Nonlinear Dynamical Analyze For Cuk Converter Based On Average State Space Method

DC-DC switching converters are the kernel parts in switching power supplies, but due to the effect of switching element in the converters, converters working between several kinds of circuit topologies, performs as a class of strongly nonlinear system. And complex nonlinear dynamical behaviors exist in this system, which will endanger the stable operation of the system. Since applying traditional linear analysis method in analyzing this nonlinear system often leads to great deviation, nonlinear dynamical theories and methods are adopted here to study the power converters. That is beneficial to design better converters in stability and reliability, to a certain extent, it enriched the contents and methods of nonlinear science.In recent years, more and more researchers begin to study the nonlinear behavior of the switching converter, however, most of them are studying on the PWM control-switching converter, rarely studies autonomous switching converter. That is because the chaotic phenomenon in nonautonomous system is universal, while in autonomous systems it exists only in the third and above high order system. The hysteretic current-controlled cuk converter is a free-running fourth-order switching converter, preforming complex dynamical behavior. According to the previous research findings and the average state space method and theory of nonlinear dynamical, this thesis establishes an average state space model, to calculate the equilibrium point based on the average state space model, and analyze the stability of the equilibrium point. Then analyze the behaviors of nonlinear dynamical of the converter, proving that the average state space method can analyze the converter’s stability.This thesis contains the following:(1) This thesis spells out the goal and significance of nonlinear of studying in power converters, reviews on the development of nonlinear dynamical research at both home and abroad, mainly introduces the research history and status about the nonlinear switching power converters. Then brings forward the goal and content of this thesis.(2) This thesis introduces the basic knowledge of nonlinear dynamical, including the concept of nonlinear dynamical system and its qualitative behavior, the theory of bifurcation, stability and chaos. Summarizes the general used research methods in nonlinear dynamical, and presents a nonlinear dynamical system——logistic model as a study object, analyzes the nonlinear behavior with the numerical analysis methods of nonlinear dynamical, and compares the different numerical method.(3) This thesis introduces the average state space method, especially the principle of average state space method and its general procedure. Then establishes an ideal buck converter operating in discontinuous conduction mode based on the average state space theory. The steady-state value and the ac small signal model of the converter is obtained with this model, and its transfer function is deduced based on the ac small signal model.(4)This thesis analyses the work principle of the hysteretic current-controlled cuk converter, establish an average state space model on the basic of average state space method. This model and Lyapunoy stability are applied in solving the equilibrium point and the eigenvalue of the converter, and verified that when the reference current increases from small to huge, the real part of the pair of complex eigenvalue of the converter through the imaginary axis from the negative half shaft in the complex plane, the process is s supercritical hopf bifurcation. Then examines the influence on the stability of the converter when the parameters in the circuit are different. Establishes a precise model of converter and studies the dynamic characteristics of converter after hopf bifurcation.