Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808128404370751488 |