On-line estimation of the Caputo fractional derivatives with application to PIµD? control

Salim Ibrir

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper proposes new procedures for calculation of the Caputo derivative of model-free measured signals. The evaluation of the non-integer derivative is realized by integrating a set of ordinary differential equations and convolution. The derivative of order ? (0 < ? < 2) is seen as an output of a linear-time-varying system driven by a time-dependent known signal. Two procedures are proposed depending on the variation range of the non-integer differentiation order. The proposed formulations facilitate the estimation of the fractional derivatives when they are associated to dynamical systems represented by integer-order differential equations. The efficiency of the developed numerical procedures are validated and compared to exact fractional derivatives for different values of ?. It is shown that PIµD? controllers can be easily realized by system augmentation and convolution. The advantages, the straightforwardness and the main features of the proposed design are given.
Original languageEnglish (US)
Title of host publicationIFAC-PapersOnLine
PublisherElsevier BV
Number of pages6
StatePublished - Apr 14 2021
Externally publishedYes


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