Robusno upravljanje dinamičkim sustavima promjenjivim s obzirom na parametre

undergraduate thesis

• Title (english): Robust control of parameter-varying dynamical systems
• Author: Bartol Periša
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2024-09, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Tema ovog završnog rada je postupak sinteze robusnog regulatora linearnog sustava
promjenjivog s ozbirom na parametre sustava, s naglaskom na rješavanje H∞
optimizacijskog problema uz pomoć linearnih matričnih nejednadžbi koje je moguće
rješavati u lako dostupnim računalnim alatima poput MATLAB-a. Pritom se
promatraju korišteni numerički algoritmi za rješavanje optimizacijskih problema poput
metode unutarnje točke i elipsoid algoritma. Nastoje se spoznati temeljni kriteriji
stabilnosti dinamičkih sustava zasnovani na direktnoj Ljapunovljevoj metodi, kao i
njihova formulacija kroz linearne matrične nejednadžbe koristeći lemu ograničene
realnosti. Iz dobivenog nelinearnog modela robotskog manipulatora cilj je uz
linearizaciju takvog modela s ozbirom na parametre rasporeda sustava ostvariti sintezu
robusnog regulatora danog sustava, s naglaskom na regulator stanja u povratnoj vezi
zatvorene petlje. Simulacijski rezultati te rješavanje linearnih matričnih nejednadžbi
provest će se uz pomoć programskih alata MATLAB i Yalmip s implementiranim
SDPT3 solverom.

Abstract (english)

This thesis presents the process of synthesizing a robust controller for a linear
parameter-varying system, with a focus on solving the H∞ optimization problem using
linear matrix inequalities that can be addressed through readily available computational
tools such as MATLAB. The study will explore the numerical algorithms used to solve
optimization problems, such as the interior-point method and the ellipsoid algorithm.
Fundamental stability criteria for dynamic systems, based on the direct Lyapunov
method, will be examined, along with their formulation through linear matrix
inequalities using the bounded-real lemma. From obtained nonlinear model of a robotic
manipulator, the goal is to synthesize a robust controller for the system by linearizing
the model concerning the system’s scheduling parameters, emphasizing state feedback
control in a closed-loop configuration. Simulation results and the solution of linear
matrix inequalities will be carried out using MATLAB and Yalmip, with the
implementation of the SDPT3 solver.

• Keywords: Robusno upravljanje; linearni sustavi promjenjivi s ozbirom na parametre; H∞ kriterij; linearne matrične nejednadžbe; Yalmip
• Keywords (english): Robust control; linear parameter-varying systems; H∞ criterion; linear matrix inequalities
• Language: croatian
• URN:NBN: urn:nbn:hr:235:352877
• Study programme: Title: Mechatronics and Robotics; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka mehatronike i robotike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka mehatronike i robotike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-09-20 10:45:54