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Vol: 54(68) No: 4 / December 2009 

Systems Modeling Based on Orthogonal Rational Functions
Bratislav Danković
Department of Automatics, University of Niš, Faculty of Electrical Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia, phone: +38118529363, e-mail: bratislav.dankovic@elfak.ni.ac.rs
Dragan Antić
Department of Automatics, University of Niš, Faculty of Electrical Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia, e-mail: dragan.antic@elfak.ni.ac.rs
Zoran Jovanović
Department of Automatics, University of Niš, Faculty of Electrical Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia, e-mail: zoran.jovanovic@elfak.ni.ac.rs
Saša Nikolić
Department of Automatics, University of Niš, Faculty of Electrical Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia, e-mail: sasa.s.nikolic@elfak.ni.ac.rs
Marko Milojković
Department of Automatics, University of Niš, Faculty of Electrical Engineering, A. Medvedeva 14, 18000 Niš, Republic of Serbia, e-mail: marko.milojkovic@elfak.ni.ac.rs


Keywords: orthogonal function, orthogonal filter, systems modeling, genetic algorithm.

Abstract
This paper deals with a possibility of modeling continuous dynamical systems, via orthogonal rational functions. Recent results in the field of orthogonal functions were used to improve accuracy of modeling. Legendre orthogonal filters were designed on the basis of orthogonal rational functions and then adjustable models were formed. Models parameters were optimized using genetic algorithm. As a case study, an experimental simple hydraulic system was considered. Simulations were performed to approve theoretical results and demonstrate that the method described in the paper is very suitable for modeling continuous systems in the sense of model accuracy and modeling algorithm speed.

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