A nested weighted framework for Podlubny-type fractional PID controllers
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Fecha
2026-12-01
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Elsevier Ltd
Resumen
This 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.
Palabras clave
Controller synthesis
Fractional calculus
Fractional-order control
Generalized fractional operators
Nested weighted operators
PID controllers
Podlubny-type fractional
Fractional calculus
Fractional-order control
Generalized fractional operators
Nested weighted operators
PID controllers
Podlubny-type fractional
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Materias
Cita
Di 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