分数阶滤波器建模与新型超级电容器研究

发布时间：2019-03-12 18:10

【摘要】：传统滤波器,例如像通频带内比较平坦而且相位和衰减特性相对较好的巴特沃斯滤波器,具有较强的适应性且易于设计,同时组成传统器件的要求不高,因此在大多数情况下可以应用,但同时也有一定的问题,例如特性以及自由度方面。随着分数阶在滤波领域的深入发展,分数阶条件下的滤波器因其拥有更好的性能,更多的自由度,较好的稳定性,越来越受到研究人员的关注。分数阶滤波器的模拟与实现是一个具有重要意义的研究方向。本文在传统滤波器的基础上,研究了分数阶次型滤波器的模拟电路实现。对于单一分数阶元素以及二阶分数阶滤波器分别按照低通、高通、带通与带阻的分类进行探索,得到了每种类型对应的电路实现形式以及仿真计算结果,并对其有源及无源情况进行分析。同时具体针对分数阶型巴特沃斯滤波器进行了深入研究。超级电容器是一种具有良好发展前景的储能元件,建立其精确的模型对于进一步研究超级电容器的实际应用具有重要的意义。本文在分数阶矢量匹配的基础上,进一步完善了传统分数阶超级电容器的模型,并提出了基于分数阶巴特沃斯低通滤波器的新型超级电容器新型模型,利用分数阶巴特沃斯低通滤波器的特点,同时结合基本超级电容器模型,可以扩大超级电容器的适用范围并提高其稳定性、抗噪性等特点。
[Abstract]:Traditional filters, such as Butterworth filters, which are relatively flat in the image-pass band and have relatively good phase and attenuation characteristics, have strong adaptability and are easy to be designed. At the same time, the requirements for the composition of traditional devices are not high. Therefore, it can be applied in most cases, but there are also some problems, such as properties and degrees of freedom. With the further development of fractional order filter in the field of filtering, more and more researchers pay attention to fractional order filter because of its better performance, more degrees of freedom and better stability. The simulation and realization of fractional filter is an important research direction. Based on the traditional filter, the analog circuit realization of fractional order filter is studied in this paper. According to the classification of low-pass, high-pass, band-pass and band-stop for single fractional element and second-order fractional filter, the corresponding circuit implementation forms and simulation results are obtained. The active and passive conditions are analyzed. At the same time, the fractional-order Butterworth filter is deeply studied. Super capacitor is a kind of energy storage element with good development prospect. The establishment of its accurate model is of great significance for further research on the practical application of supercapacitor. In this paper, on the basis of fractional vector matching, the traditional fractional supercapacitor model is further improved, and a new supercapacitor model based on fractional Butterworth low-pass filter is proposed. By using the characteristics of fractional Butterworth low-pass filter and the basic supercapacitor model, the application range and stability and anti-noise property of supercapacitor can be expanded.
【学位授予单位】：辽宁工程技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM53;TN713

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