Spatio‐Temporal Residual Extended State Observer‐Based Control for Complex Distributed Parameter Systems.

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Title: Spatio‐Temporal Residual Extended State Observer‐Based Control for Complex Distributed Parameter Systems.
Authors: Zhao, Yaru1 (AUTHOR), Luo, Biao2 (AUTHOR) biao.luo@hotmail.com, Li, Han‐Xiong3 (AUTHOR)
Source: International Journal of Robust & Nonlinear Control. 3/10/2026, Vol. 36 Issue 4, p2199-2210. 12p.
Subjects: Distributed parameter systems, Feedback control systems, Process control systems, Control theory (Engineering), Nonlinear control theory, Feedback control system stability
Abstract: It is difficult to control the complex distributed parameter system (DPS) for uniform spatial performance. In this paper, a spatio‐temporal residual extended state observer‐based control method is proposed for the DPS with both nonlinearities and unknown exogenous disturbances to achieve uniform performance throughout the entire workspace. The proposed control method encompasses four crucial components: An auxiliary DPS, a spatial mapping filter (SMF), a spatio‐temporal residual extended state observer (S‐T‐R‐ESO), and a disturbance feedback controller. Based on the auxiliary DPS and the SMF, feedback information is supplied to the S‐T‐R‐ESO. Subsequently, the observer is capable of estimating the distributed "overall disturbance" (the undesired dynamics), which includes both nonlinearities and exogenous disturbances. Thereafter, based on the estimation of the "overall disturbance", a feedback controller is implemented to suppress disturbances, enabling the state variables of the controlled plant to achieve spatially uniform stability. It is worth noting that both the proposed observer and the observer‐based controller are proven to converge based on the input‐state stability analysis method. The feasibility and effectiveness of the proposed control method are validated through the temperature control of a catalytic rod, which serves as a benchmark in chemical reactors. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Robust & Nonlinear 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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DbLabel: Engineering Source
An: 191517315
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  Data: Spatio‐Temporal Residual Extended State Observer‐Based Control for Complex Distributed Parameter Systems.
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  Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Yaru%22">Zhao, Yaru</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Luo%2C+Biao%22">Luo, Biao</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> biao.luo@hotmail.com</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Han‐Xiong%22">Li, Han‐Xiong</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Robust+%26+Nonlinear+Control%22">International Journal of Robust & Nonlinear Control</searchLink>. 3/10/2026, Vol. 36 Issue 4, p2199-2210. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Distributed+parameter+systems%22">Distributed parameter systems</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Process+control+systems%22">Process control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+control+theory%22">Nonlinear control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+system+stability%22">Feedback control system stability</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: It is difficult to control the complex distributed parameter system (DPS) for uniform spatial performance. In this paper, a spatio‐temporal residual extended state observer‐based control method is proposed for the DPS with both nonlinearities and unknown exogenous disturbances to achieve uniform performance throughout the entire workspace. The proposed control method encompasses four crucial components: An auxiliary DPS, a spatial mapping filter (SMF), a spatio‐temporal residual extended state observer (S‐T‐R‐ESO), and a disturbance feedback controller. Based on the auxiliary DPS and the SMF, feedback information is supplied to the S‐T‐R‐ESO. Subsequently, the observer is capable of estimating the distributed "overall disturbance" (the undesired dynamics), which includes both nonlinearities and exogenous disturbances. Thereafter, based on the estimation of the "overall disturbance", a feedback controller is implemented to suppress disturbances, enabling the state variables of the controlled plant to achieve spatially uniform stability. It is worth noting that both the proposed observer and the observer‐based controller are proven to converge based on the input‐state stability analysis method. The feasibility and effectiveness of the proposed control method are validated through the temperature control of a catalytic rod, which serves as a benchmark in chemical reactors. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Robust & Nonlinear 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:
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      – Type: doi
        Value: 10.1002/rnc.70261
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 2199
    Subjects:
      – SubjectFull: Distributed parameter systems
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Process control systems
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: Nonlinear control theory
        Type: general
      – SubjectFull: Feedback control system stability
        Type: general
    Titles:
      – TitleFull: Spatio‐Temporal Residual Extended State Observer‐Based Control for Complex Distributed Parameter Systems.
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            NameFull: Zhao, Yaru
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            NameFull: Luo, Biao
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            NameFull: Li, Han‐Xiong
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            – D: 10
              M: 03
              Text: 3/10/2026
              Type: published
              Y: 2026
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              Value: 36
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            – TitleFull: International Journal of Robust & Nonlinear Control
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