Abstract—This paper considers special functioning modes of a buck converter under closed loop feedback, which, depending on the type of a regulator, are characterized by the appearance of bifurcations which are transformed into the chaotic mode, or by undamped oscillations. The paper presents a simple and compact mathematical model. The model is implemented in the Matlab program, which makes it possible to carry out various calculations, including the cyclic ones, followed by graphic and numerical data processing. For normalizing the performance of buck converters, a new method of synchronizing the occurring modes proposed, and its efficiency is tested for various regulators in a feedback system. The accuracy of the proposed mathematical model, and of the adequacy of the obtained results, are tested by the Matlab-Simulink program.

Index Terms—Buck converter, control, bifurcation, chaos.

Yuval Beck is with School of Electrical Engineering, Tel Aviv University (TAU), P.O. Box 39040, Tel Aviv 69978, Israel. Yefim Berkovich is with Department of Electrical Engineering, Holon Institute of Technology, 52 Golomb st., Holon, 58102, Israel.

Cite:Yuval Beck, Yefim Berkovich, "Modes of Bifurcations, Chaos, and Undamped Oscillations in a Buck Converter with Feedback and Their Synchronizing," International Journal of Computer and Electrical Engineering vol. 11, no. 4, pp. 164-174, 2019.