Robust fractional order differentiators using generalized modulating functions method
KAUST DepartmentApplied Mathematics and Computational Science Program
Computational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Permanent link to this recordhttp://hdl.handle.net/10754/564036
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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.