Study of bifurcations in current-programmed DC/DC boost converters: from quasiperiodicity to period-doubling
- 1 January 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems I: Regular Papers
- Vol. 44 (12), 1129-1142
- https://doi.org/10.1109/81.645154
Abstract
This paper studies the bifurcation paths exhibited by a simple second-order dc/dc boost converter under current-programmed control with and without voltage feedback. Previous work in this area has reported two distinct types of bifurcation paths, namely via regions of quasi-periodic orbits and perioddoubling. This paper demonstrates that the two different types of bifurcation paths can, in fact, be viewed as part of another bifurcation in which the quasi-periodic sequence transmutes into the period-doubling sequence, and that such a bifurcation is observed regardless of the presence of the outer voltage feedback loop as long as a suitable set of bifurcation parameters is chosen. The describing iterative map is derived in closed form and is used to develop the main results via a series of computer experiments. The characteristic multipliers are calculated and the first onset of flip-bifurcation is predicted. Computer simulation based on an exact piecewise switched model confirms the predicted bifurcations. The exhibition of quasi-periodic orbits is confirmed by computation of the Lyapunov exponent. Finally, a series of return maps are generated to provide an alternative viewpoint to the reported bifurcations in terms of a transmutation from a tent-like map to a logistic-like map.Department of Electronic and Information EngineerinKeywords
This publication has 13 references indexed in Scilit:
- Studies of routes to chaos for current-programmed DC/DC convertersPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- A chaos model of subharmonic oscillations in current mode PWM boost convertersPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Switching time bifurcations in a thyristor controlled reactorIEEE Transactions on Circuits and Systems I: Regular Papers, 1996
- Chaos from a current‐programmed ćuk converterInternational Journal of Circuit Theory and Applications, 1995
- Chaos and FractalsPublished by Springer Science and Business Media LLC ,1992
- Chaos in a current-mode controlled boost DC-DC converterIEEE Transactions on Circuits and Systems I: Regular Papers, 1992
- Practical Numerical Algorithms for Chaotic SystemsPublished by Springer Science and Business Media LLC ,1989
- Topics in Multiple-Loop Regulators and Current-Mode ProgrammingIEEE Transactions on Power Electronics, 1987
- An Analytical Investigation of Current-Injected Control for Constant-Frequency Switching RegulatorsIEEE Transactions on Power Electronics, 1986
- Determining Lyapunov exponents from a time seriesPhysica D: Nonlinear Phenomena, 1985