Analiza stabilnosti nelinearnih sustava vođenih analitičkim neizrazitim regulatorom

doctoral thesis

• Title (english): Stability analysis of nonlinear systems controlled by analytic fuzzy controller
• Author: Josip Kasać
• Mentor: Branko Novaković (mentor)
• Committee member: Nikola Šerman (predsjednik povjerenstva)
• Committee member: Branko Novaković (član povjerenstva)
• Committee member: Mladen Crneković (član povjerenstva)
• Committee member: Zdravko Terze (član povjerenstva)
• Committee member: Zdenko Kovačić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2005-05-24, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering
• Universal decimal classification (UDC): 67/68 - Various industries, trades and crafts; 51 - Mathematics

Abstract

Tema ove disertacije je analiza stabilnosti nelinearnih mehaničkih sustava vođenih analitičkim neizrazitim regulatorom. Analitički neizraziti regulator je nekonvencionalni pristup koji koristi analitičke funkcije za određivanje centara izlaznih neizrazitih skupova umjesto baze pravila ponašanja. Analiza stabilnosti je zasnovana na Lyapunovljevoj izravnoj metodi i ne zahtijeva prikaz dinamike sustava upravljanja u obliku Takagi- Sugeno neizrazitog modela. Analiza stabilnosti je podijeljena na četiri osnovna dijela. Prvo se formiraju jednadžbe pogreške zatvorenog sustava upravljanja. Drugo, formira se kandidat za Lyapunovljevu funkciju. Zatim se izvode uvjeti stabilnosti koji garantiraju pozitivnu definitnost Lypunovljeve funkcije i negativnu definitnost njene vremenske derivacije. Na kraju, primjenjuje se LaSalleov princip invarijantnosti koji garantira asimptotsku stabilnost. Time su dobiveni kriteriji lokalne stabilnosti koji uključuju svega nekoliko parametara upravljačkog sustava. Na osnovu dobivenih rezultata razmatrane su neke modifikacije analitičkog neizrazitog regulatora koje osiguravaju globalnu asimptotsku stabilnost. Nadalje, Lyapunovljeve funkcije analiziranih regulatora su iskorištene za evaluaciju performansi i određivanje optimalnih vrijednosti parametara regulatora. \Navedeni pristup zasnovan je na konstrukciji parametarski ovisne Lyapunovljeve funkcije. Odgovarajućim izborom slobodnog parametra dobivena je ocjena integralnog indeksa performanse. Indeks performanse ovisi samo o nekoliko parametara regulatora i nekoliko parametara koji karakteriziraju dinamiku robota. Optimalne vrijednosti parametara regulatora dobivene su minimizacijom indeksa performanse. Procedura podešavanja parametara demonstrirana je na simulacijskom modelu dva različita tipa robota.

Abstract (english)

The subject of this thesis is the stability analysis of nonlinear mechanical systems in closed loop with analytic fuzzy PID controller. The analytic fuzzy control is a nonconventional approach that uses an analytic function for output determination, instead of a fuzzy rule base. The stability analysis is based on the Lypunov’s direct method and does not require representation of the plant dynamics in the form of Takagi-Sugeno’s fuzzy model. The stability analysis is divided in four principal parts. First, error equations for closed loop system is determined. Second, Lyapunov function candidate is proposed. Then, stability criterion on system parameters is established. Finally, LaSalle invariance principle is invoked to guarantee the asymptotic stability. The local stability condition which involve only few control systems parameters are obtained. On the base of obtained results, some modification of analytic fuzzy controllers which ensure global asymptotic stability are considered. Further, the Lyapunov functions of analyzed controllers are employed for performance evaluation and determination of the optimal values of controller parameters. The proposed approach is based on construction of a parameter dependent Lyapunov function. With the appropriate choice of the free parameter an estimation of integral performance index is obtained. The estimated performance index depends on controller parameters and few parameters which characterize the robot dynamics. The optimal values of the controller gains are obtained by minimization of the performance index. The obtained tuning rules are demonstrated by using simulation models of two robot manipulators with different structures.

• Keywords: upravljanje robotom; analitičko neizrazito upravljanje; Lyapunovljeva analiza stabilnosti; globalna stabilnost; evaluacija performansi; nelinearno upravljanje
• Keywords (english): robot control; analytic fuzzy control; Lyapunov stability analysis; global stability; performance evaluation; nonlinear control
• Language: croatian
• URN:NBN: urn:nbn:hr:235:170430
• Study programme: Title: Mechanical Engineering and Naval Architecture; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje tehničkih znanosti (doktor/doktorica znanosti, područje tehničkih znanosti)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-03 14:48:55