Matematičko modeliranje i analiza nelinearnih međusobno povezanih elektromehaničkih sustava primjenom dualnih brojeva

undergraduate thesis

• Title (english): Mathematical modelling and analysis of nonlinear interconnected electromechanical systems using dual numbers
• Author: Jakov Jonjić
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2022-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

U ovom radu predstavljen je matematički opis dualnih i hiper-dualnih brojeva i funkcija s dualnim argumentima. Izvod i motivacija za uvođenje dualnih operatora i dualnih varijabli u dinamici krutih tijela prikazani su na primjeru pravocrtnog gibanja čestice, a na osnovu fundamentalnog, drugog Newtonovog zakona. Izvod jednadžbi energija i formulacija dualnih Lagrangeovih jednadžbi gibanja za elastično povezani elektromehanički sustav kolica na klackalici bazirani su na metodi dualnih brojeva. Simulacije dinamike otvorenog kruga sustava provedene su u MATLAB-u, a utjecaj elastičnih međuveza i priroda nestabilnog ponašanja navedeni su u opisima grafova. Numeričko računanje derivacija funkcija metodom hiper-dualnih brojeva prikazano je na primjeru složene analitičke funkcije, a moguća primjena ove metode prikazana je u algoritmima optimalnog robusnog upravljanja.

Abstract (english)

In this work, the mathematical description of dual and hyper-dual numbers and functions with dual arguments are presented. Derivation of, and motivation for introducing dual operators and dual variables in rigid body dynamics are presented on the example of the uniform motion of a particle, based on the fundamental Newton's second law of motion. The derivation of the energy equations and the formulation of dual Lagrange equations of motion for an elastically interconnected electromechanical system of cart and seesaw is based on the dual numbers method. The simulations of the dynamics of the open-loop system are carried out in MATLAB, and the effects of elastic interconnections and the nature of the unstable behavior are discussed in the descriptions of the graphs. Numerical evaluation of derivatives of functions by the method of hyper-dual numbers is shown on a complex analytical function, and the possible application of this method is shown in algorithms of robust optimal control.

• Keywords: dualni brojevi; dualne Lagrangeove jednadžbe; prostor stanja; nelinearni dinamički sustav; robusno optimalno upravljanje
• Keywords (english): dual numbers; dual Lagrange dynamic equations; state space; nonlinear dynamic system; robust optimal control
• Language: croatian
• URN:NBN: urn:nbn:hr:235:259626
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-09-26 09:16:36