Abstract

In this paper, bifurcation analysis of current mode control C´ uk DCDC converter operating in continuous conduction mode is carried out. Nonlinear discrete maps as much for 1-periodic orbit as for 2- periodic orbit have been built. The stability analysis of both orbits is concerned using the Jacobian matrix and its eigenvalues. When the reference current is taken as a bifurcation parameter, it has been shown that the 1-periodic orbit loses its stability via flip bifurcation and the resulting is a stable 2-periodic orbit. By increasing the reference current further more, the 2-periodic orbit collides with a borderline and bifurcates to chaos via border collision bifurcation. A closed form expression of the borderline has been calculated.

References

• J. H. Deane and D. C. Hamill, "Chaotic behaviour in current mode controlled DC–DC converter," Electronics Letters, vol. 27, pp. 1172–1173, 1991.
• M. di Bernardo, F. Grofalo, L. Glielmo, and F. Vasca, "Quasiperiodic behaviors in DC–DC converters," in PESC'96: Power Electronics Specialist Conferences, pp. 1376–1381, 1996.
• K. W. E. Cheng, M. Liu, J. Wu, and N. C. Cheung, "Study of bifurcation and chaos in the current- mode controlled buck-boost DC–DC converter," in IECON'01: Industrial Electronics Society Conference. , pp. 838–343, 2001.
• A. E. Aroudi, M. B. Debbat, and L. Mart´?nez-Salamero, "Poincar´e maps modeling and local orbital stability analysis of discontinuous piecewise affine periodically driven systems," Nonlinear Dynamics, vol. 50, pp. 431–445, 2007.
• C. K. Tse, S. C. Fung, and M. W. Kwan, "Experimental confirmation of chaos in a current-programmed C´ uk converter," IEEE Trans. on Circuits and Systems-I, vol. 43, pp. 605–608, 1996.
• C. Y. William and C. K. Tse, "Study of bifurcations in current-programmed DC–DC converters: From quasiperiodicity to period-doubling," IEEE Trans. on Circuits and Systems-I, vol. 44, pp. 1129–1142, 1997.
• C. K. Tse, Y. M. Lai, and H. H. C. Iu, "Hopf bifurcation and chaos in a free-running autonomous uk converter," IEEE Trans. on Circuits and Systems-I, vol. 47, pp. 448–457, 2000.
• C. M. Ivan, D. Lascu, and V. Popescu, "Hopf bifurcation in a discontinuous capacitor voltage mode uk DC– DC converter," in The 6th WSEAS International Conference on Instrumentation, Measurement, Circuits and Systems, (Hangzhou), pp. 431–445, 2007.
• G. Verghese, M. Elbuluk, , and J. Kassakian, "A general approach to sample-data modeling for power electronic circuits," IEEE Transactions on Power Electronics, vol. 1, no. 2, pp. 76–89, 1986.
• M. B. Debbat, A. E. Aroudi, R. Giral, and L. Mart´?nez- Salamero, "Stability analysis and bifurcations of sepic DC–DC converter using a discrete-time model," in ICIT'02: International Conference on Industrial Technology, (Bangkok), pp. 1055–1060, 2002.
• W. Ma, M. Wang, and C. Li, "Control of bifurcation in the one-cycle controlled cuk converter," Nonlinear Dynamics, vol. 67, pp. 2573–2583, March 2012.
• M. di Bernardo, F. Garofalo, L. Glielmo, and F. Vasca, "Switchings, bifurcations and chaos in dc-dc converters," IEEE Trans. on Circuits and Systems-I, vol. 45, no. 2, pp. 133–141, 1998.
• Z. T. Zhusubaliyev, E. Soukhoterin, and E. Mosekilde, "Quasiperiodicity and border-collision bifurcations in a dcdc converter with pulsewidth modulation," IEEE Trans. on Circuits and Systems-I, vol. 50, pp. 1047–1057, August 2003.
• A. E. Aroudi, E. Rodriguez, R. Leyva, and E. Alarcon, "A design-oriented combined approach for bifurcation prediction in switched-mode power converters," IEEE Trans. on Circuits and Systems-II, vol. 57, pp. 218–222, 2010.
• M. Sattler, "Analysis of bifurcation behavior in power converters and the impact on the design process," in ESTS'11: IEEE Electric Ship Technologies Symposium, (Alexandria, VA), pp. 203–206, 2011.