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Artificial Intelligence in Fractional-Order Systems Approximation with High Performances: Application in Modelling of an Isotopic Separation Process

Author

Listed:
  • Roxana Motorga

    (Automation Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Vlad Mureșan

    (Automation Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Mihaela-Ligia Ungureșan

    (Physics and Chemistry Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Mihail Abrudean

    (Automation Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Honoriu Vălean

    (Automation Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

  • Iulia Clitan

    (Automation Department, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

Abstract

This paper presents a solution for the modelling, implementation and simulation of the fractional-order process of producing the enriched 13 C isotope, through the chemical exchange between carbamate and carbon dioxide. To achieve the goal of implementation and simulation of the considered process, an original solution for the approximation of fractional-order systems at the variation of the system’s differentiation order is proposed, based on artificial intelligence methods. The separation process has the property of being strongly non-linear and also having fractional-order behaviour. Consequently, in the implementation of the mathematical model of the process, the theory associated with the fractional-order system’s domain has to be considered and applied. For learning the dynamics of the structure parameters of the fractional-order part of the model, neural networks, which are associated with the artificial intelligence domain, are used. Using these types of approximations, the simulation and the prediction of the produced 13 C isotope concentration dynamics are made with high accuracy. In order to prove the efficiency of the proposed solutions, a comparation between the responses of the determined model and the experimental responses is made. The proposed model implementation is made based on using four trained neural networks. Moreover, in the final part of the paper, an original method for the online identification of the separation process model is proposed. This original method can identify the process of fractional differentiation order variation in relation to time, a phenomenon which is quite frequent in the operation of the real separation plant. In the last section of the paper, it is proven that artificial intelligence methods can successfully sustain the system model in all the scenarios, resulting in the feasible premise of designing an automatic control system for the 13 C isotope concentration, a method which can be applied in the case of other industrial applications too.

Suggested Citation

  • Roxana Motorga & Vlad Mureșan & Mihaela-Ligia Ungureșan & Mihail Abrudean & Honoriu Vălean & Iulia Clitan, 2022. "Artificial Intelligence in Fractional-Order Systems Approximation with High Performances: Application in Modelling of an Isotopic Separation Process," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1459-:d:802834
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    References listed on IDEAS

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    2. Zhu, Zhen & Lu, Jun-Guo, 2021. "Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    3. Akgül, Akif & Rajagopal, Karthikeyan & Durdu, Ali & Pala, Muhammed Ali & Boyraz, Ömer Faruk & Yildiz, Mustafa Zahid, 2021. "A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Jun Shen & James Lam, 2014. "State feedback control of commensurate fractional-order systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(3), pages 363-372.
    5. Ming-Hui Huang & Roland T. Rust, 2021. "A strategic framework for artificial intelligence in marketing," Journal of the Academy of Marketing Science, Springer, vol. 49(1), pages 30-50, January.
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    Cited by:

    1. Emad A. Mohamed & Mokhtar Aly & Masayuki Watanabe, 2022. "New Tilt Fractional-Order Integral Derivative with Fractional Filter (TFOIDFF) Controller with Artificial Hummingbird Optimizer for LFC in Renewable Energy Power Grids," Mathematics, MDPI, vol. 10(16), pages 1-33, August.

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