Research On Modeling Of Fractional Order Bidirectional DC/DC Converter

With the introduction of fractional calculus theory,fractional calculus theory has been widely used in various fields in recent years.The results show that the actual external characteristics of the inductance and capacitance in the circuit present fractional order characteristics,and the order of the capacitance and inductance in the DC-DC converter will cause the electrical characteristics of the circuit,which will affect the construction of its electrical model,and then affect its analysis and control design module.So the fractional calculus theory applied to DC-DC converter research is indispensable,this article is based on state space average method and the equivalent small parameter method of fractional order two-way Cuk converter model is set up,and the simulation experiment was carried out,using hardware-in-the-loop simulation device for circuit model to build the model converter of fractional order PID controller is designed.The main work of this paper is as follows:1.Introduced the related concepts of fractional calculus theory and its Laplace transform,as well as the average method to solve the fractional differential equation.The theoretical basis of fractional element construction and the common approximation algorithms are introduced,and the theoretical models of fractional capacitance and inductance are constructed based on this method.2.The state space averaging method is used to analyze the output of the Cuk converter under fractional calculus.The fractional model of Cuk converter is established by using the equivalent small parameter method,and compared with the circuit simulation model and fractional mathematical model constructed by the Oustaloup filter principle,the feasibility and advantages of the equivalent small parameter method are verified.3.Optimal fractional order PID control design is carried out for the fractional order model of Cuk converter.In this paper,based on the performance indication of ITAE,the PID controller model in open loop mode is designed.4.The simulation model is verified by experiments on the circuit with the hardware-in-the-loop simulation device.In the experiment,the 1st-order circuit and the 0.9th-order circuit were experimented respectively,and the waveform of the output current of the circuit was obtained,which verified the effectiveness of the fractional order element constructed by the Oustaloup filtering principle.