MODELING AND IDENTIFICATION OF FRACTIONAL-ORDER DYNAMICAL SYSTEMS

11th International Multidisciplinary Scientific GeoConference SGEM2011, www.sgem.org, SGEM2011 Conference Proceedings/ ISSN 1314-2704, June 20-25, 2011, Vol. 2, 553-560 pp

ABSTRACT

One of the most characteristic features of the processes in the area of mining and
processing of earth resources is their complexity. The modern methods of investigation,
monitoring and control of these processes utilize approaches based upon modeling of
the processes. In this paper we will focus only on the dynamical processes, where the
mathematical models are differential equations. As it results from the last research
works, majority of the real objects in general are fractional-order systems. Fractionalorder
models are more adequate for the description of dynamical systems than integerorder
models. But appropriate methods for the numerical calculations of fractional-order
differential equations are needed in such cases and also methods for the identification of
such systems. In this contribution we describe and compare some previous methods
used for simulation purposes with the methods based on approximate formulas for
numerical inversion of Laplace transforms. The verification and comparison will be
based mainly on the accuracy and computing time. Also an experimental method of
identification is given. The verification of identification method was performed on
systems with known parameters.

Keywords: fractional-order dynamic system, modeling, identification, optimization, Laplace inversion