基于预估-校正算法的分数阶Boost变换器倍周期分岔研究

Period Doubling Bifurcation of Fractional-order Boost Converter Based on Predictor-corrector Algorithm

基于电感电容本质是分数阶的事实,对分数阶Boost变换器的非线性动力学特性进行了深入研究。采用分数阶微积分的预估-校正算法,建立了Boost变换器的预估-校正模型,在此基础上得到了以参考电流、输入电压以及电容电感阶数为分岔参数的分岔图,研究了变换器的倍周期分岔和混沌行为,同时与整数阶Boost变换器的非线性动力学行为进行了比较。研究结果表明,在一定的工作条件下,随着变换器某些电路参数的变化,分数阶Boost变换器会出现分岔和混沌等非线性现象;在相同电路参数的条件下,整数阶和分数阶变换器的稳定参数域之间存在差异,与整数阶变换器相比,分数阶变换器的参数稳定区域更小,更真实地反映了Boost变换器的非线性动力学特性。

Based on the fact that inductance and capacitance are of fractional-order,the nonlinear dynamic characteristics of a fractional-order Boost converter are studied.The predictor-corrector model of the Boost converter is established using the predictor-corrector algorithm of fractional-order calculus.On this basis,the bifurcation diagrams with the reference current,input voltage and orders of capacitance and inductance as bifurcation parameters are obtained.The period doubling bifurcation and chaotic behaviors of the fractional-order Boost converter are studied,and its nonlinear dynamic behavior is compared with that of an integer-order Boost converter at the same time.Results show that under certain operating conditions,some nonlinear phenomena such as bifurcation and chaos will appear in the fractional-order Boost converter with changes in some circuit parameters.Under the condition of the same circuit parameters,the parameter stability domains of integer-and fractional-order converters are different.Compared with that of the integer-order converter,the parameter stability region of the fractional-order converter is smaller,which more truly reflects the nonlinear dynamic characteristics of the Boost converter.