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Fractional Calculus and Applied Analysis

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Conceptual design of a selectable fractional-order differentiator for industrial applications

Emmanuel Gonzalez
  • Existing Installation Department, Jardine Schindler Elevator Corporation, 8/F Pacific Star Bldg., Sen. Gil Puyat Ave. cor. Makati Ave., Makati City, 1209, Philippines
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/ Ľubomír Dorčák
  • Institute of Control and Informatization of Production Processes Faculty of BERG, Technical University of Košice, B. Němcovej 3, 042 00, Košice, Slovakia
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/ Concepción Monje / Juraj Valsa / Felicito Caluyo
  • School of Electrical, Electronics and Computer Engineering Mapua, Institute of Technology, Muralla St., Intramuros Manila, 1000, Philippines
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/ Ivo Petráš
  • Institute of Control and Informatization of Production Processes Faculty of BERG, Technical University of Košice, B. Němcovej 3, 042 00, Košice, Slovakia
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Published Online: 2014-06-26 | DOI: https://doi.org/10.2478/s13540-014-0195-z

Abstract

In the past decade, researchers working on fractional-order systems modeling and control have been considering working on the design and development of analog and digital fractional-order differentiators, i.e. circuits that can perform non-integer-order differentiation. It has been one of the major research areas under such field due to proven advantages over its integer-order counterparts. In particular, traditional integer-order proportional-integral-derivative (PID) controllers seem to be outperformed by fractional-order PID (FOPID or PIλDμ) controllers. Many researches have emerged presenting the possibility of designing analog and digital fractional-order differentiators, but only restricted to a fixed order. In this paper, we present the conceptual design of a variable fractional-order differentiator in which the order can be selected from 0 to 1 with an increment of 0.05. The analog conceptual design utilizes operational amplifiers and resistor-capacitor ladders as main components, while a generic microcontroller is introduced for switching purposes. Simulation results through Matlab and LTSpiceIV show that the designed resistor-capacitor ladders can perform as analog fractional-order differentiation.

MSC: Primary 26A33; Secondary 65D25, 65D30, 93C05, 93C55

Keywords: fractional calculus; fractional-order differentiator; fractional-order controller; Matlab

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About the article

Published Online: 2014-06-26

Published in Print: 2014-09-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 17, Issue 3, Pages 697–716, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0195-z.

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© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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