Nonlinear and nonsmooth dynamics in a DC-DC Buck converter: Two experimental set-ups

Abstract

It is well known that many nonlinear phenomena such as bifurcations and chaotic behavior occur in DC-DC converters mainly due to the switching action among all the different topologies of the circuit. Such behavior has been described with detail numerically, and also mathematical reasoning has been provided. In this paper we focuss on the experimental side of a DC-DC Buck converter controlled with two different strategies: classical Pulse Width Modulation (PWM) with a ramp and a more recently described Zero Average Dynamics (ZAD). We show some nonsmooth events and we explain with detail the experimental setups. In one of them, we use a FPGA card to obtain on-line results. In the other we use Virtual InstrumenPartially funded by SICONOS. tation to generate an experimental two-dimensional bifurcation diagram, which will be compared to the numerical data. After the data acquisition of the system state variables some elaborated post-processing must be made. This is done through LabView. Although the main application of these results is centered in avoiding non-periodic or high-amplitude periodic behavior, they can also be applied to reducing the generated electromagnetic interference and to the information transmission.

Virtual orbits and two-parameter bifurcation analysis in a ZAD-controlled buck converter

“…The switching behavior of this converter leads to a model which is piecewise smooth on the right hand side (also called Filippov systems), and the repeating behavior makes the system non-autonomous but periodic. This property permits the use of averaging methods for the control design, such as working with the averaged system (see for instance [11]) or the use of the so-called ZAD strategy (zero average dynamics) extensively numerically, analytically and also experimentally studied in [2,3,5,9].…”

Floquet Exponents and Bifurcations in Switched Converters

“…Replacing the perturbed solution in equation (3) and neglecting the periodic solution, the variational equation of the system is obtained by equation (4) where…”

“…We use the parameter values of an experimental prototype reported in [3]. We fix R = 20Ω, C = 40μF, L=2mH, r L = 0Ω, v re f = 32V, E=40V and the sampling period T c = 50μs..…”

“…One-delay control law implies that the duty cycle d k depends on state variables in the instant 3 . Two additional state variables can be defined x 3 (kT)=x 1 ((k − 1)T) and…”

Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller

“…Such problem has been observed particularly in power electrical systems such as power converters [1][2][3]. In most cases, designers try to avoid the chaotic behavior, considered as hazardous, by adjusting the system parameters securely far from the values that lead to chaos.…”