Bifurcations in a Generalization of the ZAD Technique: Application to a DC‐DC Buck Power Converter

Ludwing Torres,Gerard Olivar,Simeón Casanova

doi:10.1155/2012/520296

Ludwing Torres, Gerard Olivar + Show 1 more

Open Access

https://doi.org/10.1155/2012/520296

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Abstract

A variation of ZAD technique is proposed, which is to extend the range of zero averaging of the switching surface (in the classic ZAD it is taken in a sampling period), to a number K of sampling periods. This has led to a technique that has been named K‐ZAD. Assuming a specific value for K = 2, we have studied the 2‐ZAD technique. The latter has presented better results in terms of stability, regarding the original ZAD technique. These results can be demonstrated in different state space graphs and bifurcation diagrams, which have been calculated based on the analysis done about the behavior of this new strategy.

Highlights

Power electronics has an important place in industry
Early works can be found in the literature from the 1980s when first observed in 3, 4
In the literature it was found that, for the classical ZAD strategy and centered pulse, stability of the T -periodic orbit was obtained in the range ks > 3.23, approximately

Summary

Introduction

Power electronics has an important place in industry. This is largely due to the very extensive number of applications derived from these systems, including control of power converters. A new technique, both conceptually different from sliding-mode control very related to it and as a practical implementation to SMC, appeared It was called zero average dynamics ZAD by the authors. This control technique forces the system to have, at each clock cycle, a zero average of the sliding surface instead to be zero all the time, as in sliding-mode control Application of this technique to a buck converter with centered pulse and an approximation scheme needed for the practical implementations 12 has obtained very good performance. Our study has focused on the value K 2, which gives rise to 2-ZAD, that is, two sampling periods for the zero average in the surface We compare this generalization with the classical ZAD through bifurcation diagrams.

K-ZAD Strategy

Computations for the Classical ZAD Strategy

Computations for the K-ZAD Strategy

Computations for the 2-ZAD Strategy In the case K 2 we get k 1T

Results

Conclusions and Future Work