Next Article in Journal
Modeling Dynamics of Diffusion Across Heterogeneous Social Networks: News Diffusion in Social Media
Next Article in Special Issue
Development of Metrics and a Complexity Scale for the Topology of Assembly Supply Chains
Previous Article in Journal / Special Issue
The Fractional Differential Polynomial Neural Network for Approximation of Functions
Entropy 2013, 15(10), 4199-4214; doi:10.3390/e15104199

Analogue Realization of Fractional-Order Dynamical Systems

1,* , 2
, 3
, 1
, 1
 and 4
1 Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Košice, Košice 042 00, Slovakia 2 Faculty of Electrical Engineering and Computer Science, Brno University of Technology, Brno 601 90, Czech Republic 3 Department of Computer Technology, College of Computer Studies, De La Salle University Manila, Manila 1004, Philippines 4 Technical University of Košice, Institute of Computer Technology, B. Němcovej 3, Košice 042 00, Slovakia
* Author to whom correspondence should be addressed.
Received: 27 August 2013 / Revised: 24 September 2013 / Accepted: 25 September 2013 / Published: 7 October 2013
(This article belongs to the Special Issue Dynamical Systems)
Download PDF [844 KB, uploaded 24 February 2015]


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 fractional-order dynamical system; fractional dynamics; fractional calculus; fractional-order differential equation; entropy; constant phase element; analogue realization
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.

Share & Cite This Article

Export to BibTeX |

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.

View more citation formats

Article Metrics


Citing Articles

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert