Quasiperiodicity and Chaos in the Dc–dc Buck–boost Converter

Abstract

This paper is concerned with the study of nonlinear phenomena in a closed loop voltagecontrolled 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. *

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

“…The appearance of quasiperiodic dynamics has repeatedly been observed in recent numerical studies of various piecewise-smooth systems, 35,37,39,40,42,43,46 and it has been reported that such behavior can appear through a smooth Neimark-Sacker bifurcation as well as through a border collision bifurcation. Border-collision bifurcations are distinguished from the local bifurcations we know for smooth systems by the fact that the eigenvalues of the considered modes can make abrupt jumps in the complex plane.…”

“…Recent reviews on border-collision bifurcations in piecewise-smooth mechanical and power electronic systems have been published by Banerjee and Verghese, 33 Blazejczyk-Okolewska et al, 34 Leine and Nijmeijer, 35 Tse, 36 and Zhusubaliyev and Mosekilde. 37 Evidence from the study of a large number of physical systems, 35,[37][38][39][40][41][42][43] e.g., switching circuits, impact oscillators, accumulated over the years demonstrates that quasiperiodic dynamics regularly occurs in such systems. The onset of quasiperiodic behavior has been reported in impact oscillators by Piiroinen et al 43 This article discusses the changes in system behavior that arise as parameter variations lead to the appearance of grazing intersections between quasiperiodic attractor and a two-dimensional impact surface in a threedimensional state space.…”

Stability analysis of a feedback-controlled resonant DC-DC converter

“…The linear state equations for structure 1 in subperiod I using Table I are given in (6) and in dimensionless form in (7) (6) (7) where (8) and , , , , and . The state equation of structure 1 in matrix form is (9) State equations for structure 2 in subperiod I are given in (10) and they are presented in matrix form in (11) (10) where suffixes and stands for end and start, respectively. In short, (12) where the periodicity or transfer matrix (13) Multiplication of the starting value of the state variable by transforms in time forward to the end of the subperiod to calculate .…”

Chaotic Behavior in a Switched Dynamical System

“…Since then, chaos and nonlinear phenomena in power electronic circuits have stolen the spotlight and have attracted the attention of different research groups. Different nonlinear phenomena were investigated such as flip bifurcation or period doubling and its related route to chaos [3][4][5] or quasiperiodicity route to chaos [6,7] as well as border collision bifurcation [1-3, 6-16]. There are many modeling techniques, programming languages, and design toolsets for HDS.…”