Investigation of the Mechanism of Tangent Bifurcation in Current Mode Controlled Boost Converter

ABSTRACT

Tangent bifurcation is a special bifurcation in nonlinear dynamic systems. The investigation of the mechanism of the tangent bifurcation in current mode controlled boost converters operating in continuous conduction mode (CCM) is performed. The one-dimensional discrete iterative map of the boost converter is derived. Based on the tangent bifurcation theorem, the conditions of producing the tangent bifurcation in CCM boost converters are deduced mathematically. The mechanism of the tangent bifurcation in CCM boost is exposed from the viewpoint of nonlinear dynamic systems. The tangent bifurcation in the boost converter is verified by numerical simulations such as discrete iterative maps, bifurcation map and Lyapunov exponent. The simulation results are in agreement with the theoretical analysis, thus validating the correctness of the theory.

Tangent bifurcation is a special bifurcation in nonlinear dynamic systems. The investigation of the mechanism of the tangent bifurcation in current mode controlled boost converters operating in continuous conduction mode (CCM) is performed. The one-dimensional discrete iterative map of the boost converter is derived. Based on the tangent bifurcation theorem, the conditions of producing the tangent bifurcation in CCM boost converters are deduced mathematically. The mechanism of the tangent bifurcation in CCM boost is exposed from the viewpoint of nonlinear dynamic systems. The tangent bifurcation in the boost converter is verified by numerical simulations such as discrete iterative maps, bifurcation map and Lyapunov exponent. The simulation results are in agreement with the theoretical analysis, thus validating the correctness of the theory.

KEYWORDS

Tangent Bifurcation, Discrete Iterative Map, Boost Converter, Continuous Current Mode (CCM)

Tangent Bifurcation, Discrete Iterative Map, Boost Converter, Continuous Current Mode (CCM)

Cite this paper

nullL. Xie, R. Gong, K. Wang and H. Zhuo, "Investigation of the Mechanism of Tangent Bifurcation in Current Mode Controlled Boost Converter,"*Circuits and Systems*, Vol. 2 No. 1, 2011, pp. 38-44. doi: 10.4236/cs.2011.21007.

nullL. Xie, R. Gong, K. Wang and H. Zhuo, "Investigation of the Mechanism of Tangent Bifurcation in Current Mode Controlled Boost Converter,"

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[17] B. Basak and S. Parui, “Exploration of Bifurcation and Chaos in Buck Converter Supplied from a Rectifier,” IEEE Transactions on Power Electronics, Vol. 25, No. 6, 2010, pp. 1556-1564. doi:10.1109/TPEL.2009.2035500

[18] F.-H. Hsieh, K.-M. Lin and J.-H. Su, “Chaos Phenomenon in UC3842 Cur-rent-Programmed Flyback Converters,” Proceedings IEEE Conference on Industrial Electronics and Applications, Xi’an, 25-27 May 2009, pp. 166-171.

[19] J. H. Chen, K. T. Chau and C. C. Chan, “Analysis of Chaos in Current-Mode-Controlled DC Drive Systems,” IEEE Transactions on Industrial Electronics, Vol. 47, No. 1, 2000, pp. 67-76. doi:10.1109/41.824127

[20] K. W. E. Cheng, M. J. Liu and Y. L. Ho, “Experimental Confirmation of Frequency Correlation for Bifurcation in Current-Mode Controlled Buck-Boost Converters,” IEEE Power Electronics Letters, Vol. 1, No. 4, 2003, pp. 101-103. doi:10.1109/LPEL.2004.825548

[1] F. Angulo, G. Olivar and M. di Bernardo, “Two-Pa- rameter Discontinuity-Induced Bifurcation Curves in a ZAD-Strategy-Controlled DC–DC Buck Converter,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, No. 8, 2008, pp. 2393-2401. doi:10.1109/TCSI. 2008.918226

[2] X. Q. Wu, S.-C. Wong, C. K. Tse and J. Lu, “Bifurcation Behavior of SPICE Simulation of Switching Converters: A Systematic Analysis of ErroneousResults,” IEEE Transactions on Power Electronics, Vol. 22, No. 5, 2007, pp. 1743-1752. doi:10.1109/TPEL.2007.904207

[3] A. El Aroudi and R. Lewa, “Quasi-Periodic Route to Chaos in a PWM Voltage-Controlled DC-DC Boost Converter,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 48, No. 8, 2001, pp. 967-978. doi:10.1109/81.940187

[4] Ch. Bi, J. M. Wang, Z. W. Lan, K. L. Jia and T. Hu, “Investigation of Bifurcation and Chaos in Forward Converter,” Proceedings International Conference on Mechatronics and Automation, Harbin, 5-8 August 2007, pp. 663-668. doi:10.1109/ICMA.2007.4303622

[5] X.-M. Wang, B. Zhang and D.-Y. Qiu, “Mechanism of Period-Doubling Bifurcation in DCM DC-DC Converter,” Acta Physica Sinice, Vol. 57, No. 6, 2008, pp. 2728-2736.

