Research On Modeling And Control Of Single-Inductor Dual-Output Buck Converter Based On Fractional-Order Definition

Fractional-order calculus theory can better describe,explain and analyze systems in nature than traditional integer-order calculus theory,and open up new ways to study systems for more accurate modeling and more precise control.The single-inductor dual-output(SIDO)Buck converter can use only one inductor to provide different voltage levels for two loads,which has the advantages of small size,low cost and high conversion efficiency in DC microgrid,and has become a hot spot for domestic and foreign in recent years.However,due to the SIDO Buck converter system is coupled,there is cross-regulation phenomenon between the output branches.Therefore,it is important to study modeling to improve model accuracy and design control to reduce cross-regulation.In order to obtain a more accurate model to describe the dynamics of the converter,the fractional-order calculus theory is combined to establish a equivalent fractance proximation circuit and a fractional-order SIDO Buck converter model,and the analytical equations of the steady-state gain,the a-branch and b-branch step-down ratios,the inductor current,and the a-branch and b-branch output ripple voltages of the R-L fractional-order SIDO Buck converter in the complete inductor supply mode(CISM)are studied,the relationship between the analytical equations and the fractional-order is summarized.In order to analyze the necessity of fractional-order model,the percentage error curves of inductor current,a-branch and b-branch output voltages are obtained according to the circuit model and mathematical model of integer-order modeling and fractional-order modeling SIDO Buck converter,and the results of the study found that the fractional-order modeling fits better dynamic process and has less modeling error.Aiming at the problem of cross-regulation phenomenon at the output of fractional-order modeling SIDO Buck converter,the small signal model of fractional-order modeling SIDO Buck converter under IVF control is obtained by combining the independent voltage-feedback control(IVF)loop.Based on this model,the cross-regulation of integer-order model and fractional-order model are compared and analyzed in the frequency domain using a bode diagram,and the results show that the cross-regulation of fractional-order modeling is smaller;at the same time,the cross-regulation of different orders of fractional-order modeling of the SIDO Buck converter are compared and analyzed,and the results show that the cross-regulation are larger when the fractional order increases and tends to be closer to 1.In order to reduce the cross-regulation of fractional-order modeling SIDO Buck converter,the IVF control is extended to fractional-order independent voltage-feedback control(FOIVF),fractional-order Lyapunov theory is introduced,and according to the characteristic of fractional-order SIDO Buck converter dual output,the fractional-order back-stepping independent voltage-feedback control(FOBIVF)method is proposed,combined with fractional-order SIDO Buck converter and FOBIVF control method,a fully fractional-order SIDO Buck converter system is realized with better dynamic performance and stronger robustness,and reduce the cross-regulation.The simulation experimental platform is built,and the simulation experimental results verify the rationality of fractional-order modeling,cross-regulation theory analysis and control method.