本文選題：分數(shù)階微積分算子 + 有理函數(shù)逼近　； 參考：《電機與控制學(xué)報》2017年06期

【摘要】：針對分數(shù)階微積分算子的實現(xiàn)問題,基于對數(shù)幅頻特性,導(dǎo)出分數(shù)階積分算子1/sγ(0γ1)的一種有理函數(shù)逼近公式,該式與Manabe提出的公式類似,但比它更便于分析和應(yīng)用,討論了該式應(yīng)用范圍的拓展。為了改善相位逼近精度,提出有理函數(shù)構(gòu)建頻率區(qū)間概念,它包含逼近頻率區(qū)間。在滿足逼近精度和逼近頻率區(qū)間條件下,提出使有理函數(shù)階數(shù)最小化的兩點措施:(1)充分利用對數(shù)幅頻特性漸近線與準(zhǔn)確曲線之差,適當(dāng)加寬分數(shù)階積分算子與有理函數(shù)二者對數(shù)幅頻特性之間的誤差帶;(2)根據(jù)逼近頻率區(qū)間,合理選擇函數(shù)構(gòu)建頻率區(qū)間。計算實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 緯 0 緯 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.
【作者單位】： 大連交通大學(xué)電氣信息學(xué)院;
【基金】：國家科技支撐計劃(2015BAF20B02) 國家自然科學(xué)基金(61471080,No.61201419) 國家留學(xué)基金資助(201608210308)
【分類號】：O174.41;O177

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