Publication:
Design of Fractional Order Controllers Using the PM Diagram

dc.affiliation.dptoUC3M. Departamento de Ingeniería de Sistemas y Automáticaes
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Laboratorio de Robótica (Robotics Lab)es
dc.contributor.authorGarrido Bullón, Luis Santiago
dc.contributor.authorMonje Micharet, Concepción Alicia
dc.contributor.authorMartín Monar, Fernando
dc.contributor.authorMoreno Lorente, Luis Enrique
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-07-06T11:21:01Z
dc.date.available2021-07-06T11:21:01Z
dc.date.issued2020-11
dc.descriptionThis article belongs to the Special Issue Fractional Calculus and Nonlinear Systemsen
dc.description.abstractThis 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.en
dc.format.extent18
dc.identifier.bibliographicCitationGarrido, S., Monje, C. A., Martín, F. & Moreno, L. (2020). Design of Fractional Order Controllers Using the PM Diagram. Mathematics, 8(11), 2022.en
dc.identifier.doihttps://doi.org/10.3390/math8112022
dc.identifier.issn2227-7390
dc.identifier.publicationfirstpage2022
dc.identifier.publicationissue11
dc.identifier.publicationtitleMathematicsen
dc.identifier.publicationvolume8
dc.identifier.urihttps://hdl.handle.net/10016/33008
dc.identifier.uxxiAR/0000027256
dc.language.isoeng
dc.publisherMDPI
dc.relation.projectIDGobierno de España. DPI2016-75330-Pes
dc.rights© 2020 by the authors.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaBiología y Biomedicinaes
dc.subject.ecienciaRobótica e Informática Industriales
dc.subject.otherNon-rational systemsen
dc.subject.otherPhase magnitude diagramen
dc.subject.otherOptimal controlen
dc.subject.otherDifferential evolutionen
dc.subject.otherFractional order controlen
dc.titleDesign of Fractional Order Controllers Using the PM Diagramen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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