Conceptual Design of a Selectable Fractional-Order Differentiator for Industrial Applications

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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 PIlambdaDmu) 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.
Fractional calculus, Fractional-order differentiator, Fractional-order controller, Matlab
Bibliographic citation
Gonzalez, E. A., Dorčák, U., Monje, C. A., Valsa, J., Caluyo, F. S. & Petráš, I. (2014). Conceptual design of a selectable fractional-order differentiator for industrial applications. Fractional Calculus and Applied Analysis, 17(3), 697-716.