Analogue Realization of Fractional-Order Dynamical Systems
| Autor: | Ľubomír Dorčák, L. Pivka, Jan Terpak, Ivo Petras, Emmanuel A. Gonzalez, Juraj Valsa |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Mathematical model
Dynamical systems theory Differential equation General Physics and Astronomy analogue realization fractional-order differential equation lcsh:Astrophysics fractional-order dynamical system fractional dynamics fractional calculus entropy constant phase element lcsh:QC1-999 Fractional calculus Differentiator Fractional dynamics Control theory Integrator lcsh:QB460-466 lcsh:Q lcsh:Science lcsh:Physics Network model Mathematics |
| Zdroj: | Entropy; Volume 15; Issue 10; Pages: 4199-4214 Entropy, Vol 15, Iss 10, Pp 4199-4214 (2013) |
| ISSN: | 1099-4300 |
| DOI: | 10.3390/e15104199 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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