A nested weighted framework for Podlubny-type fractional PID controllers

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dc.contributor.authorDi Teodoro, Antonio
dc.contributor.authorGude, Juan José
dc.contributor.authorCamacho, Oscar
dc.date.accessioned2026-11-13T09:37:52Z
dc.date.available2026-11-13T09:37:52Z
dc.date.issued2026-12-01
dc.date.updated2026-11-13T09:37:52Z
dc.description.abstractThis paper presents a unified nested weighted framework for the systematic synthesis of Podlubny-type fractional PID controllers through the constructive generation of generalized fractional operators. The proposed methodology adopts a composition-based perspective in which generalized fractional operators are recursively constructed from weighted differential and integral mappings, allowing classical formulations, including the Riemann–Liouville and Caputo operators, to be recovered as particular cases. Within this framework, a novel pulling-type weighted fractional operator is introduced and its fundamental analytical properties, including linearity, kernel characterization, boundedness, semigroup behavior, and Laplace-domain representation, are rigorously established. These results provide the mathematical foundation for deriving a generalized family of weighted Podlubny-type fractional PID controllers, where the weighting functions become explicit design parameters governing memory distribution and closed-loop dynamics. Consequently, the proposed framework transforms the construction of generalized fractional operators into a systematic methodology for fractional controller synthesis, establishing a constructive link between generalized fractional calculus and fractional-order control design.en
dc.description.sponsorshipThis work was supported by the Universidad San Francisco de Quito through the Poli-Grants Program under Grant No. 41983. The authors also acknowledge the financial support provided by the Basque Government through the consolidated research group D4K–Deusto for Knowledge under Grants IT1528-22 and IT1796-26.en
dc.identifier.citationDi Teodoro, A., Gude, J. J., & Camacho, O. (2026). A nested weighted framework for Podlubny-type fractional PID controllers. Chaos, Solitons and Fractals, 213. https://doi.org/10.1016/J.CHAOS.2026.119217
dc.identifier.doi10.1016/J.CHAOS.2026.119217
dc.identifier.issn0960-0779
dc.identifier.urihttps://hdl.handle.net/20.500.14454/6959
dc.language.isoeng
dc.publisherElsevier Ltd
dc.rights© 2026 The Author(s)
dc.subject.otherController synthesis
dc.subject.otherFractional calculus
dc.subject.otherFractional-order control
dc.subject.otherGeneralized fractional operators
dc.subject.otherNested weighted operators
dc.subject.otherPID controllers
dc.subject.otherPodlubny-type fractional
dc.titleA nested weighted framework for Podlubny-type fractional PID controllersen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.titleChaos, Solitons and Fractals
oaire.citation.volume213
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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