Study On Nonlinear Dynamics Of Fractional Order Switching Converters

Modeling and analysis of the fractional order switching converters are the hot topics in the field of the switching converters. The current modeling methods have their own limitations, so it is impossible to analyze completely the chaotic phenomena of the switching converters. Based on the above problems, the steady state and the nonlinear dynamics of the system have been study by predictor corrector method, especially the influence of fractional order on the bifurcation behavior of the system. The research results have theoretical significance and application value.According to the engineering widely used continuous inductor current mode Buck converter and synchronous switching Z source converter, in order to study the steady state characteristics of the systems, the state average models were established, and the steady working points, ripples and transfer functions were analyzed. Two kinds of the predictor corrector models of these converters were set up, and the influence of circuit parameters on the nonlinear dynamic behaviors of systems was analyzed, by using symmetric, asymmetric fractional order and other circuit parameters as variables, from bifurcation diagrams and average entropy diagrams of the systems. The Oustaloup filter models were established to verify the correctness of theoretical analysis. The results show that the predictor corrector algorithm is simple, high accuracy and unlimited to fractional order, which can describe the chaos of converters more deeply and completely,and provide the theoretical basis for the study of nonlinear dynamics of fractional converter.Bifurcation diagrams and other results show that the capacitor’s and the inductor’s fractional order and other circuit parameters have significant influence on the chaos of the Buck converter and Z source converter. The inductor’s fractional order is more effective than capacitor. When fix inductor order, and change capacitor order, the system will appear mirrored bifurcation phenomenon. When fix capacitor order and change inductor order, the system will transform between periodic state and chaotic state. For Buck converter, the change of symmetric fractional order will not affect the system working state, but the change of asymmetric fractional order will result in system in the work of continuous current mode shift to intermittent current working mode. And the synchronous switching Z converter always keeps in the inductor continuous current mode. The above modeling methods and research results have guiding significance to the chaos theory study of fractional order switching convertors,also have great reference value for the design and application of fractional order switching convertors.