ZAD strategy with lateral PWM applied to a boost converter

En este trabajo mostramos algunos resultados sobre la dinámica de un convertidor Boost cuando es controlado por la estrategia PWM (Modulador de Ancho de Pulso) lateral y ZAD (Dinámica de Promedio Cero). Se reportan diferentes fenómenos no lineales como bifurcaciones y caos cuando se varían los parám...

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Autores:
Hurtado López, Julián
Amador, Andrés
Casanova, Simeón
Olivar Sánchez, Gerard
Tipo de recurso:
Article of journal
Fecha de publicación:
2013
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/11942
Acceso en línea:
http://red.uao.edu.co//handle/10614/11942
Palabra clave:
Boost converter
ZAD
Bifurcations
Chaos Control
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openAccess
License
Derechos Reservados - Universidad Autónoma de Occidente
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network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv ZAD strategy with lateral PWM applied to a boost converter
title ZAD strategy with lateral PWM applied to a boost converter
spellingShingle ZAD strategy with lateral PWM applied to a boost converter
Boost converter
ZAD
Bifurcations
Chaos Control
title_short ZAD strategy with lateral PWM applied to a boost converter
title_full ZAD strategy with lateral PWM applied to a boost converter
title_fullStr ZAD strategy with lateral PWM applied to a boost converter
title_full_unstemmed ZAD strategy with lateral PWM applied to a boost converter
title_sort ZAD strategy with lateral PWM applied to a boost converter
dc.creator.fl_str_mv Hurtado López, Julián
Amador, Andrés
Casanova, Simeón
Olivar Sánchez, Gerard
dc.contributor.author.none.fl_str_mv Hurtado López, Julián
Amador, Andrés
Casanova, Simeón
Olivar Sánchez, Gerard
dc.subject.proposal.eng.fl_str_mv Boost converter
ZAD
Bifurcations
Chaos Control
topic Boost converter
ZAD
Bifurcations
Chaos Control
description En este trabajo mostramos algunos resultados sobre la dinámica de un convertidor Boost cuando es controlado por la estrategia PWM (Modulador de Ancho de Pulso) lateral y ZAD (Dinámica de Promedio Cero). Se reportan diferentes fenómenos no lineales como bifurcaciones y caos cuando se varían los parámetros asociados al sistema. Por último, el caos presente en el convertidor se controla mediante las técnicas FPIC (control inducido por puntos fijos) y TDAS (sincronización automática con retardo temporal).
publishDate 2013
dc.date.issued.none.fl_str_mv 2013-08-09
dc.date.accessioned.none.fl_str_mv 2020-02-19T21:21:23Z
dc.date.available.none.fl_str_mv 2020-02-19T21:21:23Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.relation.spa.fl_str_mv Matemáticas:Enseñanza Universitaria.Escuela Regional de Matemáticas Universidad del Valle. Volumen xx, número 1, (junio 2012); páginas 3-19
dc.relation.citationendpage.none.fl_str_mv 19
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dc.relation.citationstartpage.none.fl_str_mv 3
dc.relation.citationvolume.none.fl_str_mv XX
dc.relation.cites.spa.fl_str_mv Hurtado López, J., Amador, A., Casanova, S., Olivar Sánchez, G.(2012). ZAD strategy with lateral PWM applied to a boost converter. Matemáticas: Enseñanza Universitaria. XX (1), 3-19. http://red.uao.edu.co//handle/10614/11942
dc.relation.ispartofjournal.spa.fl_str_mv Matemáticas: Enseñanza Universitaria
dc.relation.references.none.fl_str_mv Deane, J.H.B. and Hamill, D.C. Instability, subharmonics, and chaos in power electronic systems. IEEE Power Electronics Society, pp. 260–268, (1990).
Deane, J.H.B. and Hamill, D.C. Analysis, simulation and experimental study of chaos in the buck converter. Proc IEEE Power Electronics Specialists Conference (PESC’90), San Antonio, TX, pp. 491–498, (1990).
Gerard Olivar. Chaos in the Buck Converter. PhD Tesis, UPC, (1997).