[6] A. Kavitha and G. Uma, “ Experimental Verification of Hopf Bifurcation in DC-DC Luo Converter,” IEEE Transactions on Power Electronics, Vol. 23, No. 6, 2008, pp. 2878-2883. doi:10.1109/TPEL.2008.2004703

[7] M. B. D’Amico, J. L. Moiola and E. E. Paolini, “Hopf Bifurcation for Maps: A Frequency-Domain Approach,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 49, No. 3, 2002, pp. 281-288. doi:10.1109/81.989161

[8] M. Debbat, A. El Aroud, R. Giral and L. Martinez-Salamero, “Hopf Bifurcation in PWM Controlled Asymmetrical Interleaved Dual Boost DC-DC Converter,” Proceedings IEEE International Conference on Industrial Technology, Vol. 2, Maribor, 10-12 December 2003, pp. 860-865.

[9] Z. T. Zhusubaliyev, E. A. Soukhoterin and E. Mosekilde, “Quasi-Periodicity and Bor-der-Collision Bifurcations in a DC-DC Converter with Pulse-width Modulation,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 50, No. 8, 2003, pp. 1047- 1057. doi:10.1109/TCSI.2003.815196

[10] M. Yue, C. K. Tse, T. Kousaka and H. Kawakami, “Connecting Border Collision with Saddle-Node in Switched Dynamical Systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 52, No. 9, 2005, pp. 581-585. doi:10.1109/TCSII.2005.850488

[11] H. Khammari and M. Benrejeb, “Tangent Bifurcation in Doubling Period Process of a Resonant Circuit’s Responses,” Proceedings IEEE International Conference on Industrial Technology, Vol. 3, Hammamet, 8-10 December 2004, pp. 1281-1286.

[12] Y. F. Zhou and J. N. Chen, “Tangent Bifurcation and Intermittent Chaos in Current-Mode Controlled Boost Converter,” Proceedings of the Chinese Society for Electrical Engineering, Vol.25, No.1, 2005, pp. 23-26.

[13] B. L. Hao, “Starting with Parabolas, an Intro-duction to Chaotic Dynamics,” Shanghai Scientific and Tech-nological Education Publishing House, Shanghai, 1993.

[14] R. C. Robinson, “An Introduction to Dynamical Systems: Conti-nuous and Discrete,” Pearson Prentice Hall, New Jersey, 2004.

[15] C. K. Tse, “Flip Bifimcation and Chaos in the Three- State Boost Switching Regulars,” IEEE Transactions on Circuits Systems I: Fundamental Theory and Applica-tions, Vol. 41, No. 1, 1994, pp. 16-23. doi:10.1109/81.260215

[16] C. K. Tse and M. di Bernardo, “Complex Behavior in Switching Power Converters,” Pro-ceedings of the IEEE, Vol. 90, No. 5, 2002, pp. 768-781. doi:10.1109/JPROC. 2002.1015006

[17] B. Basak and S. Parui, “Exploration of Bifurcation and Chaos in Buck Converter Supplied from a Rectifier,” IEEE Transactions on Power Electronics, Vol. 25, No. 6, 2010, pp. 1556-1564. doi:10.1109/TPEL.2009.2035500

[18] F.-H. Hsieh, K.-M. Lin and J.-H. Su, “Chaos Phenomenon in UC3842 Cur-rent-Programmed Flyback Converters,” Proceedings IEEE Conference on Industrial Electronics and Applications, Xi’an, 25-27 May 2009, pp. 166-171.

[19] J. H. Chen, K. T. Chau and C. C. Chan, “Analysis of Chaos in Current-Mode-Controlled DC Drive Systems,” IEEE Transactions on Industrial Electronics, Vol. 47, No. 1, 2000, pp. 67-76. doi:10.1109/41.824127

[20] K. W. E. Cheng, M. J. Liu and Y. L. Ho, “Experimental Confirmation of Frequency Correlation for Bifurcation in Current-Mode Controlled Buck-Boost Converters,” IEEE Power Electronics Letters, Vol. 1, No. 4, 2003, pp. 101-103. doi:10.1109/LPEL.2004.825548