Modeling And Analysis Of The Fractional Buck Converter

A large number of studies have shown that the inductors and capacitors in circuits have fractional characteristics,and ideal integer-order inductors and capacitors do not exist.Inductors and capacitors are important components of switching converters.The fractional characteristics of inductors and capacitors will directly affect the performance of the converter.However,the modeling and analysis of switching converters are mostly based on integer-order inductors and integer-order capacitors.The modeling and analysis methods for fractional-order switching converters are mostly numerical modeling methods,and the analytical solution of the switching converter state variables cannot be obtained.Therefore,the equivalent smallparameter method is used to analyze the fractional Buck converter,and the steady-state periodic solution and the transient analytical solution expression of the state variables are obtained.The influence of the component order on the state variables can be accurately reflected from the analytical solution.It helps to deeply understand the working mechanism and working process of the circuit and facilitates the design and optimization of the circuit.The main work of the dissertation is as follows:(1)First,introduce several basic special definitions of fractional calculus,several basic definitions of the fractional calculus,and the equivalence between definitions.Also introduce the nature of fractional calculus and the operation of fractional calculus.A method to solve the fractional differential equations,and introduced the related theory of fractional order device construction.(2)Secondly,the nonlinear mathematical model of the open-loop system of fractional Buck converter is established,and the steady-state periodic solution and transient solution of the system variables are obtained by the equivalent small parameter method.The corresponding fractional-order capacitors and inductors are constructed using Charef's rational approximation algorithm.The corresponding PSIM simulation model is constructed based on the constructed fractional inductors and capacitors.The results of PSIM circuit simulation,the results obtained by ABM algorithm,and equivalent small parameters are compared and analyzed.As a result of the method,the equivalent small-parameter method has the advantage of being less computationally intensive and easily describing changes in the ripple of the state variables.The influence of the order of fractional-order inductors and fractional-order capacitors on the state variables of fractional Buck converters is also analyzed.(3)Then,the nonlinear mathematical model of the closed-loop system of fractional Buck converter is established.The steady-state periodic solution and transient solution of the system variables are also obtained by the equivalent small parameter method.The fractional order constructed by the open-loop system of fractional Buck converter Inductive and capacitive,a closed-loop PSIM simulation model was constructed.The results of the PSIM circuit simulation and the equivalent small parametric method were compared and analyzed.It was verified that the equivalent small-parameter method has a small amount of calculation and is easy to describe the state-variable ripple.The advantages.(4)Finally,based on the above theoretical analysis results,the circuit of the fractional Buck converter closed-loop system is designed,including the driving circuit,the inductor current sampling circuit and the capacitor voltage sampling circuit,and the corresponding experimental platform verification platform is built.The results obtained by the equivalent small parameter method,PSIM simulation and experimental results are compared and analyzed,and the advantages of the equivalent small parameter method in analyzing the fractional Buck converter are verified.