Skip to main content
Log in

Nonlinear and nonsmooth dynamics in a DC-DC Buck converter: Two experimental set-ups

  • Original Article
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

It is well known that many nonlinear phenomena such as bifurcations and chaotic behavior occur in DC–DC converters mainly due to the switching action among all the different topologies of the circuit. Such behavior has been described with detail numerically, and also mathematical reasoning has been provided. In this paper we focuss on the experimental side of a DC–DC Buck converter controlled with two different strategies: classical Pulse Width Modulation (PWM) with a ramp and a more recently described Zero Average Dynamics (ZAD). We show some nonsmooth events and we explain with detail the experimental set-ups. In one of them, we use a FPGA card to obtain on-line results. In the other we use Virtual Instrumentation to generate an experimental two-dimensional bifurcation diagram, which will be compared to the numerical data. After the data acquisition of the system state variables some elaborated post-processing must be made. This is done through LabView. Although the main application of these results is centered in avoiding non-periodic or high-amplitude periodic behavior, they can also be applied to reducing the generated electro-magnetic interference and to the information transmission.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hamill, D.C.: Power electronics: A field rich in nonlinear dynamics. In: Proceedings of the 3rd International Specialists Workshop on Nonlinear Dynamics of Electronic Systems NDES’95, pp. 165–178 (1995)

  2. Deane, J.H.B., Hamill, D.C.: Improvement of power supply EMC by chaos. Electronic Letters 32(12), (1996)

  3. Deane, J.H.B., Ashwin, P., Hamill, D.C., Jefferies, D.J.: Calculation of the periodical spectral components in a chaotic DC–DC converter. IEEE Transactions. Circuits Systems I Fundamental Theory and Applications 46, 1313–1319 (1999)

    Article  Google Scholar 

  4. Chakrabarty, K., Banerjee, S.: Control of chaos in piecewise linear systems with switching nonlinearity. Phys. Letters A 200, 115–120 (1995)

    Article  Google Scholar 

  5. Batlle, C., Fossas, E., Olivar, G.: Stabilization of periodic orbits in variable structure systems. Application to DC–DC power converters. Int. J. Bifur. Chaos. Appl. Sci. and Eng. 6(12B), 2635–2643 (1996)

    Article  Google Scholar 

  6. Deane, J.H.B., Hamill, D.C.: Analysis, simulation and experimental study of chaos in the buck converter. In: IEEE Power Electronics Specialists Conference, pp. 491–498 (1990)

  7. Biel, D., Fossas, E., Ramos, R., Sudria, A.: Programmable logic device applied to the quasi-sliding control implementation based on zero averaged dynamics. In: Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 2, pp. 1825–1830 (2001)

  8. Hasler, M.: Tutorial 6: Chaos from basic concepts to engineering applications. In: Proceedings of ISCAS’94, pp. 287-364 (1994)

  9. Carroll, T.L., Peccora, L.M. (eds.): Nonlinear Dynamics in Circuits, World Scientific, Singapore (1995)

  10. Verghese, G., Banerjee, S. (eds.): Nonlinear Phenomena in Power Electronics, IEEE Press, Piscataway, NJ (2001)

  11. Fossas, E., Olivar, G.: Study of Chaos in the Buck Converter. IEEE Transactions on Circuits Systems I Fundamental Theory and Applications 43(1), 13–25 (1996)

    Article  Google Scholar 

  12. Chakrabarty, K., Poddar, G., Banerjee, S.: Bifurcation behavior of the buck converter. IEEE Transactions on Power Electronics 11(3), 439–447 (1996)

    Article  Google Scholar 

  13. di Bernardo, M., Fossas, E., Olivar, G., Vasca, F.: Secondary bifurcations and high periodic orbits in voltage controlled buck converter. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 7(12), 2755–2771 (1997)

    Article  MATH  Google Scholar 

  14. Olivar, G.: Chaos in the Buck Converter. Ph. D. Thesis, Technical University of Catalonia, Barcelona (1997)

  15. di Bernardo, M., Budd, C., Champneys, A.: Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC–DC buck converter. Nonlinearity 11(4), 858–890 (1998)

    Article  MathSciNet  Google Scholar 

  16. Banerjee, S.: Coexisting attractors, chaotic saddles, and fractal basins in a power electronic circuit. IEEE Transactions on Circuits Systems I Fund. Theory Appl. 44(9), 847–849 (1997)

    Google Scholar 

  17. Angulo, F.: Dynamical analysis of PWM-controlled power electronic converters based on the zero average dynamics (ZAD) strategy. (in Spanish)’, Ph. D. Thesis, Technical University of Catalonia, Barcelone (2004)

  18. Angulo, F., Fossas, E., Olivar, G.: Transition from periodicity to Chaos in a PWM-controlled buck converter with ZAD strategy. Int. J. of Bifur. Chaos (accepted for publication in October 2005)

  19. Ramos, R., Biel, D., Fossas, E., Guinjoan, F.: A fixed-frequency quasi-sliding control algorithm: Application to power inverters design by means of FPGA implementation. Power IEEE Trans. on Power Electron. 18(1), 344–355 (2003)

    Article  Google Scholar 

  20. Digilent Inc. Digilab 2 reference manual and digilab DIO1 reference manual. www.digilentinc.com. May 7 (2002)

  21. Ramos, R., Biel, D., Guinjoan, F., Fossas, E.: Distributed control strategy for parallel-connected inverters. sliding mode control approach and FPGA-based implementation. IEEE 2002 28th Annual Conference of the IECON 2002 (Industrial Electronics Society) 1, 111–116 (2002)

    Google Scholar 

  22. Ramos, R., Biel, D., Guinjoan, F., Fossas, E.: Design considerations in sliding-mode controlled parallel-connected inverters. IEEE International Symposium on Circuits and Systems, 2002. ISCAS 2002, 4, IV-357–IV-360 (2002)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gerard Olivar.

Additional information

Partially funded by SICONOS.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Angulo, F., Ocampo, C., Olivar, G. et al. Nonlinear and nonsmooth dynamics in a DC-DC Buck converter: Two experimental set-ups. Nonlinear Dyn 46, 239–257 (2006). https://doi.org/10.1007/s11071-006-9046-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-006-9046-8

Keywords

Navigation