high computational burden typically associated with existing DRO formulations. Given the proposed formulations, numerically efficient computation methods based on column-and-constraint generation (CCG) are also developed. Extensive simulations across three case studies are performed to demonstrate the effectiveness of the proposed schemes.
{"title":"On data-driven robust optimization with multiple uncertainty subsets: Unified uncertainty set representation and mitigating conservatism","authors":"Yun Li , Neil Yorke-Smith , Tamas Keviczky","doi":"10.1016/j.jprocont.2025.103611","DOIUrl":"10.1016/j.jprocont.2025.103611","url":null,"abstract":"<div><div>Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate research questions. The first concerns the computational challenge in applying these uncertainty sets in RO-based predictive control. To address this, a monolithic mixed-integer representation of the uncertainty set is proposed to uniformly describe the union of multiple subsets, enabling the computation of the worst-case uncertainty scenario across all subsets within a single mixed-integer linear programming (MILP) problem. The second research question focuses on mitigating the conservatism of conventional RO formulations by leveraging the structure of the uncertainty set. To achieve this, a novel objective function is proposed to exploit the uncertainty set structure and integrate the existing RO and distributionally robust optimization (DRO) formulations, yielding less conservative solutions than conventional RO formulations, while avoiding the high-dimensional continuous uncertainty distributions and the high computational burden typically associated with existing DRO formulations. Given the proposed formulations, numerically efficient computation methods based on <em>column-and-constraint generation</em> (CCG) are also developed. Extensive simulations across three case studies are performed to demonstrate the effectiveness of the proposed schemes.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103611"},"PeriodicalIF":3.9,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work develops a tube-based model predictive control (MPC) scheme for quasi–linear parameter-varying (quasi-LPV) systems affected by bounded disturbances and time-varying but measurable scheduling parameters. The controller uses a polytopic model together with a gain-scheduled feedback law to maintain robustness against parameter variations and external disturbances. To describe the terminal region more flexibly, a parameter-dependent terminal cost is introduced. In addition, an auxiliary cost function, evaluated only at the vertices of the polytope, removes the need to update parameters at every prediction step. Although the proposed formulation increases the computational load slightly, it provides stronger disturbance rejection and improved constraint handling. Experiments on a coupled-tank setup demonstrate that the method is both effective and practical for real-time implementation.
{"title":"Gain-scheduled tube-based MPC for quasi-LPV systems using vertex models","authors":"Rangoli Singh , Sandip Ghosh , Devender Singh , Pawel Dworak","doi":"10.1016/j.jprocont.2025.103617","DOIUrl":"10.1016/j.jprocont.2025.103617","url":null,"abstract":"<div><div>This work develops a tube-based model predictive control (MPC) scheme for quasi–linear parameter-varying (quasi-LPV) systems affected by bounded disturbances and time-varying but measurable scheduling parameters. The controller uses a polytopic model together with a gain-scheduled feedback law to maintain robustness against parameter variations and external disturbances. To describe the terminal region more flexibly, a parameter-dependent terminal cost is introduced. In addition, an auxiliary cost function, evaluated only at the vertices of the polytope, removes the need to update parameters at every prediction step. Although the proposed formulation increases the computational load slightly, it provides stronger disturbance rejection and improved constraint handling. Experiments on a coupled-tank setup demonstrate that the method is both effective and practical for real-time implementation.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103617"},"PeriodicalIF":3.9,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-04DOI: 10.1016/j.jprocont.2025.103612
Shaoyuan Li, Haolei Yin, Xiaohong Yin, Wenjian Cai
The width in rubber extrusion-calendering is a crucial process parameter in the rubber production workflow, as it directly influences both the quality and performance of rubber products, as well as overall production efficiency. However, the rubber extrusion-calendering process involves strong coupling among multiple parameters, with operating condition variations and significant external disturbances, leading to complex dynamic characteristics such as nonlinearity and time delays, which severely impact the accuracy of width prediction. To address these challenges, a hybrid modeling approach that integrates physical mechanisms with data-driven methods has been proposed within the framework of Physics-Informed Neural Networks (PINN). Firstly, a data-driven prediction model for calendering width was developed using a combination of a Temporal Convolutional Network and a Bidirectional Long Short-Term Memory network (TCN-BiLSTM). Secondly, an analysis of the physical mechanism underlying the extrusion-calendering process was conducted based on the power-law constitutive relationship to provide essential physical constraints for the prediction model. Furthermore, a dynamically adaptive weighting strategy was proposed to effectively reconcile conflicts between physical constraints and data fitting in the PINN model. Validation experiments demonstrate that this hybrid modeling approach can sustain high prediction accuracy even when faced with limited training data, noise interference, and varying operating conditions.
