文章基本信息

标题：On-line estimation of the Caputo fractional derivatives with application to PI µ D ν control ⁎
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作者：Salim Ibrir
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：3632-3637
DOI：10.1016/j.ifacol.2020.12.2552
语种：English
出版社：Elsevier
摘要：AbstractThis 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 ν (0 < ν < 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 ν.It is shown thatPIµDνcontrollers can be easily realized by system augmentation and convolution. The advantages, the straightforwardness and the main features of the proposed design are given.
关键词：KeywordsFractional-order derivativesEstimationTime-varying SystemsSystem TheoryPIµDνcontrol