Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 526394, 19 pages
Research Article

Quantization Effects on Period Doubling Route to Chaos in a ZAD-Controlled Buck Converter

1Universidad del Magdalena, Facultad de Ingeniería, Programa de Ingeniería Electrónica, Magma Ingeniería, Carrera 32 No 22 - 08 Santa Marta, Colombia
2Percepción y Control Inteligente, Departamento de Ingeniería Eléctrica, Electrónica y Computación, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia Sede Manizales, Bloque Q, Campus La Nubia, Manizales 170003, Colombia

Received 2 February 2012; Accepted 31 July 2012

Academic Editor: Cristian Toma

Copyright © 2012 John Alexander Taborda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The quantization effect in transitions to chaos and periodic orbits is analyzed in this paper through a specific application, the zero-average-dynamics- (ZAD-) controlled buck power converter. Several papers have studied the quantization effects in the one periodic orbit and some authors have given guidelines to design digitally controlled power converter avoiding limit cycles. On the other hand many studies have been devoted to analyze the ZAD-controlled buck power converter, but these past studies did not include hardware considerations. In this paper, analog-to-digital conversion process is explicitly introduced in the modeling stage. As the feedback gain is varied, the dynamic behavior depending on the analog-to-digital converter resolution is numerically analyzed. Particularly, it is observed that including the quantizer in the model carries out several changes in the transitions to chaos, which include interruption of band-merging process by cascades of periodic inclusions, disappearing of band transitions, and multiple coexisting of periodic orbits. Many of these phenomena have not been reported as a consequence of the quantization effects.