摘要
基于电感和电容本质上是分数阶的事实,采用分数阶微积分理论建立了电感电流伪连续模式下Boost变换器的区间分数阶数学模型.依据状态平均建模方法,建立了Boost变换器工作于电感电流伪连续模式下的分数阶状态平均模型.通过所建的分数阶数学模型对其电感电流和输出电压进行了理论分析以及传递函数的推导,并比较了与整数阶数学模型的区别.根据改进的Oustaloup分数阶微积分滤波器近似算法,采用电感和电容的等效分数阶电路模型,在Matlab/Simulink的仿真环境下,对其数学模型和电路模型进行了仿真对比,分析了模型误差产生的原因,验证了所建的分数阶数学模型以及对其理论分析的正确性.最后,指出了分数阶Boost变换器工作于电感电流伪连续模式与连续模式、断续模式的区别与联系.
Based on the fact that the inductor and the capacitor are fractional in nature, the fractional order mathematical model of the Boost converter in pseudo-continuous conduction mode is established by using fractional order calculus theory. According to the state average modeling method, the fractional order state average model of Boost converter in pseudo-continuous conduction mode is built. In view of the mathematical model, the inductor current and the output voltage are analyzed and the transfer functions are derived. Then the differences between the integer order and the fractional order mathematical models are analyzed. On the basis of the improved Oustaloup fractional order calculus for filter approximation algorithm and the model of fractional order inductance and capacitance, the simulation results have been compared between the mathematical model and circuit model with Matlab/Simulink software; the origins of model error are analyzed and the correctness of the modeling in fractional order and the theoretical analysis is verified. Finally, the differences and the relations of Boost converter among the continuous conduction mode, the discontinuous conduction mode, and the pseudo-continuous conduction mode are indicated.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2014年第7期50-59,共10页
Acta Physica Sinica
基金
国家自然科学基金(批准号:51071176)
中国石油大学(北京)前瞻导向基金(批准号:2010QZ03)资助的课题~~
关键词
分数阶
BOOST变换器
伪连续模式(三态模式)
数值仿真
fractional order, Boost converter, pseudo continuous conduction mode（tri-state mode）,numerical simulation
