实验技术与管理2025，Vol.42Issue(10)：90-97,8.DOI:10.16791/j.cnki.sjg.2025.10.011
分数阶反激变换器非线性动力学分析实验设计
Design of experiments for nonlinear dynamic analysis of fractional-order flyback converters
摘要
Abstract
[Objective]Fractional-order modeling and nonlinear dynamic analysis of isolated DC-DC converters have theoretical and practical value in power electronics.Traditional integer-order models fail to accurately capture the memory effects and complex dynamics of real-world inductors and capacitors,which exhibit fractional-order characteristics.This study focuses on the flyback converter,a widely used isolated topology,to overcome the limitations of integer-order modeling when characterizing nonlinear behaviors such as low-frequency oscillations(LFOs).By establishing a precise fractional-order model,this work reveals the influence of fractional orders on system stability and dynamic performance,providing a foundation for optimizing control strategies and enhancing operational reliability in applications like renewable energy systems and electric vehicles.[Methods]A fractional-order state-space averaging model for a flyback converter in continuous conduction mode was developed based on Caputo fractional calculus.The Oustaloup approximation algorithm was used to construct rational equivalent circuits for fractional-order inductors(order α)and capacitors(order β),replacing integer-order components in the Simulink circuit model.Key parameters such as DC operating points,current/voltage ripples,and transfer functions were derived analytically.The nonlinear dynamics,particularly LFOs under proportional-integer(PI)voltage control,were investigated through bifurcation diagrams,phase portraits,and time-domain waveforms,using PI gain(Ki)as the bifurcation parameter.MATLAB/Simulink simulations and hardware-in-the-loop(HIL)experiments on an NI PXIe-1082 platform validated the theoretical models.Stability boundaries for the LFOs were predicted using fractional-order small-signal transfer functions and Bode analysis.[Results]By changing the Ki of the PI controller,the evolutions of the integer-order flyback converter and the fractional-order flyback converter from stable operating states to an LFO state were captured.For the integer-order converter,when Ki=70,the system is in a stable operating state,and when Ki=75,the system is in an LFO state.For the fractional-order converter,when Ki=290,the system is in a stable operating state,and when Ki=295,the system is in an LFO state.The fractional-order model(α=0.95,β=0.95)demonstrated larger stability regions compared to the integer-order model(α=1,β=1).Bifurcation analysis revealed that the critical points of the LFOs shifted toward higher Ki values(e.g.,from 70 to 290 at instability onset),indicating enhanced robustness against parameter variations.Bode plots confirmed superior dynamic performance in the fractional-order system,with phase margins exceeding those of integer-order models and transfer function poles shifting to higher frequencies.Experimental results validated that state-variable ripples(inductor current iL,output voltage vo)increased with reduced α and β due to weakened filtering capabilities.The state-space model accurately predicted LFO boundaries,aligning with simulation and HIL results.[Conclusions]Fractional-order modeling effectively captures the inherent dynamics of flyback converters,overcoming the limitations of integer-order approximations.The reduced orders(α,β<1)expand the stable parameter regions,making the system less prone to LFOs and improving dynamic performance.The state-space averaging model and stability analysis method derived in this work provide accurate predictions for nonlinear behavior boundaries,enabling optimized control design.This work establishes a theoretical foundation for enhancing the stability and efficiency of isolated DC-DC converters in practical applications,demonstrating the critical role of fractional calculus in advancing power electronics.关键词
非线性动力学/分数阶/反激变换器/Oustaloup算法Key words
nonlinear dynamic analysis/fractional-order/flyback converter/Oustaloup algorithm分类
信息技术与安全科学引用本文复制引用
王晓刚,陈俊宇,张泽天,蔡俊雄,林积桂..分数阶反激变换器非线性动力学分析实验设计[J].实验技术与管理,2025,42(10):90-97,8.基金项目
广东省本科高校教学质量与教学改革工程建设项目(粤教高函[2024]9号和[2024]30号) （粤教高函[2024]9号和[2024]30号）
广州大学探索性实验建设项目(SJ202305,SJ202404) （SJ202305,SJ202404）
广州市高等教育教学质量与教学改革工程项目(2023QTJG071,2024BQWGC001) （2023QTJG071,2024BQWGC001）
