Robust fractional order differentiators using generalized modulating functions method
Name:
Exact_fractional_differentiator_removed.pdf
Size:
836.3Kb
Format:
PDF
Description:
Preprint
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Date
2015-02Permanent link to this record
http://hdl.handle.net/10754/564036
Metadata
Show full item recordAbstract
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.Citation
Liu, D.-Y., & Laleg-Kirati, T.-M. (2015). Robust fractional order differentiators using generalized modulating functions method. Signal Processing, 107, 395–406. doi:10.1016/j.sigpro.2014.05.016Publisher
Elsevier BVJournal
Signal Processingae974a485f413a2113503eed53cd6c53
10.1016/j.sigpro.2014.05.016