The Structure Of Fractional-order Circuit And Its Application In DC Chopper

The systems in practical applications are not all integer-order,but there are a large number of fractional-order phenomena.Therefore,using an integer-order model to describe a fractional system with higher complexity will cause errors that cannot be ignored.The introduction of the theory of fractional calculus can better characterize complex systems or phenomena more accurately.In actual DC choppers,inductors and capacitors,as the main components,have fractional-order characteristics.Based on this,the establishment of a fractional-order model of the circuit system and the fractional-order correlation analysis will more accurately describe the relevant performance of the chopper circuit,which is of great significance to the design of the chopper and its effectiveness.Based on the above analysis,this article takes the influence of the fractional order in the DC chopper converter on its performance as the main research object.It focuses on the fractional order determination of actual capacitance and inductance and the structure of the fractional order circuit.Through reference and expansion of traditional modeling analysis and theory,and then launched the following research:（1）On the basis of the integer-order mathematical model of ideal capacitance and inductance,the fractional-order mathematical model of practical capacitance and inductance is established by using the related theory of fractional calculus.After mathematical processing by Fourier transform.Then use the function signal generator,oscilloscope,etc.to obtain a series of experimental data such as current and voltage,and then determine the fitting fractional order of the experimental capacitance and inductance.（2）The fractional order of actual capacitance and inductance is the characteristic of the component itself.In order to meet the application of a wider range of fractional orders in actual systems,the problem of constructing a certain order of fractional-order circuits is studied.Use actual fractional capacitors,fractional inductances,resistances,etc.,to form a circuit that is close to a certain order,so as to fit the fractional properties as much as possible in a certain frequency band.According to the improved Newton’s regular iteration method,gradient descent method and Oustaloup algorithm,the rational fraction is used to gain on the ideal fractional operatorin the Laplace domain.After getting the approximate rational fraction,it is transformed into continued fraction or partial fraction expansion.Then get the corresponding Cauer circuit or Foster circuit form and its component values.Then build and verify the actual fractional-order approximation circuit.（3）The fractional-order circuit is introduced into the buck-boost chopper,and the CCM and DCM modes of the chopper system are modeled and analyzed respectively.Using the improved equivalent small parameter method to analyze the nonlinear chopper system,the approximate analytical solution expression of each state variable can be obtained.From the analytical solution,the direct current and the harmonic components can be analyzed intuitively,and the relevant performance of the chopper can be further studied.In the process of modeling and analysis,taking the fractional order changes of energy storage components as variables,the influence of fractional order circuits on the performance of the converter system is explored,which has guiding significance for the actual design of the system.Finally,build an actual circuit to verify the results.