A Study on Fractional Power-Law Applications and Approximations

Salma Emad, Ahmed M. Hassanein, Amr M. AbdelAty, Ahmed H. Madian, Ahmed G. Radwan, Lobna A. Said

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations

    Abstract

    The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results.

    Original languageBritish English
    Article number591
    JournalElectronics (Switzerland)
    Volume13
    Issue number3
    DOIs
    StatePublished - Feb 2024

    Keywords

    • FPAA
    • fractional-order approximations
    • fractional-order circuits
    • fractional-order compensators
    • fractional-order filters
    • power-law filters

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