Design of Fractional Order Controllers Using the PM Diagram

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Show simple item record Garrido Bullón, Luis Santiago Monje Micharet, Concepción Alicia Martín Monar, Fernando Moreno Lorente, Luis Enrique 2021-07-06T11:21:01Z 2021-07-06T11:21:01Z 2020-11
dc.identifier.bibliographicCitation Garrido, S., Monje, C. A., Martín, F. & Moreno, L. (2020). Design of Fractional Order Controllers Using the PM Diagram. Mathematics, 8(11), 2022.
dc.identifier.issn 2227-7390
dc.description This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems
dc.description.abstract This work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the contribution of this research, four different non-rational reference systems have been considered. The method proposed here contributes first to a simpler and graphical modeling of these complex systems, and second to provide an effective tool to face the unsolved control problem of these systems.
dc.format.extent 18
dc.language.iso eng
dc.publisher MDPI
dc.rights © 2020 by the authors.
dc.rights Atribución 3.0 España
dc.subject.other Non-rational systems
dc.subject.other Phase magnitude diagram
dc.subject.other Optimal control
dc.subject.other Differential evolution
dc.subject.other Fractional order control
dc.title Design of Fractional Order Controllers Using the PM Diagram
dc.type article
dc.subject.eciencia Biología y Biomedicina
dc.subject.eciencia Robótica e Informática Industrial
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. DPI2016-75330-P
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 2022
dc.identifier.publicationissue 11
dc.identifier.publicationtitle Mathematics
dc.identifier.publicationvolume 8
dc.identifier.uxxi AR/0000027256
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Ingeniería de Sistemas y Automática
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Laboratorio de Robótica (Robotics Lab)
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