一种分数阶微积分算子的有理函数逼近阶数最小化方法

发布时间：2018-04-12 15:55

本文选题：分数阶微积分算子 + 有理函数逼近　；参考：《电机与控制学报》2017年06期

【摘要】：针对分数阶微积分算子的实现问题,基于对数幅频特性,导出分数阶积分算子1/sγ(0γ1)的一种有理函数逼近公式,该式与Manabe提出的公式类似,但比它更便于分析和应用,讨论了该式应用范围的拓展。为了改善相位逼近精度,提出有理函数构建频率区间概念,它包含逼近频率区间。在满足逼近精度和逼近频率区间条件下,提出使有理函数阶数最小化的两点措施:(1)充分利用对数幅频特性渐近线与准确曲线之差,适当加宽分数阶积分算子与有理函数二者对数幅频特性之间的误差带;(2)根据逼近频率区间,合理选择函数构建频率区间。计算实例表明上述工作的有效性。
[Abstract]:In view of the realization of fractional calculus operator, a rational function approximation formula of fractional integral operator 1 / s 纬 0 纬 1 is derived on the basis of logarithmic amplitude-frequency characteristic. The formula is similar to that proposed by Manabe, but more convenient for analysis and application.The extension of the scope of application of the formula is discussed.In order to improve the precision of phase approximation, a rational function is proposed to construct the frequency interval, which contains the approximation frequency interval.Under the condition of satisfying the approximation accuracy and the approximation frequency interval condition, two measures to minimize the order of rational function: 1) are put forward to make full use of the difference between the asymptotic line of logarithmic amplitude-frequency characteristic and the exact curve.The error band between the two logarithmic amplitude-frequency characteristics of fractional integral operator and rational function is widened properly.An example is given to show the effectiveness of the above work.
【作者单位】：大连交通大学电气信息学院;
【基金】：国家科技支撑计划(2015BAF20B02) 国家自然科学基金(61471080,No.61201419) 国家留学基金资助(201608210308)
【分类号】：O174.41;O177

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