Skip to main content
SpringerLink
Log in

Using Bifurcation Diagrams for Controlling Chaos

  • Conference paper
  • First Online:
Applied Non-Linear Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 93))

  • 2647 Accesses

Abstract

In this chapter, a methodology to compute chaos controllers based on bifurcation diagrams is proposed and applied to PWM-controlled power converters. The technique is based on an adaptive control where the offset of the T-periodic sawtooth signal is modified. Basically, the sawtooth is redefined as a function of the output and reference voltages. This control technique reduces the percentage of regulation error as well as eliminates orbits of period greater than one and the chaotic behavior when the voltage source is varied. Finally, numerical results are obtained to validate the performance of the proposed scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bouzahir, H., El Guezar, F., El Aroudi, A., Ueta, T.: Partial time delayed feedback control of chaos in a hybrid model of a DC–DC converter. In: Proceedings of 3rd International Symposium on Communications, Control and Signal Processing, 2008. doi:10.1109/ISCCSP.2008.4537211

  2. Deane, J.H.B., Hamill, D.C.: Analysis, simulation and experimental study of chaos in the buck converter. In: Proceedings of 21st Annual IEEE Power Electronics Specialists Conference, PESC’90, 1990. doi:10.1109/PESC.1990.131228

  3. El Aroudi, A., Debbat, M., Giral, R., Olivar, G., Benadero, L., Toribio, E.: Bifurcations in DC-DC switching converters: review of methods and applications. Int. J. Bifurcat. Chaos Appl. Sci. Eng. 15, 1549–1578 (2005). doi:10.1142/S0218127405012946

    Article  MATH  Google Scholar 

  4. Giaouris, D., Banerjee, S., Zahawi, B., Pickert, V.: Stability analysis of the continuous-conduction-mode buck converter Via Filippov’s method. IEEE Trans. Circ. Syst. I Regular Papers 55(4), 1084–1096 (2008). doi:10.1109/TCSI.2008.916443

    Article  MathSciNet  Google Scholar 

  5. Karppanen, M., Suntio, T., Sippola, M.: Dynamical characterization of input-voltage-feedforward-controlled buck converter. IEEE Trans. Ind. Electron 54, 1005–1013 (2007). doi:10.1109/TIE.2007.892732

    Article  Google Scholar 

  6. Liyu, Y., Jinseok, P., Huang, A.Q.: An adaptive external ramp control of the peak current controlled Buck converters for high control bandwidth and wide operation range. In: Proceedings of 25th Annual IEEE Applied Power Electronics Conference and Exposition, APEC’2010, 2010. doi:10.1109/APEC.2010.5433539

  7. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett 64, 1196–1199 (1990). doi:10.1103/PhysRevLett.64.1196

    Article  MathSciNet  MATH  Google Scholar 

  8. Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421–428(1992). http://dx.doi.org/10.1016/0375-9601(92)90745-8

  9. Samosir, A.S., Yatim, A.H.M.: Dynamic evolution control for synchronous buck DC-DC converter: theory, model and simulation. Simul. Model. Pract. Theory 18(5), 663–676 (2010). http://dx.doi.org/10.1016/j.simpat.2010.01.010

  10. Xiaohui, Q., Siu-Chung, W., Tse, C.K.: Resonant assisted buck converter for offline driving of high brightness LED replacement lamps. In: Proceedings of 2010 IEEE Energy Conversion Congress and Exposition (ECCE), 2010. doi:10.1109/ECCE.2010.5618054

Download references

Acknowledgements

This work was partially supported by Universidad Nacional de Colombia - Manizales, project 12475, Vicerrectoría de Investigación, DIMA, and Programa Jóvenes Investigadores e Innovadores 2011 (COLCIENCIAS) convenio No. 0043 de 2012.

Author information

Authors and Affiliations

  1. Department of Ingeniería Eléctrica, Electrónica y Computación, Universidad Nacional de Colombia, Campus La Nubia, Manizales, Colombia

    Daniel Morcillo, Fabiola Angulo & Gerard Olivar

  2. Department of Systems and Computer Sciences, University of Naples Federico II, Via Claudio 21, 80125, Napoli, Italy

    Daniel Burbano

Authors
  1. Daniel Morcillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Burbano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fabiola Angulo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gerard Olivar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Morcillo .

Editor information

Editors and Affiliations

  1. Department of Automation, Biomechanics and Mechatronics, Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Morcillo, D., Burbano, D., Angulo, F., Olivar, G. (2014). Using Bifurcation Diagrams for Controlling Chaos. In: Awrejcewicz, J. (eds) Applied Non-Linear Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-319-08266-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation