MANDELBROT-LIKE BIFURCATION STRUCTURES IN CHAOS BAND SCENARIO OF SWITCHED CONVERTER WITH DELAYED-PWM CONTROL

Abstract

In this paper, we report Mandelbrot-like bifurcation structures in a one-dimensional parameter space of real numbers corresponding to a dc-dc power converter modeled as a piecewise-smooth system with three zones. These fractal patterns have been studied in two-dimensional parameter space for smooth systems, but for nonsmooth systems has not been reported yet. The Mandelbrot-like sets we found are created in transition from the torus band to chaos band scenarios exhibited by a dc-dc buck power converter controlled by Delayed Pulse-Width Modulator (PWM) based on Zero Average Dynamics (or ZAD strategy), which corresponds to a piecewise-smooth system (PWS). The real parameter is provided by the PWM control strategy, namely ZAD strategy, and it can be varied in a large range, ideally (-∞, +∞). At -∞ and +∞ the dynamical behavior is the same, and thus we will describe the synamics in an ring-like parameter space. Mandelbrot-like borders are built by four chaotic bands, therefore these structures can be thought as instability islands where the state variables cannot be located. Using the Poincaré map approach we characterize the bifurcation structures and we describe recurrent patterns in different scales.