Chan, Willian C. Y. and Tse, C. K. Bifurcations in current-programmed DC/DC buck switching regulators-conjecturing a universal bifurcation path. International Journal of Circuit Theory and Applications, Vol. 26, pp. 127– 145, (1998).
Tse, C.K. and Lai, Y.M. Control of bifurcation in current-programmed DC/DC converters: a reexamination of slope compensation. Circuits and Systems, Vol. 1, pp. 671–674, (2000).
Banerjee, Soumitro and Verghese, George. Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control. WileyIEEE Press, (2001).
Tse, C.K. and di Bernardo, M. Complex behavior in switching power converters. IEEE, pp. 768–781, (2002).
Maity, Somnath and Bhattacharya, Tapas K. and Banerjee, Soumitro. Experimental Study of Chaos and Bifurcation in the Buck Converter. National Conference on Nonlinear Systems & Dynamics, (2005).
Taborda, J.A. and Angulo, F. and Olivar, G. Smooth bifurcations in 3Dparameter space of Digital-PWM Switched Converter. Circuits and Systems (LASCAS), 2011 IEEE, pp. 1–4, (2011).
Deane, J.H.B. Chaos in a Current-Mode Controlled Boost dc-dc. IEEE Trans. Circuit Syst. I, Vol. 39, pp. 680–683, (1992).
Zafrany, I. and Ben-Yaakov, S. A chaos model of subharmonic oscillations in current mode PWM boost converters. Proc IEEE Power Electronics Specialists Conference, pp. 1111–1117, (1995).
Fossas E. and Olivar G. Study of Chaos in the Buck Converter. IEEE Trans. Circuits Syst. I, pp. 13–25, (1996).
Chan, W. and Tse, C. Study of Bifurcations in Current-Programmed DC/DC Boost Converters: From Quasi-Periodicity to Period-Doubling. IEEE Trans. Circuits Syst. I., pp. 1129–1142, (1997).
di Bernardo M., Garofalo F., Glielmo L. and Vasca F. Switchings, Bifurcations, and Chaos in DC/DC Converters. IEEE Trans. Circuits Syst. I, pp. 133–141, (1998).
Banerjee S and Chakrabarty, K. Nonlinear Modeling and Bifurcations in the Boost Converter. IEEE Trans. Power Electr., pp. 252–260, (1998).
El Aroudi, A., Benadero, L., Toribio, E. and Olivar, G. Bifurcation and Chaos from Torus Breakdown in a PWM Voltage-Controlled DC-DC Boost Converters. IEEE Trans. Circuits Syst. I., pp. 1374–1382, (1999).
Cheng, K.W.E. and Liu, M. and Wu, J. and Cheung, N.C. Study of Bifurcation and Chaos in the Current-Mode Controlled Buck-Boost DC-DC Converter. Proc IEEE Industrial Electronics Society (IECON’01), Denver, CO, pp. 838–843, (2001).
Kocewiak, Lukasz and Bak, Claus Leth and Munk-Nielsen, Stig. Bifurcations and Chaos in a Pulse Width Modulation Controlled Buck Converter. Proceedings of the 6th EUROSIM Congress on Modelling and Simulation, (2007), pp. 1–6.
Angulo, Fabiola and Fossas, Enric and Olivar, Gerard. Transition From Periodicity To Chaos In A Pwm-Controlled Buck Converter With Zad Strategy. Int. J. Bifurcation and Chaos, Vol. 15, No. 10, pp. 3245–3264, (2009).
Fossas, E and Hogan, S. J. and Seara,T. M. Two-parameter bifurcation curves in power electronic converters. Int. J. Bifurcation and Chaos, Vol. 19, pp. 349–357, (2009).
Angulo Fabiola. Análisis de la dinámica de convertidores electrónicos de potencia usando PWM basado en promediado cero de la dinámica del error (ZAD). Tesis de doctorado, UPC. Mayo de (2004).
Fossas E., Gri˜n´o R. and Biel D. Quasi-sliding control based on pulse width modulation, zero average and the L2 norm. In Advances in Variable Structure System, Analysis, Integration and Applications. Ed. World Scientific. (2001), pp. 335–344.
