Period Addition Phenomenon and Chaos Control in a ZAD Controlled Boost Converter

Abstract

In this paper, we present an analytical, numerical, and experimental description of the period addition phenomenon in a dynamical system arising from a boost converter controlled by ZAD strategy. The ideal model is presented, and compared with a model that includes parasitic resistances. We show the presence of chaos in the two systems, which is controlled by TDAS. In particular, numerical simulation shows the chaos control zone is greater in the system with internal resistances.

Performance of the Boost Converter Controlled with ZAD to Regulate DC Signals

“…In [19], the authors studied the behavior of a two-dimensional system defined by a boost converter controlled with ZAD, where saturated periodic orbits and a period addition phenomenon are found. In [20], a boost converter was controlled, chaos control was carried out with TDAS, and the period addition phenomenon was demonstrated in a model where parasitic resistances were included, making it closer to the experimental model. Additionally, in [21], it was considered a switching surface that includes the current in the capacitor, chaos control was achieved with FPIC and some branches were classified.…”

On the dynamic behavior of the current in the condenser of a boost converter controlled with ZAD

“…Of special interest is the boost converter [7], which is a voltage booster circuit that is widely used at the industrial level and that exhibits a nonlinear behavior by virtue of its switching system. Power converters, due to their configuration, can be seen as systems of variable structures [8,9]. In the 1980s, drivers in sliding modes for this type of system began to be designed.…”

“…In [9], an analysis of the dynamics of a boost converter controlled with ZAD was conducted using the switching surface ( ( )) = 1 ( 1 ( ) − 1 ) + 2 ( 2 ( ) − 2 ) and it was shown analytically that the approximation of the switching surface by straight lines is as good as desired. In other words, the error in the approximation can be made as small as we want; moreover, the maximum and minimum of the error in the approximation occur just at the ends of the sub-intervals, a fact that was corroborated by simulation in MATLAB.…”

Simulation, bifurcation, and stability analysis of a SEPIC converter controlled with ZAD

“…In [10] , it has been implemented making use of the switching surface (x( )) = ( 1 ( ) − 1 ) + (̇1( ) −̇1 ), where good results are shown in terms of robustness and low output error. In [11,12] it is also applied to analyze the dynamics present in the boost converter to study present non-linear phenomena, driven by a center aligned pulse width modulation converter (CPWM).…”

“…In the present article, the ZAD technique has been implemented to control a SEPIC converter, which has been used to control boost and buck converters in previous Works [11,13,14]. A linear combination of the error in voltage and current has also been taken as the switching surface (x( )) = 1 ( 1 ( ) − 1 ) +…”