Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics

Detalhes bibliográficos
Autor(a) principal: Cristiano, Rony
Data de Publicação: 2017
Outros Autores: Carvalho, Tiago [UNESP], Tonon, Durval J., Pagano, Daniel J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.physd.2017.02.005
http://hdl.handle.net/11449/169521
Resumo: In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc–dc boost converter with sliding mode control and washout filter is analyzed. This device is modeled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the converter is a stable pseudo-equilibrium and it undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and disappears when it touches the visible–invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point. The study of these dynamic phenomena that can be found in different power electronic circuits controlled by sliding mode control strategies are relevant from the viewpoint of the global stability and robustness of the control design.
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spelling Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronicsBoost converterFilippov systemsSliding Homoclinic bifurcationSliding Hopf bifurcationSliding mode controlIn this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc–dc boost converter with sliding mode control and washout filter is analyzed. This device is modeled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the converter is a stable pseudo-equilibrium and it undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and disappears when it touches the visible–invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point. The study of these dynamic phenomena that can be found in different power electronic circuits controlled by sliding mode control strategies are relevant from the viewpoint of the global stability and robustness of the control design.Department of Automation and Systems Federal University of Santa CatarinaFC–UNESPInstitute of Mathematics and Statistics of Federal University of Goiás, CEP 74001-970, GoiâniaFC–UNESPUniversidade Federal de Santa Catarina (UFSC)Universidade Estadual Paulista (Unesp)Universidade Federal de Goiás (UFG)Cristiano, RonyCarvalho, Tiago [UNESP]Tonon, Durval J.Pagano, Daniel J.2018-12-11T16:46:14Z2018-12-11T16:46:14Z2017-05-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article12-20application/pdfhttp://dx.doi.org/10.1016/j.physd.2017.02.005Physica D: Nonlinear Phenomena, v. 347, p. 12-20.0167-2789http://hdl.handle.net/11449/16952110.1016/j.physd.2017.02.0052-s2.0-850146833182-s2.0-85014683318.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysica D: Nonlinear Phenomena0,861info:eu-repo/semantics/openAccess2023-10-12T06:08:06Zoai:repositorio.unesp.br:11449/169521Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:42:15.440281Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
title Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
spellingShingle Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
Cristiano, Rony
Boost converter
Filippov systems
Sliding Homoclinic bifurcation
Sliding Hopf bifurcation
Sliding mode control
title_short Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
title_full Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
title_fullStr Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
title_full_unstemmed Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
title_sort Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
author Cristiano, Rony
author_facet Cristiano, Rony
Carvalho, Tiago [UNESP]
Tonon, Durval J.
Pagano, Daniel J.
author_role author
author2 Carvalho, Tiago [UNESP]
Tonon, Durval J.
Pagano, Daniel J.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Federal de Santa Catarina (UFSC)
Universidade Estadual Paulista (Unesp)
Universidade Federal de Goiás (UFG)
dc.contributor.author.fl_str_mv Cristiano, Rony
Carvalho, Tiago [UNESP]
Tonon, Durval J.
Pagano, Daniel J.
dc.subject.por.fl_str_mv Boost converter
Filippov systems
Sliding Homoclinic bifurcation
Sliding Hopf bifurcation
Sliding mode control
topic Boost converter
Filippov systems
Sliding Homoclinic bifurcation
Sliding Hopf bifurcation
Sliding mode control
description In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc–dc boost converter with sliding mode control and washout filter is analyzed. This device is modeled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the converter is a stable pseudo-equilibrium and it undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and disappears when it touches the visible–invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point. The study of these dynamic phenomena that can be found in different power electronic circuits controlled by sliding mode control strategies are relevant from the viewpoint of the global stability and robustness of the control design.
publishDate 2017
dc.date.none.fl_str_mv 2017-05-15
2018-12-11T16:46:14Z
2018-12-11T16:46:14Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.physd.2017.02.005
Physica D: Nonlinear Phenomena, v. 347, p. 12-20.
0167-2789
http://hdl.handle.net/11449/169521
10.1016/j.physd.2017.02.005
2-s2.0-85014683318
2-s2.0-85014683318.pdf
url http://dx.doi.org/10.1016/j.physd.2017.02.005
http://hdl.handle.net/11449/169521
identifier_str_mv Physica D: Nonlinear Phenomena, v. 347, p. 12-20.
0167-2789
10.1016/j.physd.2017.02.005
2-s2.0-85014683318
2-s2.0-85014683318.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physica D: Nonlinear Phenomena
0,861
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 12-20
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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