Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 732039, 20 pages
Research Article

Bounding the Output Error in a Buck Power Converter Using Perturbation Theory

Fabiola Angulo,1 Enric Fossas,2 Tere M. Seara,3 and Gerard Olivar1

1Departamento de Ingeniería Eléctrica, Electrónica y Computación, Universidad Nacional de Colombia, Cra 27 No. 64-60 Manizales, Caldas, Colombia
2Institute of Industrial and Control Engineering, Technical University of Catalonia, 08028 Barcelona, Spain
3Departamento de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

Received 20 January 2008; Revised 30 May 2008; Accepted 20 July 2008

Academic Editor: Oleg Gendelman

Copyright © 2008 Fabiola Angulo 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.


We show the main results obtained when applying the average theory to Zero Average Dynamic control technique in a buck power converter with pulse-width modulation (PWM). In particular, we have obtained the bound values for output error and sliding surface. The PWM with centered and lateral pulse configurations were analyzed. The analytical results have confirmed the numerical and experimental results already obtained in previous publications. Moreover, through an important lemma, we have generalized the theory for any stable second-order system with relative degree 2, using properties related to transformations and stability of linear systems.