Two direct Tustin discretization methods for fractional-order differentiator/integrator

被引：285

作者：

Vinagre, BM

Chen, YQ

Petrás, I

机构：

[1] Utah State Univ, Dept Elect & Comp Engn, Ctr Self Organizing & Intelligent Syst, Coll Engn, Logan, UT 84322 USA

[2] Tech Univ Kosice, BERG Fac, Dept Informat & Proc Control, Kosice 04200, Slovakia

[3] Univ Extremadura, Sch Ind Engn, Dept Elect & Electromech Engn, E-06071 Badajoz, Spain

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2003年 / 340卷 / 05期

基金：

美国国家科学基金会;

关键词：

fractional differentiator; fractional-order controllers; tustin operator; power series expansion; continued fraction expansion; discretization;

D O I：

10.1016/j.jfranklin.2003.08.001

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given. (C) 2003 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：349 / 362

页数：14

共 19 条

[1]

[Anonymous], 1995, Integral Transforms and Their Applications

[2]

[Anonymous], IMACS SMC P LILL FRA

[3]

AXTELL M, 1990, PROC NAECON IEEE NAT, P563, DOI 10.1109/NAECON.1990.112826

[4]

Chen YQ, 2002, IEEE T CIRCUITS-I, V49, P363, DOI 10.1109/81.989172

[5]

Claerbout J., 1976, Fundamentals of Geophysical Data Processing

[6]

DORCAK L, 1994, UEF0494 AC SCI I EXP, P1

[7] Adaptive Control of a Single-Link Flexible Manipulator [J].

Feliu, Vincente ;

Rattan, Kuldip S. ;

Brown, H. Benjamin, Jr. .

IEEE CONTROL SYSTEMS MAGAZINE, 1990, 10 (02) :29-33

[8]

Hilfer R., 2000, Applications of Fractional Calculus in Physics, V35

[9]

Khinchin A. Ya., 1997, CONTINUED FRACTIONS

[10] DISCRETIZED FRACTIONAL CALCULUS [J].

LUBICH, C .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (03) :704-719

← 1 2 →