Cevantes, I. and Alvarez-Ramirez, J. A simple chaos control strategy for DC-DC power converters. Industrial Electronics Society, Vol. 1, pp. 193– 198, (2004). IECON 2004.
Pyragas, K. Continuous control of chaos by self-controlling feedback. Physics Letters, Vol. A, No. 170, pp. 421–428, (1992).
Angulo F. Burgos J.E. and Olivar G. Chaos Stabilization with TDAS and FPIC in a Buck Converter controlled by Lateral PWM and ZAD. Mediterranean Conference on Control and Automation, (2007).
Angulo, F. Fossas, E. Olivar, G T´ecnica ZAD Aplicada a un Convertidor Buck: An´alisis de Estabilidad y de Transici´on al Caos. Revista Iberoamericana de Autom´atica e Inform´atica Industrial, Vol. 2, No. 4. October (2005), pp. 25–35.
Angulo F. Fossas E. and Olivar G. Stabilization of Chaos with FPIC: Application to ZAD-Strategy Buck Converters. 16th IFAC World Congress, Prague, (2005).
Angulo F. Olivar G. Taborda J. A. and Hoyos, F. E. Nonsmooth dynamics and FPIC chaos control in a DC-DC ZAD-strategy power converter. Proceeding of the VI EUROMECH Nonlinear Dynamics Conference ENOC, Saint Petersburg, Russia, (2008).
Fossas, E. and Zinober, A. Adaptive Tracking Control of Nonlinear Power Converters. Proceedings IFAC Workshop on Adaptation in Control and Signal Processing, Connobio, Italia, pp. 264–266, (2001).
Carpita, M. and Marchesoni, M. and Oberti, M. and Puglisi, L. Power conditioning system using sliding model control. Power Electronics Specialists Conference (PESC’88 Record), 19th Annual IEEE, Kyoto, Japan, pp. 626– 633, (1988).
Parker T.S. and Chua L.O. Practical numerical algorithms for chaotic systems. Springer Verlag, New York. (1989). pp. 66–81.
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spelling Hurtado López, Juliánvirtual::2356-1Amador, Andrés80ea50e25e9bf647b2032320004d6fb6Casanova, Simeón75f4ab32a7a7198b23c0a15127a8b82bOlivar Sánchez, Gerard5129bd95186732fea18294f494184fe2Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2020-02-19T21:21:23Z2020-02-19T21:21:23Z2013-08-09http://red.uao.edu.co//handle/10614/11942En este trabajo mostramos algunos resultados sobre la dinámica de un convertidor Boost cuando es controlado por la estrategia PWM (Modulador de Ancho de Pulso) lateral y ZAD (Dinámica de Promedio Cero). Se reportan diferentes fenómenos no lineales como bifurcaciones y caos cuando se varían los parámetros asociados al sistema. Por último, el caos presente en el convertidor se controla mediante las técnicas FPIC (control inducido por puntos fijos) y TDAS (sincronización automática con retardo temporal).In this paper we show some results about the dynamics of a Boost converter when it is con- trolled by lateral PWM (Pulse Width Modulator) and ZAD (Zero Average Dynamics) strategy. Different nonlinear phenomena like bifurcations and chaos are reported when the parameters associated to the system are varied. Finally, chaos present in the converter is controlled using FPIC (Fixed Point Induced Control) and TDAS (Time-Delay Autosynchronization) techniques.application/pdf17 páginasengUniversidad del ValleMatemáticas:Enseñanza Universitaria.Escuela Regional de Matemáticas Universidad del Valle. Volumen xx, número 1, (junio 2012); páginas 3-191913XXHurtado López, J., Amador, A., Casanova, S., Olivar Sánchez, G.