Discretization schemes for fractional-order differentiators and integrators

Author

Chen, Yang Quan ; Moore, Kevin L.

Author_Institution

Dept. of Electr. & Comput. Eng., Utah State Univ., Logan, UT, USA

Volume

49

Issue

3

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

363

Lastpage

367

Abstract

For fractional-order differentiator s^r where r is a real number, its discretization is a key step in digital implementation. Two discretization methods are presented. The first scheme is a direct recursive discretization of the Tustin operator. The second one is a direct discretization method using the Al-Alaoui operator via continued fraction expansion (CFE). The approximate discretization is minimum phase and stable. Detailed discretization procedures and short MATLAB scripts are given. Examples are included for illustration

Keywords

differentiation; integration; mathematical operators; Al-Alaoui operator; MATLAB; Tustin operator; approximate discretization; continued fraction expansion; direct discretization; direct recursive discretization; fractional calculus; fractional-order differentiator; fractional-order integrator; Automotive engineering; Books; Control systems; Fractals; Fractional calculus; Frequency synthesizers; MATLAB; Mathematical model; Robust control; Three-term control;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.989172

Filename

989172