Entropy 2013, 15(10), 4199-4214; doi:10.3390/e15104199

Analogue Realization of Fractional-Order Dynamical Systems

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Received: 27 August 2013; in revised form: 24 September 2013 / Accepted: 25 September 2013 / Published: 7 October 2013
(This article belongs to the Special Issue Dynamical Systems)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models with the same number of parameters. A great deal of modern methods for investigation, monitoring and control of the dynamical processes in different areas utilize approaches based upon modeling of these processes using not only mathematical models, but also physical models. This paper is devoted to the design and analogue electronic realization of the fractional-order model of a fractional-order system, e.g., of the controlled object and/or controller, whose mathematical model is a fractional-order differential equation. The electronic realization is based on fractional-order differentiator and integrator where operational amplifiers are connected with appropriate impedance, with so called Fractional Order Element or Constant Phase Element. Presented network model approximates quite well the properties of the ideal fractional-order system compared with e.g., domino ladder networks. Along with the mathematical description, circuit diagrams and design procedure, simulation and measured results are also presented.
Keywords: fractional-order dynamical system; fractional dynamics; fractional calculus; fractional-order differential equation; entropy; constant phase element; analogue realization
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MDPI and ACS Style

Dorčák, Ľ.; Valsa, J.; Gonzalez, E.; Terpák, J.; Petráš, I.; Pivka, L. Analogue Realization of Fractional-Order Dynamical Systems. Entropy 2013, 15, 4199-4214.

AMA Style

Dorčák Ľ, Valsa J, Gonzalez E, Terpák J, Petráš I, Pivka L. Analogue Realization of Fractional-Order Dynamical Systems. Entropy. 2013; 15(10):4199-4214.

Chicago/Turabian Style

Dorčák, Ľubomír; Valsa, Juraj; Gonzalez, Emmanuel; Terpák, Ján; Petráš, Ivo; Pivka, Ladislav. 2013. "Analogue Realization of Fractional-Order Dynamical Systems." Entropy 15, no. 10: 4199-4214.

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