A unified procedure for the identification of reduced-order fractional models based on the process reaction curve

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dc.contributor.authorGude, Juan José
dc.contributor.authorCamacho, Oscar
dc.contributor.authorDi Teodoro, Antonio
dc.contributor.authorGarcía Bringas, Pablo
dc.date.accessioned2026-08-04T06:43:06Z
dc.date.available2026-08-04T06:43:06Z
dc.date.issued2026-06-05
dc.date.updated2026-08-04T06:43:06Z
dc.description.abstractThis paper introduces a unified analytical method for the identification of fractional reduced-order models, specifically the fractional first-order plus dead time (FFOPDT) and fractional dual-pole plus dead time (FDPPDT) structures, using only three points from the open-loop step response. The method provides explicit parameter-estimation formulas that eliminate the need for iterative optimization, reducing computational effort while preserving the simplicity of traditional reaction-curve techniques. Numerical simulations demonstrate superior accuracy and robustness compared to existing analytical and hybrid techniques, especially for overdamped and S-shaped responses typical of thermal and chemical processes. The method is validated for fractional orders within the range α ∈ [0.5, 1.0], covering the most relevant dynamics observed in practice. Laboratory experiments on a thermal system confirm the model’s applicability under real-world conditions, including measurement noise, limited sensor resolution, and hardware constraints. Because the workflow aligns with standard industrial identification practices and does not require specialized knowledge of fractional calculus, it provides a practical means to incorporate fractional-order modeling into proportional-integral-derivative (PID)-based process control.en
dc.description.sponsorshipThe authors acknowledge funding support from the Basque Government through the Research Group D4K-Deusto for Knowledge (IT1528 and IT1796-26). Universidad San Francisco de Quito also supported this work through the Poligrants Program under Grant 41983. This work was additionally supported by the Spanish Ministry of Science and Innovation through the projects QSERV (PID2021-124054OB-C33) and ATHENA-AEGIS (PID2024-155693NB-C43)en
dc.identifier.citationGude, J. J., Camacho, O., Teodoro, A. D., & Bringas, P. G. (2026). A unified procedure for the identification of reduced-order fractional models based on the process reaction curve. AIMS Mathematics, 11(6), 15851-15886. https://doi.org/10.3934/MATH.2026653
dc.identifier.doi10.3934/MATH.2026653
dc.identifier.eissn2473-6988
dc.identifier.urihttps://hdl.handle.net/20.500.14454/6455
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.rights© 2026 the Author(s)
dc.subject.otherFractional PID control
dc.subject.otherFractional-order systems
dc.subject.otherProcess identification
dc.subject.otherReaction curve
dc.subject.otherReduced-order models
dc.titleA unified procedure for the identification of reduced-order fractional models based on the process reaction curveen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage15886
oaire.citation.issue6
oaire.citation.startPage15851
oaire.citation.titleAIMS Mathematics
oaire.citation.volume11
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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