Skip to main content
Log in

Robust Feedback Stabilization of Limit Cycles in PWM DC-DC Converters

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Local feedback stabilization of limit cycles in PWM DC-DC converters isconsidered, using recently developed general sampled-data models. Thepaper focuses on converters for which the nominal operating conditionhas lost stability due to off-design operation. The results apply tostabilization of the nominal periodic operating condition. In addition,the same approach can be used to stabilize other limit cycles such asthose embedded in a possible chaotic trajectory. Two feedbackstabilization schemes are proposed and studied in detail. The firststabilization technique uses voltage reference compensation and thesecond uses dynamic ramp compensation. Both employ discrete-time washoutfilters to ensure preservation of the size and shape of the limit cycle.Washout filters ensure that the nominal operating branch is unaffectedby the control, without the need for accurate knowledge of the limitcycle.

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. Abed, E., Wang, H., and Chen, R., 'Stabilization of period doubling bifurcations and implications for control of chaos', Physics D 70(1-2), 1994, 154-164.

    Google Scholar 

  2. Aston, P., Deane, J., and Hamill, D., 'Targeting in systems with discontinuities, with applications to power electronics', IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 44(10), 1997, 1034-1039.

    Google Scholar 

  3. Banerjee, S., Ott, E., Yorke, J. A., and Yuan, G. H., 'Anomalous bifurcations in DC-DC converters: Borderline collisions in piecewise smooth maps', in IEEE Power Electronics Specialists Conference Record, IEEE, New York, 1997, pp. 1337-1344.

    Google Scholar 

  4. Batlle, C., Fossas, E., and Olivar, G., 'Time-delay stabilization of the buck converter', in Proceedings International Conference, Control of Oscillations and Chaos, Vol. 3, F. L. Chernousko and A. L. Fradkov (ed.), IEEE, New York, 1997, pp. 590-593.

    Google Scholar 

  5. Deane, J., 'Chaos in a current-mode controlled boost DC-DC converter', IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 39(8), 1992, 680-683.

    Google Scholar 

  6. Deane, J. and Hamill, D., 'Instability, subharmonics, and chaos in power electronics circuits', IEEE Transactions on Power Electronics 5(3), 1990, 260-268.

    Google Scholar 

  7. Fang, C.-C., 'Sampled-data analysis and control of DC-DC switching converters', Ph.D. Thesis, University of Maryland, College Park, 1997. Available: www.isr.umd.edu/TechReports/ISR/1997/.

    Google Scholar 

  8. Fang, C.-C. and Abed, E., 'Sampled-data modeling and analysis of PWM DC-DC converters I. Closed-loop circuits', Technical Report 98-54, Institute for Systems Research, University of Maryland, College Park, 1998. Available: www.isr.umd.edu/TechReports/ISR/1998/. Summarized in 'Sampled-data modeling and analysis of closed-loop PWM DC-DC converters', IEEE International Symposium on Circuits and Systems 5, 1998, 110-115.

    Google Scholar 

  9. Hamill, D., Deane, J., and Jefferies, J., 'Modeling of chaotic DC-DC converters by iterated nonlinear mappings', IEEE Transactions on Power Electronics 7(1), 1992, 25-36.

    Google Scholar 

  10. Kailath, T., Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.

    Google Scholar 

  11. Krein, P. and Bass, R., 'Types of instability encountered in simple power electronic circuits: Unboundedness, chattering, and chaos', in Applied Power Electronics Conference and Exposition, IEEE, New York, 1990, pp. 191-194.

    Google Scholar 

  12. Mohan, N., Undeland, T., and Robbins,W., Power Electronics: Converters, Applications, and Design, Wiley, New York, 1995.

    Google Scholar 

  13. Ott, E., Chaos in Dynamical Systems, Cambridge University Press, New York, 1993.

    Google Scholar 

  14. Ott, E., Grebogi, C., and Yorke, J., 'Controlling chaos', Physical Review Letters 84(11), 1990, 1196-1199.

    Google Scholar 

  15. Poddar, G., Chakrabarty, K., and Banerjee, S., 'Control of chaos in DC-DC converters', IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 45(6), 1998, 672-676.

    Google Scholar 

  16. Podder, G., Chakrabarty, K., and Banerjee, S., 'Control of chaos in the boost converter', Electronics Letters 31(11), 1995, 25.

    Google Scholar 

  17. Podder, G., Chakrabarty, K., and Banerjee, S., 'Experimental control of chaotic behavior of buck converter', IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 42(8), 1995, 100-101.

    Google Scholar 

  18. Tse, C., 'Flip bifurcation and chaos in three-state boost switching regulators', IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 41(1), 1994, 16-23.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fang, CC., Abed, E.H. Robust Feedback Stabilization of Limit Cycles in PWM DC-DC Converters. Nonlinear Dynamics 27, 295–309 (2002). https://doi.org/10.1023/A:1014402431119

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014402431119

Navigation