Nonlinear Analysis of Discretization Effects in a Digital Current Mode Controlled Boost Converter

Abstract

Digital current mode control finds wide spread application in point of load power converters in DC nano-grid because of its technical benefits. However, finite current-loop sampling effects introduce undesirable sub-harmonic oscillations. This paper presents an analytical framework to investigate such nonlinear phenomena in a digitally current mode controlled boost converter. Discrete-time models for multi-sampled current loops and uniform sample with compensating ramp are derived under continuous conduction mode. We show that the discrete-time maps for such systems are discontinuous in nature. While the error voltage using a proportional-integral controller stays within the zero-error-bin (ZEB), the reference current becomes constant and 1-D maps of the inner current-loop can be used for stability analysis. Uniform sampling may lead to chaos, period doubling or stable period-1 behavior depending on slope of the compensating ramp. Multi-sampled current loop imposes several borders in the discrete parameter space and may eventually lead to high periodic behavior. In a counter-based compensating ramp, staircase effects may lead to sub-harmonic oscillation. Such instability eventually brings the error voltage outside the ZEB and 2-D map models have to be used for further investigating the nonlinear phenomena. A boost converter prototype was made. Digital current mode control is realized using an FPGA device. Test results demonstrate close agreement with the analysis.