ABSTRACT
Modelling of an actual measurement system consisting of many devices requires considering the response dynamics of each of them (Luft & Cio« 2005). When one knows the input signal and the response signal, it is possible to obtain a description of the system dynamics in the form of a differential equation. The accuracy of a thus obtained model depends mainly on the applied method of identification. Application of fractional order derivativeintegral calculus (in brief: fractional calculus) for identification purposes provides new possibilities of obtaining a model which reflects the dynamics of the examined object in a more accurate way. (Kaczorek 2009), (Podlubny 1999)
Fractional calculus is not a new concept. It dates back to the 17th century. References to it can be found in the letters of G. W. Leibnitz to de l’Hopital (1695), in the works of L. Euler (1738) or P. S. Laplace (1812). (Ostalczyk 2008)
Many physical phenomena, such as liquid permeation through porous substances, load transfer through an actual insulator, or heat transfer through a heat barrier are described more accurately by means of derivative-integral equations. The dynamics of physical processes such as acceleration, displacement, liquid flow, electric current power or magnetic field flux are modelled by means of differential equations. The courses of these processes are actually continuous variables, 1 m -fold differentiable, where m is determined subject to the order of the examined fractional derivative. Mass cannot be relocated from one place to another in an infinitely short time. Neither is it possible to change temperature or pressure in an actual object infinitely fast.