{"title":"A physics-guided hybrid model for calendering width prediction in rubber tire manufacturing","authors":"Shaoyuan Li, Haolei Yin, Xiaohong Yin, Wenjian Cai","doi":"10.1016/j.jprocont.2025.103612","DOIUrl":"10.1016/j.jprocont.2025.103612","url":null,"abstract":"<div><div>The width in rubber extrusion-calendering is a crucial process parameter in the rubber production workflow, as it directly influences both the quality and performance of rubber products, as well as overall production efficiency. However, the rubber extrusion-calendering process involves strong coupling among multiple parameters, with operating condition variations and significant external disturbances, leading to complex dynamic characteristics such as nonlinearity and time delays, which severely impact the accuracy of width prediction. To address these challenges, a hybrid modeling approach that integrates physical mechanisms with data-driven methods has been proposed within the framework of Physics-Informed Neural Networks (PINN). Firstly, a data-driven prediction model for calendering width was developed using a combination of a Temporal Convolutional Network and a Bidirectional Long Short-Term Memory network (TCN-BiLSTM). Secondly, an analysis of the physical mechanism underlying the extrusion-calendering process was conducted based on the power-law constitutive relationship to provide essential physical constraints for the prediction model. Furthermore, a dynamically adaptive weighting strategy was proposed to effectively reconcile conflicts between physical constraints and data fitting in the PINN model. Validation experiments demonstrate that this hybrid modeling approach can sustain high prediction accuracy even when faced with limited training data, noise interference, and varying operating conditions.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103612"},"PeriodicalIF":3.9,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-03DOI: 10.1016/j.jprocont.2025.103616
Kaiqiang Lou, Shunyi Zhao, Xiaoli Luan, Fei Liu
Modeling fermentation processes is challenging due to their nonlinear dynamics, time-dependent behavior, and inherent system uncertainties. Data-driven approaches, including black-box and gray-box models, are widely used in practice, but their performance relies heavily on the consistency and reliability of input data. A common issue affecting fermentation datasets is the presence of batch effects, which refer to systematic differences between datasets collected from separate fermentation runs conducted under similar conditions. These differences reduce data comparability and hinder reliable modeling. To address this problem, this study proposes an empirical Bayes-based method for fermentation datasets. A key component of the proposed approach is an unsupervised batch clustering strategy that enables more stable parameter estimation in the absence of within-batch replicates. The clustering-assisted ComBat method is applied to two representative cases: penicillin fermentation and Saccharomyces cerevisiae yeast fermentation. On the penicillin dataset (20 batches), the results demonstrate that the method effectively reduces batch-to-batch variability by 70.3% (median standard deviation) and improves data consistency by 74.4% (median coefficient of variation). Evaluation using the median absolute deviation confirms its advantage over conventional correction methods, resulting in a 64.4% reduction relative to the raw data. Additional tests on larger datasets further support its robustness and practical applicability.
{"title":"Correcting batch effects in fermentation processes using empirical Bayesian approach","authors":"Kaiqiang Lou, Shunyi Zhao, Xiaoli Luan, Fei Liu","doi":"10.1016/j.jprocont.2025.103616","DOIUrl":"10.1016/j.jprocont.2025.103616","url":null,"abstract":"<div><div>Modeling fermentation processes is challenging due to their nonlinear dynamics, time-dependent behavior, and inherent system uncertainties. Data-driven approaches, including black-box and gray-box models, are widely used in practice, but their performance relies heavily on the consistency and reliability of input data. A common issue affecting fermentation datasets is the presence of batch effects, which refer to systematic differences between datasets collected from separate fermentation runs conducted under similar conditions. These differences reduce data comparability and hinder reliable modeling. To address this problem, this study proposes an empirical Bayes-based method for fermentation datasets. A key component of the proposed approach is an unsupervised batch clustering strategy that enables more stable parameter estimation in the absence of within-batch replicates. The clustering-assisted ComBat method is applied to two representative cases: penicillin fermentation and <em>Saccharomyces cerevisiae</em> yeast fermentation. On the penicillin dataset (20 batches), the results demonstrate that the method effectively reduces batch-to-batch variability by 70.3% (median standard deviation) and improves data consistency by 74.4% (median coefficient of variation). Evaluation using the median absolute deviation confirms its advantage over conventional correction methods, resulting in a 64.4% reduction relative to the raw data. Additional tests on larger datasets further support its robustness and practical applicability.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103616"},"PeriodicalIF":3.9,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145891211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01DOI: 10.1016/j.jprocont.2025.103615
Rania Tafat , Jaime A. Moreno , Stefan Streif
Alternative protein sources are becoming essential for achieving a sustainable food system. The Black Soldier Fly larvae (BSFL), a protein-rich insect capable of feeding on a wide range of organic materials, shows immense potential for use in bio-conversion. It is already being used in poultry and fish aquaculture and is currently under evaluation for human consumption. Consequently, the farming of this insect is of great interest, and advanced control methods could significantly optimize the process and improve resource efficiency. One of the main challenges in applying these advanced techniques is the lack of information about certain critical system states, particularly the estimation of dry biomass weight. Measuring the dry biomass weight of the larvae is a destructive process that can only be performed at the beginning and end of the cycle. This low sampling frequency is insufficient for the application of advanced control strategies. Thus, a non-invasive estimation method is required. This work addresses the observer design problem for estimating the dry biomass weight of BSFL. The objective is to obtain an online estimation of this weight before the larvae reach maturity. To achieve this, a reduced version of the existing BSFL full-fledged model is proposed, based on specific assumptions. A subsystem is extracted from this BSFL reduced model, for which, a necessary and sufficient condition is provided for its global strong observability. Moreover, an interconnection of Generalized Super-Twisting Observers is designed, and a comparison is made between this method and the high-gain observer.
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