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Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay.

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Title: Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay.
Authors: Moadeli, Behrad1 (AUTHOR) moadeli@ualberta.ca, Dubljevic, Stevan1 (AUTHOR)
Source: Canadian Journal of Chemical Engineering. Jun2026, Vol. 104 Issue 6, p3018-3037. 20p.
Subjects: Tubular reactors, Predictive control systems, Closed loop system stability, Partial differential equations, Distributed parameter systems
Abstract: We develop a delay‐aware estimation and control framework for a non‐isothermal axial dispersion tubular reactor modelled as a coupled parabolic‐hyperbolic PDE system with recycle‐induced state delay. The infinite‐dimensional dynamics are preserved without spatial discretization by representing the delay as a transport PDE and adopting a late‐lumping approach. Closed‐form resolvent operators for the generator and its adjoint are derived, enabling Cayley–Tustin time discretization that maintains key system properties such as stability. The resulting discrete‐time representation is used to design a model predictive controller (MPC) with terminal equality constraints that guarantee closed‐loop stability under input constraints. Concurrently, a moving horizon estimator (MHE) is constructed for output‐based state reconstruction, exploiting inner‐product formulations in the lifted Hilbert space. Estimation and control are integrated via a modular architecture that maintains functional separation while enabling consistent state feedback. Numerical simulations demonstrate that the full‐state MPC successfully stabilizes the unstable reactor under input constraints, while the integrated MHE‐MPC framework enables output‐based feedback control by reconstructing distributed states from noisy measurements, maintaining constraint satisfaction and overall closed‐loop performance. [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.)
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DbLabel: Engineering Source
An: 193710925
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay.
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  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="%22Dubljevic%2C+Stevan%22">Dubljevic, Stevan</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Canadian+Journal+of+Chemical+Engineering%22">Canadian Journal of Chemical Engineering</searchLink>. Jun2026, Vol. 104 Issue 6, p3018-3037. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Tubular+reactors%22">Tubular reactors</searchLink><br /><searchLink fieldCode="DE" term="%22Predictive+control+systems%22">Predictive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Closed+loop+system+stability%22">Closed loop system stability</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Distributed+parameter+systems%22">Distributed parameter systems</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: We develop a delay‐aware estimation and control framework for a non‐isothermal axial dispersion tubular reactor modelled as a coupled parabolic‐hyperbolic PDE system with recycle‐induced state delay. The infinite‐dimensional dynamics are preserved without spatial discretization by representing the delay as a transport PDE and adopting a late‐lumping approach. Closed‐form resolvent operators for the generator and its adjoint are derived, enabling Cayley–Tustin time discretization that maintains key system properties such as stability. The resulting discrete‐time representation is used to design a model predictive controller (MPC) with terminal equality constraints that guarantee closed‐loop stability under input constraints. Concurrently, a moving horizon estimator (MHE) is constructed for output‐based state reconstruction, exploiting inner‐product formulations in the lifted Hilbert space. Estimation and control are integrated via a modular architecture that maintains functional separation while enabling consistent state feedback. Numerical simulations demonstrate that the full‐state MPC successfully stabilizes the unstable reactor under input constraints, while the integrated MHE‐MPC framework enables output‐based feedback control by reconstructing distributed states from noisy measurements, maintaining constraint satisfaction and overall closed‐loop performance. [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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        Value: 10.1002/cjce.70189
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 3018
    Subjects:
      – SubjectFull: Tubular reactors
        Type: general
      – SubjectFull: Predictive control systems
        Type: general
      – SubjectFull: Closed loop system stability
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Distributed parameter systems
        Type: general
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      – TitleFull: Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay.
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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