prikaz prve stranice dokumenta LQR i LQG kontrola - teorija i primjene
  Download
PDF 816.85 KB
master's thesis
LQR i LQG kontrola - teorija i primjene
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:975484
Banušić, Gregor Boris
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Banušić, G. B. (2017). LQR i LQG kontrola - teorija i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:975484

Banušić, Gregor Boris. "LQR i LQG kontrola - teorija i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:975484

Banušić, Gregor Boris. "LQR i LQG kontrola - teorija i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:975484

Banušić, G. B. (2017). 'LQR i LQG kontrola - teorija i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:975484

Banušić GB. LQR i LQG kontrola - teorija i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:975484

G. B. Banušić, "LQR i LQG kontrola - teorija i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:975484

Metadata
TitleLQR i LQG kontrola - teorija i primjene
AuthorGregor Boris Banušić
MentorZlatko Drmač (mentor)
Committee memberZlatko Drmač (predsjednik povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberVedran Čačić (član povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Automatsko upravljanje sustavima je bitna sastavnica suvremenih tehnoloških rješenja. Sustav je uređena cjelina pojedinih dijelova koji s okolinom komuniciraju preko ulaznih i izlaznih signala. Pomoću fizičkih zakona, potrebno je napraviti matematički model sustava iz kojeg nastaje reprezentacija sustava u vremenskoj domeni, tj. prostor stanja sustava. Pomoću definicija upravljivosti, osmotrivosti, stabilnosti i detektabilnosti otkrivaju se važna svojstva sustava koja govore o mogućnosti implementacije automatskog upravljanja na željeni način. Kako bismo stabilizirali sustav, koristeći odgovarajući upravljački signal, potrebno je dizajnirati povratnu vezu metodom namještanja svojstvenih vrijednosti. Nedostatak određenih smjernica gdje postaviti svojstvene vrijednosti predstavlja problem u praksi. Pitanje dizajna sustava rješava se najčešće kompromisom, tako da se zadovolje traženi kriteriji performanse sustava. Stabilnost sustava, s obzirom na tražene kriterije, postiže se linearno kvadratnim regulatorom LQR (engl. Linear Quadratic Regulator) ili linearno kvadratnim Gaussovim regulatorom LQG (engl. Linear Quadratic Gaussian). LQR optimizira determinističke sustave, dok se LQG bavi optimizacijom performansi stohastičkih sustava. Za pronalaženje LQR i LQG regulatora potrebno je numeričko rješavanje neprekidne algebarske Riccatijeve jednadžbe. U radu je pokazano da se sustavi sa više ulaza i izlaza mogu kontrolirati pomoću LQR i LQG regulatora u vremenskoj domeni.
Abstract (english)
Control systems have many applications in modern world and play an important role in technology. To control a system, its mathematical model needs to be developed. Modelling is a process of defining a corresponding system of differential equations for a physical problem. Systems state space can be derived from its mathematical model. Generic concepts like controllability, observability, stability and detectability can lead to some significant system specifications, telling whether the system can be controlled in a specific way. The main goal is to prevent the system from diverging or ”blowing up”, so it needs to be stabilized. With the right control signal, a feedback control loop is set up through pole placement. In the absence of instructions on how to place poles, a more convenient way is used to obtain certain specifications, called linear quadratic regulation. For deterministic system optimizations linear quadratic regulator LQR is used, while for stohastic system optimizations linear quadratic Gaussian regulator is in charge. In order to obtain LQR and LQG regulators, a solution of algebraic Riccati equation needs to be computed. This work shows that multi-input and multi-output systems can be controlled with LQR and LQG regulators in time domain.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:975484
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-27 13:04:24