(2012). ZAD strategy with lateral PWM applied to a boost converter. Matemáticas: Enseñanza Universitaria. XX (1), 3-19. http://red.uao.edu.co//handle/10614/11942Matemáticas: Enseñanza UniversitariaDeane, J.H.B. and Hamill, D.C. Instability, subharmonics, and chaos in power electronic systems. IEEE Power Electronics Society, pp. 260–268, (1990).Deane, J.H.B. and Hamill, D.C. Analysis, simulation and experimental study of chaos in the buck converter. Proc IEEE Power Electronics Specialists Conference (PESC’90), San Antonio, TX, pp. 491–498, (1990).Gerard Olivar. Chaos in the Buck Converter. PhD Tesis, UPC, (1997).Chan, Willian C. Y. and Tse, C. K. Bifurcations in current-programmed DC/DC buck switching regulators-conjecturing a universal bifurcation path. International Journal of Circuit Theory and Applications, Vol. 26, pp. 127– 145, (1998).Tse, C.K. and Lai, Y.M. Control of bifurcation in current-programmed DC/DC converters: a reexamination of slope compensation. Circuits and Systems, Vol. 1, pp. 671–674, (2000).Banerjee, Soumitro and Verghese, George. Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control. WileyIEEE Press, (2001).Tse, C.K. and di Bernardo, M. Complex behavior in switching power converters. IEEE, pp. 768–781, (2002).Maity, Somnath and Bhattacharya, Tapas K. and Banerjee, Soumitro. Experimental Study of Chaos and Bifurcation in the Buck Converter. National Conference on Nonlinear Systems & Dynamics, (2005).Taborda, J.A. and Angulo, F. and Olivar, G. Smooth bifurcations in 3Dparameter space of Digital-PWM Switched Converter. Circuits and Systems (LASCAS), 2011 IEEE, pp. 1–4, (2011).Deane, J.H.B. Chaos in a Current-Mode Controlled Boost dc-dc. IEEE Trans. Circuit Syst. I, Vol. 39, pp. 680–683, (1992).Zafrany, I. and Ben-Yaakov, S. A chaos model of subharmonic oscillations in current mode PWM boost converters. Proc IEEE Power Electronics Specialists Conference, pp. 1111–1117, (1995).Fossas E. and Olivar G. Study of Chaos in the Buck Converter. IEEE Trans. Circuits Syst. I, pp. 13–25, (1996).Chan, W. and Tse, C. Study of Bifurcations in Current-Programmed DC/DC Boost Converters: From Quasi-Periodicity to Period-Doubling. IEEE Trans. Circuits Syst. I., pp. 1129–1142, (1997).di Bernardo M., Garofalo F., Glielmo L. and Vasca F. Switchings, Bifurcations, and Chaos in DC/DC Converters. IEEE Trans. Circuits Syst. I, pp. 133–141, (1998).Banerjee S and Chakrabarty, K. Nonlinear Modeling and Bifurcations in the Boost Converter. IEEE Trans. Power Electr., pp. 252–260, (1998).El Aroudi, A., Benadero, L., Toribio, E. and Olivar, G. Bifurcation and Chaos from Torus Breakdown in a PWM Voltage-Controlled DC-DC Boost Converters. IEEE Trans. Circuits Syst. I., pp. 1374–1382, (1999).Cheng, K.W.E. and Liu, M. and Wu, J. and Cheung, N.C. Study of Bifurcation and Chaos in the Current-Mode Controlled Buck-Boost DC-DC Converter. Proc IEEE Industrial Electronics Society (IECON’01), Denver, CO, pp. 838–843, (2001).Kocewiak, Lukasz and Bak, Claus Leth and Munk-Nielsen, Stig. Bifurcations and Chaos in a Pulse Width Modulation Controlled Buck Converter. Proceedings of the 6th EUROSIM Congress on Modelling and Simulation, (2007), pp. 1–6.Angulo, Fabiola and Fossas, Enric and Olivar, Gerard. Transition From Periodicity To Chaos In A Pwm-Controlled Buck Converter With Zad Strategy. Int. J. Bifurcation and Chaos, Vol. 15, No. 10, pp. 3245–3264, (2009).Fossas, E and Hogan, S. J. and Seara,T. M. Two-parameter bifurcation curves in power electronic converters. Int. J. Bifurcation and Chaos, Vol. 19, pp. 349–357, (2009).Angulo Fabiola. Análisis de la dinámica de convertidores electrónicos de potencia usando PWM basado en promediado cero de la dinámica del error (ZAD). Tesis de doctorado, UPC. Mayo de (2004).Fossas E., Gri˜n´o R. and Biel D. Quasi-sliding control based on pulse width modulation, zero average and the L2 norm. In Advances in Variable Structure System, Analysis, Integration