Quasiperiodicity and chaos in the DC-DC Buck-Boost converter

This paper is concerned with the study of nonlinear phenomena in a closed loop voltage-controlled DC-DC Buck-Boost converter when suitable parameters are varied. The dynamics is analyzed using both the continuous-time model and the numerically computed stroboscopic map. The analysis of the one-dimensional bifurcation diagram shows that Neimarck-Sacker bifurcation occurs at certain values of the parameters. Phase-locking periodic windows, the period-adding sequence, and transition from quasiperiodicity to period-doubling via torus breakdown are also obtained. The two-dimensional bifurcation diagram is carefully computed. This shows that phase-locking orbits produce so-called Arnold tongues in the parameter space. It is shown that the winding number plotted as a function of the bifurcation parameter is a devil's staircase. As typically occurs in general circle maps, the fine structures of the Arnold tongues and the devil's staircase show self-similarity.