Design of fractional order differentiators and interators using improved indirect discretization approach

Abstract

Abstract: This paper attempts to achieve the rational approximation of fractional order differentiators and interators by using improved operator and Continued Fraction Expansion（CFE） based indirect discretization scheme. The discretized transfer functions is a IIR-type filter, it not only has the stable minimum phase and also has low computational complexity. Compared with the traditional operator model , the improved operator shows a great advantage in frequency response and magnitude errors. The Matlab simulation is presented to demonstrate the effectiveness of the proposed method.

Key words: fractional order differentiators and interators, Continued Fraction Expansion（CFE）, improved operator, discretization

摘要： 利用改进的算子模型以及CFE连分式展开的方法对分数阶微积分进行间接离散的有理化逼近。经过变换后的传递函数为IIR型滤波器，不仅逼近理想的频率响应，而且具有稳定的最小相位和低的计算复杂性。改进的算子模型在频率响应和误差上相对于传统的算子模型表现出很大的优势。通过Matlab验证了算法的有效性。

关键词: 分数阶微积分, 连分式展开（CFE）, 改进的算子, 离散化

SUN Haiyang, TENG Jianfu. Design of fractional order differentiators and interators using improved indirect discretization approach[J]. Computer Engineering and Applications, 2012, 48(28): 150-153.

孙海洋，滕建辅. 改进的分数阶微积分器间接离散化设计[J]. 计算机工程与应用, 2012, 48(28): 150-153.

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Design of fractional order differentiators and interators using improved indirect discretization approach

改进的分数阶微积分器间接离散化设计

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