Analogue Realization of Fractional-Order Dynamical Systems

Entropy

Ľubomír Dorčák³  Juraj Valsa¹  Emmanuel Gonzalez²  Ján Terpák³  Ivo Petráš³ 

[1] Faculty of Electrical Engineering and Computer Science, Brno University of Technology, Brno 601 90, Czech Republic; E-Mail:;Department of Computer Technology, College of Computer Studies, De La Salle University Manila, Manila 1004, Philippines; E-Mail:;Institute of Control and Informatization of Production Processes, Faculty BERG, Technical University of Košice, Košice 042 00, Slovakia; E-Mails:

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

DOI  :  10.3390/e15104199

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.