A synergistic approach to proportional‐integral controller design in linear time‐delay systems.

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Title: A synergistic approach to proportional‐integral controller design in linear time‐delay systems.
Authors: Hernández‐Gallardo, Julián‐Alejandro1,2 (AUTHOR), Méndez‐Barrios, César‐Fernando1 (AUTHOR) cerfranfer@gmail.com, Guel‐Cortez, Adrian‐Josue3 (AUTHOR)
Source: Asian Journal of Control. Jul2026, Vol. 28 Issue 4, p1690-1704. 15p.
Subjects: Time delay systems, PID controllers, Metaheuristic algorithms, Closed loop systems, Mathematical optimization, Optimal control theory, Exponential decay law, Stability theory
Abstract: This paper proposes a novel method for optimizing proportional–integral (PI) controllers to produce fast and energy‐efficient responses in linear time‐delay systems. The proposed methodology combines analytical‐geometric stability analysis with meta‐heuristic or numerical optimization techniques to systematically minimize a cost function based on quadratic regulator principles. This synergy effectively reduces the search space and ensures convergence to an optimal solution. The paper also compares the performance of the proposed synergistic method against a fully analytical tuning approach for PI controllers, focusing on achieving the highest rate of exponential decay in the system response. Results indicate that our method effectively mitigates the challenges associated with temporal delays in control systems while meeting multiple performance requirements. Furthermore, numerical simulations and experimental validations demonstrate significant improvements in closed‐loop performance, highlighting the practical advantages of the proposed approach. [ABSTRACT FROM AUTHOR]
Copyright of Asian Journal of Control 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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  Data: A synergistic approach to proportional‐integral controller design in linear time‐delay systems.
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  Data: <searchLink fieldCode="AR" term="%22Hernández‐Gallardo%2C+Julián‐Alejandro%22">Hernández‐Gallardo, Julián‐Alejandro</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Méndez‐Barrios%2C+César‐Fernando%22">Méndez‐Barrios, César‐Fernando</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cerfranfer@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Guel‐Cortez%2C+Adrian‐Josue%22">Guel‐Cortez, Adrian‐Josue</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. Jul2026, Vol. 28 Issue 4, p1690-1704. 15p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink><br /><searchLink fieldCode="DE" term="%22PID+controllers%22">PID controllers</searchLink><br /><searchLink fieldCode="DE" term="%22Metaheuristic+algorithms%22">Metaheuristic algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Closed+loop+systems%22">Closed loop systems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+decay+law%22">Exponential decay law</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper proposes a novel method for optimizing proportional–integral (PI) controllers to produce fast and energy‐efficient responses in linear time‐delay systems. The proposed methodology combines analytical‐geometric stability analysis with meta‐heuristic or numerical optimization techniques to systematically minimize a cost function based on quadratic regulator principles. This synergy effectively reduces the search space and ensures convergence to an optimal solution. The paper also compares the performance of the proposed synergistic method against a fully analytical tuning approach for PI controllers, focusing on achieving the highest rate of exponential decay in the system response. Results indicate that our method effectively mitigates the challenges associated with temporal delays in control systems while meeting multiple performance requirements. Furthermore, numerical simulations and experimental validations demonstrate significant improvements in closed‐loop performance, highlighting the practical advantages of the proposed approach. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Asian Journal of Control 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/asjc.3771
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 1690
    Subjects:
      – SubjectFull: Time delay systems
        Type: general
      – SubjectFull: PID controllers
        Type: general
      – SubjectFull: Metaheuristic algorithms
        Type: general
      – SubjectFull: Closed loop systems
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Exponential decay law
        Type: general
      – SubjectFull: Stability theory
        Type: general
    Titles:
      – TitleFull: A synergistic approach to proportional‐integral controller design in linear time‐delay systems.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Hernández‐Gallardo, Julián‐Alejandro
      – PersonEntity:
          Name:
            NameFull: Méndez‐Barrios, César‐Fernando
      – PersonEntity:
          Name:
            NameFull: Guel‐Cortez, Adrian‐Josue
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          Dates:
            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 15618625
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              Value: 28
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              Value: 4
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            – TitleFull: Asian Journal of Control
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