Robust fractional order differentiators using generalized modulating functions method

Handle URI:
http://hdl.handle.net/10754/564036
Title:
Robust fractional order differentiators using generalized modulating functions method
Authors:
Liu, Dayan; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Signal Processing
Issue Date:
Feb-2015
DOI:
10.1016/j.sigpro.2014.05.016
Type:
Article
ISSN:
01651684
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Dayanen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-08-03T12:29:19Zen
dc.date.available2015-08-03T12:29:19Zen
dc.date.issued2015-02en
dc.identifier.issn01651684en
dc.identifier.doi10.1016/j.sigpro.2014.05.016en
dc.identifier.urihttp://hdl.handle.net/10754/564036en
dc.description.abstractThis paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.en
dc.publisherElsevier BVen
dc.subjectFractional order differentiatoren
dc.subjectGeneralized modulating functions methoden
dc.subjectNoiseen
dc.subjectRiemann-Liouville derivativeen
dc.titleRobust fractional order differentiators using generalized modulating functions methoden
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalSignal Processingen
dc.contributor.institutionINSA Centre Val de Loire, Université DOrléans, PRISME EA 4229Bourges, Franceen
kaust.authorLaleg-Kirati, Taous-Meriemen
kaust.authorLiu, Dayanen
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