Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs.
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| Title: | Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs. |
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| Authors: | Moadeli, Behrad1 (AUTHOR) moadeli@ualberta.ca, Cassol, Guilherme Ozorio1 (AUTHOR), Dubljevic, Stevan1 (AUTHOR) |
| Source: | Canadian Journal of Chemical Engineering. Aug2025, Vol. 103 Issue 8, p3751-3766. 16p. |
| Subjects: | Distributed parameter systems, Tubular reactors, Chemical engineering, Partial differential equations, Operator equations |
| Abstract: | The optimal control of an axial tubular reactor with a recycle stream is addressed as a key type of setting for distributed parameter systems in chemical engineering. The intrinsic time delay from the recycle process, thus far overlooked in relevant literature, is modelled as a transport partial differential equation (PDE), resulting in a system of coupled parabolic and hyperbolic PDEs. Utilizing Danckwerts boundary conditions, the reactor is boundary‐controlled with the control input at the inlet. A continuous‐time optimal linear quadratic regulator is developed to stabilize the infinite‐dimensional system, employing a late lumping approach in order to preserve the properties of the original infinite dimensional system in controller design. The full‐state feedback regulator is designed by solving the Operator Riccati Equation (ORE), leveraging the system's Riesz‐spectral properties. To address practical limitations of full‐state feedback, a Luenberger observer is also proposed, enabling state reconstruction from boundary measurements. Numerical simulations are conducted to evaluate the proposed control strategies. The results demonstrate that the full‐state feedback regulator effectively stabilizes the system. A comparison is made between two configurations where different numbers of eigenmodes were selected to design the controller. The observer‐based regulator also stabilizes the system successfully using merely output measurements, effectively overcoming the challenge of limited state access. [ABSTRACT FROM AUTHOR] |
| Copyright of Canadian Journal of Chemical Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 186414369 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Moadeli%2C+Behrad%22">Moadeli, Behrad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> moadeli@ualberta.ca</i><br /><searchLink fieldCode="AR" term="%22Cassol%2C+Guilherme+Ozorio%22">Cassol, Guilherme Ozorio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dubljevic%2C+Stevan%22">Dubljevic, Stevan</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Canadian+Journal+of+Chemical+Engineering%22">Canadian Journal of Chemical Engineering</searchLink>. Aug2025, Vol. 103 Issue 8, p3751-3766. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Distributed+parameter+systems%22">Distributed parameter systems</searchLink><br /><searchLink fieldCode="DE" term="%22Tubular+reactors%22">Tubular reactors</searchLink><br /><searchLink fieldCode="DE" term="%22Chemical+engineering%22">Chemical engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+equations%22">Operator equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The optimal control of an axial tubular reactor with a recycle stream is addressed as a key type of setting for distributed parameter systems in chemical engineering. The intrinsic time delay from the recycle process, thus far overlooked in relevant literature, is modelled as a transport partial differential equation (PDE), resulting in a system of coupled parabolic and hyperbolic PDEs. Utilizing Danckwerts boundary conditions, the reactor is boundary‐controlled with the control input at the inlet. A continuous‐time optimal linear quadratic regulator is developed to stabilize the infinite‐dimensional system, employing a late lumping approach in order to preserve the properties of the original infinite dimensional system in controller design. The full‐state feedback regulator is designed by solving the Operator Riccati Equation (ORE), leveraging the system's Riesz‐spectral properties. To address practical limitations of full‐state feedback, a Luenberger observer is also proposed, enabling state reconstruction from boundary measurements. Numerical simulations are conducted to evaluate the proposed control strategies. The results demonstrate that the full‐state feedback regulator effectively stabilizes the system. A comparison is made between two configurations where different numbers of eigenmodes were selected to design the controller. The observer‐based regulator also stabilizes the system successfully using merely output measurements, effectively overcoming the challenge of limited state access. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Canadian Journal of Chemical Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/cjce.25629 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 3751 Subjects: – SubjectFull: Distributed parameter systems Type: general – SubjectFull: Tubular reactors Type: general – SubjectFull: Chemical engineering Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Operator equations Type: general Titles: – TitleFull: Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport PDEs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Moadeli, Behrad – PersonEntity: Name: NameFull: Cassol, Guilherme Ozorio – PersonEntity: Name: NameFull: Dubljevic, Stevan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00084034 Numbering: – Type: volume Value: 103 – Type: issue Value: 8 Titles: – TitleFull: Canadian Journal of Chemical Engineering Type: main |
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