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Identification of Continuous-Time Fractional Models from Noisy Input and Output Signals

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Fractional Order Systems—Control Theory and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 364))

Abstract

It is well known that, in some practical system identification situations, measuring both input and output signals can commonly be affected by additive noises. In this paper, we consider the problem of identifying continuous-time fractional systems from noisy input and output measurements. The bias correction scheme, which aims at eliminating the bias introduced by the fractional order ordinary least squares method, is presented, based on the estimation of variances of the input and output measured noises. The compensation method for the input and output noises is also studied by introducing an augmented high-order fractional-order system in the identification algorithm. The presented algorithm is established to perform unbiased coefficients and fractional orders estimation. The promising performances of the proposed method are assessed via the identification of a fractional model and a fractional real electronic system.

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Notes

  1. 1.

    All differentiation orders are exactly divisible by the same number, an integral number of times.

  2. 2.

    The difference between the open-loop transfer function phase and \(180^\circ \).

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Authors and Affiliations

  1. Research Laboratory Modeling, Analysis and Control of Systems (MACS -LR16ES22), National Engineering School of Gabes, University of Gabes, Gabes, Tunisia

    Z. Yakoub, M. Aoun, M. Amairi & M. Chetoui

Authors
  1. Z. Yakoub
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  2. M. Aoun
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  3. M. Amairi
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  4. M. Chetoui
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Editor information

Editors and Affiliations

  1. CEM Laboratory, Department of Electrical Engineering, National School of Engineers of Sfax, University of Sfax, Sfax, Tunisia

    Omar Naifar

  2. Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia

    Abdellatif Ben Makhlouf

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Yakoub, Z., Aoun, M., Amairi, M., Chetoui, M. (2022). Identification of Continuous-Time Fractional Models from Noisy Input and Output Signals. In: Naifar, O., Ben Makhlouf, A. (eds) Fractional Order Systems—Control Theory and Applications. Studies in Systems, Decision and Control, vol 364. Springer, Cham. https://doi.org/10.1007/978-3-030-71446-8_10

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