LAPSE:2026.0446
Published Article

LAPSE:2026.0446
Virtual Plant-Model Pair as a Step Towards Real-Time Optimization of a Simulated Moving Bed System
June 12, 2026
Abstract
Simulated Moving Bed (SMB) chromatography is widely used for a variety of separations, yet, when applicable, these systems are typically operated using offline optimization strategies. Over time, process degradation and unforeseen disturbances may cause SMB units to deviate from the calculated optimal conditions, reducing overall performance. Real-Time Optimization (RTO) offers a promising solution by continuously monitoring and adjusting operating conditions to maintain optimal performance, despite such perturbations. However, experimental implementation of RTO in industrial SMB processes is costly and requires significant interdisciplinary coordination.To address this challenge, a virtual framework is proposed for the preliminary development of a model-based RTO system. The methodology employs a virtual plant-model pair, in which a representative plant model generates in silico experimental data, while a structurally distinct predictive model reproduces these results. Structural mismatch was intentionally introduced to mimic real-world differences between a plant and its mathematical model, and measurement noise was added to enhance realism. Within this methodology, the in silico experiments were successfully generated and the parameters of the predictive model were then estimated using a Particle Swarm Optimization algorithm that sought to minimize the residuals between the in silico experimental data and the predictive model outputs. The parameters were successfully estimated, allowing the predictive model to closely reproduce the behavior of a structurally distinct plant model without introducing additional complications, which is expected to be analogous to a real-scenario RTO system. Hence, this work establishes a critical step towards the foundation of a virtual RTO framework.
Simulated Moving Bed (SMB) chromatography is widely used for a variety of separations, yet, when applicable, these systems are typically operated using offline optimization strategies. Over time, process degradation and unforeseen disturbances may cause SMB units to deviate from the calculated optimal conditions, reducing overall performance. Real-Time Optimization (RTO) offers a promising solution by continuously monitoring and adjusting operating conditions to maintain optimal performance, despite such perturbations. However, experimental implementation of RTO in industrial SMB processes is costly and requires significant interdisciplinary coordination.To address this challenge, a virtual framework is proposed for the preliminary development of a model-based RTO system. The methodology employs a virtual plant-model pair, in which a representative plant model generates in silico experimental data, while a structurally distinct predictive model reproduces these results. Structural mismatch was intentionally introduced to mimic real-world differences between a plant and its mathematical model, and measurement noise was added to enhance realism. Within this methodology, the in silico experiments were successfully generated and the parameters of the predictive model were then estimated using a Particle Swarm Optimization algorithm that sought to minimize the residuals between the in silico experimental data and the predictive model outputs. The parameters were successfully estimated, allowing the predictive model to closely reproduce the behavior of a structurally distinct plant model without introducing additional complications, which is expected to be analogous to a real-scenario RTO system. Hence, this work establishes a critical step towards the foundation of a virtual RTO framework.
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Amaral GC, Ferreira AFP, Ribeiro AM, Nogueira IBR, Rodrigues D. Virtual Plant-Model Pair as a Step Towards Real-Time Optimization of a Simulated Moving Bed System. Systems and Control Transactions 5:1950-1957 (2026) https://doi.org/10.69997/sct.150995
Author Affiliations
Amaral GC: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
Ferreira AFP: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
Ribeiro AM: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
Nogueira IBR: Chemical Engineering Department, Norwegian University of Science and Technology, Sem Sælandsvei 4, Kjemiblokk 5, Trondheim, 793101, Norway [ORCID]
Rodrigues D: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
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Ferreira AFP: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
Ribeiro AM: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
Nogueira IBR: Chemical Engineering Department, Norwegian University of Science and Technology, Sem Sælandsvei 4, Kjemiblokk 5, Trondheim, 793101, Norway [ORCID]
Rodrigues D: LSRE-LCM, ALiCE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal [ORCID]
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Journal Name
Systems and Control Transactions
Volume
5
First Page
1950
Last Page
1957
Year
2026
Publication Date
2026-06-12
Version Comments
Original Submission
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PII: 1950-1957-92-SCT-5-2026, Publication Type: Journal Article
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LAPSE:2026.0446
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LAPSE:2026.0031
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References Cited
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