Buck变换器的分数阶仿真模型与混沌分析

基于电感和电容本质上是分数阶的事实,基于分数阶微积分理论结合改进的Oustaloup分数阶微积分滤波器近似算法,在Matlab/Simulink下建立了电流连续模式下的电压控制型Buck变换器的分数阶数学仿真模型和对应的电路仿真模型,通过仿真验证了该模型的正确性。基于建立的分数阶数学仿真模型研究了很少有文献研究的以参考电压和比例放大系数作为混沌控制变量的Buck变换器的混沌行为,得到了分别以参考电压、比例放大系数为变量的Buck变换器的V-I混沌相图。此模型可以对电压控制型Buck变换器的所有能导致混沌行为的7种情况进行仿真分析,利用此模型仿真分析了Buck变换器的阶数对系统动态响应过程的影响。该模型的建立方法也适用于其他DC/DC变换器的分数阶模型的建立。

Fractional order simulation model and chaos analysis of Buck converter

According to the fact that inductance and capacitance is essentially fractional order,in combination with fraction？al calculus theory and improved Oustaloup fractional calculus filter approximation algorithm,the fractional？order mathematical simulation model and the corresponding circuit simulation model of Buck converter controlled by voltage and worked in continu？ous current mode were established in MATLAB/Simulink. the correctness of the models was verified by simulation. The chaotic behavior of Buck converter,which few people select reference voltage and scaling factor as chaos control variable,is studies on the basis of fractional mathematical simulation model. Two VI chaotic phase diagrams of Buck converter taking reference voltage and scaling factor as control variable were obtained. This model can analysis seven cases that all variables may lead to chaotic behavior of voltage？controlled Buck converter. Meanwhile the impact of the order of Buck converter on dynamic response is also analyzed in this paper. The establishment method of this model is applied to the fractional model establishment of other DC / DC converters.