Sinteza multivarijabilnog PID regulatora međusobno spregnutih mehaničkih sustava primjenom linearnih matričnih nejednadžbi

undergraduate thesis

• Title (english): Multivariable PID controller synthesis for coupled mechanical systems via linear matrix inequality approach
• Author: Srećko Arandia-Krešić
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2020-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering; Automation and Robotics

Abstract

Završni rad pokušat će prvotno predstaviti matematički pristup regulaciji primjenom linearnih matričnih nejednadžbi (LMN), odnosno optimizacijskim problemima s konveksnim ograničenjima, i to s posebnim naglaskom na H_beskonačno stabilizaciju. Razmatraju se dosadašnje spoznaje LMN-a u teoriji regulacije te se navode i obrađuju optimizacijski alati, posebice metoda unutarnje točke za njihovo rješavanje. Vrhunac takvog teorijskog razmatranja bit će PID regulacija.
Sekundarno, iznjedriti će se na isti način sinteza PID regulatora mehaničkog nelinearnog sustava sastavljenog od dva elastično spregnuta mehanička podsustava. Pristupit će se pritom linearnim matričnim nejednadžbama, budući da danas predstavljaju jedan od glavnih smjerova napretka u sličnim primjenama. Štoviše, koristeći dosadašnje spoznaje disipativnih sustava, koncept će se temeljiti na lemi ograničene realnosti (eng. bounded-real lemma), odnosno oslanjanju na H_boskonačno normu prijenosne funkcije.

Abstract (english)

This thesis will attempt firstly to present mathematical approach to the synthesis of controllers based on Linear Matrix Inequalities (LMI), and more so H_infinity stabilization. Current acknowledgements of LMI-s, or generally constrained optimization in control synthesis, as well as modern optimization tools, including interior-point method for finding their solutions shall be discussed. The peak of such theoretical considerations shall be PID control.
Secondly, PID controller synthesis of the mechanical nonlinear system incorporated by two elastically interconnected subsystems shall be derived accordingly. LMI approach will be taken as it represents one of the most important niches of modern optimal control theory. Furthermore, taking in to account current knowledge of dissipative systems, concept will be based on bounded-real lemma and H_infinity norm of the transfer function.

• Keywords: linearne matrične nejednadžbe; optimizacija; interior-point metoda; PID regulacija; bounded-real lema; H_beskonačno norma
• Keywords (english): linear matrix inequalities; optimization; interior-point method; PID control; bounded-real lemma; H_infinity norm
• Language: croatian
• URN:NBN: urn:nbn:hr:235:311543
• 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: 2020-09-18 09:44:20