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Practical Design of RC Approximants of Constant Phase Elements and Their Implementation in Fractional-Order PID Regulators Using CMOS Voltage Differencing Current Conveyors

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Abstract

This paper brings a practical and straightforward view on the design of circuit elements described by fractional-order dynamics known as the constant phase element (CPE) and their implementation in a novel structure of a PIαDβ (or PIλDμ in some literature) regulator based on fabricated CMOS voltage differencing current conveyors. Comparison of presented topology with known solutions indicates significant improvements regarding overall simplification, simpler electronic controllability of time constants, and having all passive elements in grounded form. Step-by-step design of the CPE as well as the PIαDβ regulator is supported by experiments with active devices fabricated using the C07 I2T100 0.7 μm CMOS process (ON Semiconductor). Laboratory tests in frequency and time domain confirm the correct operation of the designed application and the accuracy of the derived results in comparison with the theoretical expectations.

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Acknowledgements

Research described in this paper was financed by Czech Science Foundation under Grant No. 16-06175S and the National Sustainability Program under Grant LO1401. For the research, infrastructure of the SIX Research Center was used. This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

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Authors and Affiliations

  1. Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology (BUT), Technicka 3082/12, Brno, 616 00, Czech Republic

    Ondrej Domansky, Roman Sotner & Lukas Langhammer

  2. Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology (BUT), Technicka 3082/12, Brno, 616 00, Czech Republic

    Jan Jerabek

  3. Department of Physics, University of Patras, 26504, Rio Patras, Greece

    Costas Psychalinos & Georgia Tsirimokou

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  1. Ondrej Domansky
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  2. Roman Sotner
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Correspondence to Ondrej Domansky.

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Domansky, O., Sotner, R., Langhammer, L. et al. Practical Design of RC Approximants of Constant Phase Elements and Their Implementation in Fractional-Order PID Regulators Using CMOS Voltage Differencing Current Conveyors. Circuits Syst Signal Process 38, 1520–1546 (2019). https://doi.org/10.1007/s00034-018-0944-z

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