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[1]张旭秀,李卫东,盛虎,等.一种分数阶微积分算子的有理函数逼近阶数最小化方法 [J].电机与控制学报,2017,21(06):96-103.[doi:10.15938/j.emc.2017.06.013]
 ZHANG Xu-xiu,LI Wei-dong,SHENG Hu,et al.Minimum method of rational function orders for approximation fractional differential and integral operators [J].,2017,21(06):96-103.[doi:10.15938/j.emc.2017.06.013]
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一种分数阶微积分算子的有理函数逼近阶数最小化方法
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《电机与控制学报》[ISSN:1007-449X/CN:23-1 408/TM]

卷:
21
期数:
2017年06
页码:
96-103
栏目:
出版日期:
2017-06-01

文章信息/Info

Title:
Minimum method of rational function orders for approximation fractional differential and integral operators
作者:
?张旭秀 李卫东 盛虎 丁鸣艳
?( 大连交通大学电气信息学院,辽宁大连116028)
Author(s):
ZHANG Xu-xiu LI Wei-dong SHENG Hu DING Ming-yan
( School of Electronics and Information Engineering,Dalian Jiaotong University,Dalian 116028,China)
关键词:
分数阶微积分算子 有理函数逼近 Manabe 近似式 有理函数阶数最小化 应用范围拓展
Keywords:
fractional differential and integral operator rational function approximation Manabe-approximation formula minimum of rational function orders extension of application scope
分类号:
TN 713
DOI:
10.15938/j.emc.2017.06.013
文献标志码:
A
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 ( 0 < γ < 1 ) 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:
?Aiming at the problem of implementation of fractional differential and integral operators,an rational function approximation formula for 1 /sγ ( 0 < γ < 1) is derived based on logarithmic frequency characteristic.The formula is similar to the Manabe formula,but is more convinient for analysis and application.Its extension of application scope was discussed. In order to improve the accuracy of phase approximation, a rational function constructing the frequency interval is proposed. It contained the approximation frequency interval. To meet the conditions of approximation accuracy and frequency interval approximation, two measures to minimize rational function orders was presented: firtly,make full use of the error between the asymptote and the actual value of the logarithm amplitude-frequency characteristic,and appropriately broaden the error strip of the logarithm amplitude-frequency characteristic of the fractional integral operator vs the rational function; secondly,select the rational function formation frequency area reasonably based on the approximation of the frequency interval. Computation examples show that above work is valid.

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备注/Memo

备注/Memo:
收稿日期: 2015 - 12 - 30
基金项目: 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)
作者简介: 张旭秀( 1968—) ,女,博士,教授,研究方向为分数阶微积分理论及应用、智能控制等;
李卫东( 1963—) ,男,博士,教授,研究方向为铁路信息与通信智能化技术、复杂系统分析与控制、智能控制等;
盛虎( 1978—) ,男,博士,副教授,研究方向分数阶微积分理论及应用;
丁鸣艳( 1979—) ,女,硕士,讲师,研究方向为自动控制理论与应用。
更新日期/Last Update: 2017-08-24