Application of the Wavelet Packet Transform for the Identification of Chaotic Signals in the Current-Programmed DC/DC Boost Converters

The wavelet packet transform (WPT), a digital realization of the wavelet transform (WT), has been used in this work for identifying and characterizing sub-harmonic and chaotic signals in a current-mode-controlled boost converter. The operation of the boost converter under current-programmed control is explained, and some computer-generated waveforms are presented in order to illustrate the various possible operating regimes of the current-programmed dc/dc converters. Samples of the state variables of different periodic and chaotic operating conditions of the converter are decomposed up to a certain level of resolution of the wavelet packet tree using a selected mother wavelet in order to characterize different sub-harmonic and chaotic signals occurred in the converter. The wavelet-transformed coefficients of the sampled state variables of different frequency sub bands of the wavelet packet tree are able to differentiate effectively between different periodic and chaotic operating conditions of the converter.

1. Introduction

The current mode controlled dc/dc boost converter, being one of the most commonly used switch converters in communication and control systems for its high efficiency, is prone to sub-harmonic behavior and chaos. The occurrence of the nonlinear phenomena in the converter has long been a universal experience of practicing engineers [1]. Since the converter has wide industrial application, it becomes necessary to characterize and identify sub harmonics and chaotic signals occurring in the system in order to design stable and reliable dc/dc converters. The first detailed analysis of chaos in power electronics was carried out in reference [2]. Wood, et. al., [3]–[4] have described chaos in the controlled switch mode dc/dc converters. Several other techniques were developed in references [5]–[6] dealing with prediction and experimental confirmation of chaos in dc/dc converters under various control schemes. Most of the conducted research relating to chaotic signals in converter circuits concentrated on the identification of bifurcation path with variations of different parameters in the time-domain trajectory plane. However, a detailed investigation of chaotic signals having different periodicities of the current mode controlled dc/dc boost converter in both time and frequency domains has not been carried out to date. In the last ten years, the wavelet transform has been introduced as a new approach in digital signal processing analysis. The wavelet theory states that a signal can be represented by superposition of some special signals called wavelets. Wavelets are waveforms of limited duration, with zero average value. Apart from the Fourier transform (FT), where a signal is represented by superposition of only one fundamental function (sine or cosine), the WT has an unlimited number of fundamental functions [7]. The WT is somewhat similar to finite response filters, and as such it does not transform the signal into discrete harmonics. However, it transforms signal into frequency bandwidths, which cover all significant harmonics.