Robust fractional order differentiators using generalized modulating functions method
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