Modeling And Nonlinear Dynamics Of DC-DC Converter

DC-DC converter exhibits abundant nonlinear phenomena,such as bifurcation,intermittency,quasi-periodicity and chaos.The key procedure in analysing these phenomena is deciding what model to use to describe converter dynamics.This dissertation introduces the two basic modeling approaches,namely,discrete-time modeling and averaging method.Based on different perspectives,we establish the models of some converters to study the fast-scale and slow-scale bifurcation in DC-DC converter.The main work of this dissertation is shown as follows:(1)The discrete-time modeling is introduced.The discrete-time map of voltage-mode controlled buck converter is derived and the period-1 stability of converter is analysed by characteristic multiplier.(2)The averaging method is introduced.By the method of averaging model,the slow-scale bifurcation of hysteristic-current cuk converter is studied.When the reference current increases,the cuk converter loses stability through Hopf bifurcation.Furthermore,the cuk converter also operates limit cycle and quasi-periodicity.(3)The current-mode-controlled boost converter based on nonlinear inductor is analysed.J-A(Jiles-Atherton)model is adopted to handle the nonlinear behavior of inductor.The simulation results indicate that the analysis of stable operation region is more accurate when taken account of nonlinear inductor.Bifurcation diagrams further indicate that nonlinear inductor and slope compensation have similar effect on the stability of the current-mode controlled boost converter.(4)The dynamical behaviour of voltage-mode-controlled buck converter with triangular-wave modulation is investigated.Compared to traditional sawtooth modulation,triangular-wave modulated buck converter loses stability through border collision bifurcation.Research also shows that converters modulated by dual triangular waves have similar behaviour.Furthermore,with the modulated signal becomes more symmetrical,the stability region of converter becomes wider,namely,the isosceles triangular-wave modulated buck converter have best stability.To verify the theoretical analysis and simulation results,the voltage-mode-controlled buck converter circuit is built.The triangular-wave modulation will increase the small signal stability of voltage-mode-controlled converter.