Identifikacija dinamičkih sustava metodom najmanjih kvadrata

master's thesis

• Author: Kristina Komar
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu, proučavali smo kako modelirati analitički dinamički sustav u frekvencijskoj domeni. To nam je bilo od interesa jer s algebarskim jednadžbama možemo računati na ograničenoj aritmetici računala. Kao pomoćni alat tu nam je poslužila Laplaceova transformacija. Pomoću nje smo dobili funkciju prijelaza koja je od velike važnosti za interpretaciju rezultata početnog sustava diferencijalnih jednadžbi u frekvencijskoj domeni. Definirali smo što je to dinamički sustav, njegova važna svojstva, te vidjeli primjere iz fizikalnog svijeta gdje se dinamički sustav koristi. Na kraju smo opisali iterativnu numeričku metodu vector fitting. Njome aproksimiramo funkciju prijelaza u smislu najmanjih kvadrata. Prikazali smo neke rezultate u programskom paketu MATLAB.

Abstract (english)

In this thesis, we studied how to model analytical dynamical system in frequency domain. That was of our interest because with the algebraic equations we can easily do the computing on a limited computer arithmetic. Laplace transform was helpful auxiliary tool for that purpose. With it, we get the transfer function which is of great importance for the interpretation of the results of initial system of differential equations in frequency domain. We defined what dynamical system is, its important characteristics, and we saw examples from the physical world where dynamical system is used. Finally, we described the iterative numerical method named vector fitting. It approximates transfer function in the least square fit. We show some results in software package MATLAB.

• Keywords: analitički dinamički sustav; frekvencijska domena; algebarske jednadžbe; Laplaceova transformacija; iterativna numerička metoda; vector fitting; MATLAB
• Keywords (english): analytical dynamical system; frequency domain; algebraic equations; Laplace transform; iterative numerical method; vector fitting; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:043356
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-14 11:57:58