Title: Design of fractional order integrators and differentiators using novel rational approximations

Authors: Richa Yadav; Maneesha Gupta

Addresses: Netaji Subhash Institute of Technology, Sector-3, Dwarka, New Delhi-110078, India ' Netaji Subhash Institute of Technology, Sector-3, Dwarka, New Delhi-110078, India

Abstract: This paper contributes a relatively broader realm of new improved rational approximations based on Halley's iterative method incorporating different orders of one-half, one-third and one-fourth fractional order integrators (FOIs) and fractional order differentiators (FODs) when conceived by existing first and higher order s-to-z transformations for indirect discretisation. The proposed approach has been observed to gear up towards more efficient discretised models when compared with those of existing well established approximation techniques namely continued fraction expansion (CFE) and power series expansion (PSE). Responses of proposed models of FOIs/differentiators based on Al-Alaoui operator and new optimised four segment operator have been reported to have relative magnitude error (dB) as low as -40 dB and linear phase curves in almost full band of normalised frequency. FOIs and FODs based on Tustin operator have presented constant phase response in full range resulting in tremendous improvement over phase responses of its respective existing models.

Keywords: fractional order integrators; FOIs; FOI design; fractional order differentiators; FODs; FOD design; Halley's iterative method; indirect discretisation; s-to-z transformations.

DOI: 10.1504/IJCAD.2014.060689

International Journal of Circuits and Architecture Design, 2014 Vol.1 No.2, pp.156 - 173

Received: 31 Jan 2013
Accepted: 08 Aug 2013

Published online: 21 Jun 2014 *

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