and Applications. Ed. World Scientific. (2001), pp. 335–344.Cevantes, I. and Alvarez-Ramirez, J. A simple chaos control strategy for DC-DC power converters. Industrial Electronics Society, Vol. 1, pp. 193– 198, (2004). IECON 2004.Pyragas, K. Continuous control of chaos by self-controlling feedback. Physics Letters, Vol. A, No. 170, pp. 421–428, (1992).Angulo F. Burgos J.E. and Olivar G. Chaos Stabilization with TDAS and FPIC in a Buck Converter controlled by Lateral PWM and ZAD. Mediterranean Conference on Control and Automation, (2007).Angulo, F. Fossas, E. Olivar, G T´ecnica ZAD Aplicada a un Convertidor Buck: An´alisis de Estabilidad y de Transici´on al Caos. Revista Iberoamericana de Autom´atica e Inform´atica Industrial, Vol. 2, No. 4. October (2005), pp. 25–35.Angulo F. Fossas E. and Olivar G. Stabilization of Chaos with FPIC: Application to ZAD-Strategy Buck Converters. 16th IFAC World Congress, Prague, (2005).Angulo F. Olivar G. Taborda J. A. and Hoyos, F. E. Nonsmooth dynamics and FPIC chaos control in a DC-DC ZAD-strategy power converter. Proceeding of the VI EUROMECH Nonlinear Dynamics Conference ENOC, Saint Petersburg, Russia, (2008).Fossas, E. and Zinober, A. Adaptive Tracking Control of Nonlinear Power Converters. Proceedings IFAC Workshop on Adaptation in Control and Signal Processing, Connobio, Italia, pp. 264–266, (2001).Carpita, M. and Marchesoni, M. and Oberti, M. and Puglisi, L. Power conditioning system using sliding model control. Power Electronics Specialists Conference (PESC’88 Record), 19th Annual IEEE, Kyoto, Japan, pp. 626– 633, (1988).Parker T.S. and Chua L.O. Practical numerical algorithms for chaotic systems. Springer Verlag, New York. (1989). pp. 66–81.Derechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2ZAD strategy with lateral PWM applied to a boost converterArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Boost converterZADBifurcationsChaos ControlPublication77636374-92e2-4d63-9b49-bdb0a2ea1182virtual::2356-177636374-92e2-4d63-9b49-bdb0a2ea1182virtual::2356-1https://scholar.google.com/citations?user=7Pqx31YAAAAJ&hl=esvirtual::2356-10000-0002-3773-0598virtual::2356-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000828963virtual::2356-1TEXTA0270_ZAD strategy with lateral PWM applied to a boost converter.pdf.txtA0270_ZAD strategy with lateral PWM applied to a boost converter.pdf.txtExtracted texttext/plain28596https://red.uao.edu.co/bitstreams/dcc744f3-5731-4c85-aad8-beeedb0837ea/download6c7a7e1e10aed653fdd51990852e4863MD55THUMBNAILA0270_ZAD strategy with lateral PWM applied to a boost converter.pdf.jpgA0270_ZAD strategy with lateral PWM applied to a boost converter.pdf.jpgGenerated Thumbnailimage/jpeg14663https://red.uao.edu.co/bitstreams/1635ce72-25c3-4f9a-8225-ea17319568c6/downloadb76ac9a75125387cd7d5a7fc75ac6b5cMD56CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/b9077950-d709-401e-b7de-a158b9ba5ff0/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/95b2fc06-cfe9-41c8-ae7a-acc79a27bc76/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALA0270_ZAD strategy with lateral PWM applied to a boost converter.pdfA0270_ZAD strategy with lateral PWM applied to a boost converter.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf1083184https://red.uao.edu.co/bitstreams/5e5223a9-1612-42d0-8b42-84870a15a263/downloada031acd9d938c9391e6188037171f6daMD5410614/11942oai:red.uao.edu.co:10614/119422024-03-06 14:58:47.839https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidenteopen.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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