H-beskonačno optimalno upravljanje nestabilnim elektromehaničkim sustavom

master's thesis

• Title (english): H-infinity optimal control of unstable electromechanical system
• Author: Krešimir Jukić
• Mentor: Marko Jokić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2020-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Tema ovog diplomskog rada je H-beskonačno optimalno upravljanje nestabilnim elektromehaničkim sustavom. H-beskonačno optimizacija temelji se na sustavnom snižavanju H-beskonačno norme koja predstavlja najveću singularnu vrijednost matrice prijenosnih funkcija, tj. najveći omjer 2-norme izlaznog signala s 2-normom ulaznog signala po frekvenciji i po vektoru ulaznog signala. Ipak, sinteza regulatora koji je optimalan po H-beskonačno normi daje nominalno dobar frekvencijski odziv, ali ne uvjetuje nužno dobro ponašanje u realnim uvjetima. Uvođenjem težinskih filtera, tj. prijenosnih funkcija kojima se modificiraju ulazni i izlazni signali, modificira se prijenosna funkcija sustava za potrebe H-beskonačno optimizacije kako bi se penalizirali ciljani izlazni signali za ciljane ulazne signale. Ciljanim odabirom filtera može se postići povoljan frekvencijski i tranzijentni odziv. U ovom radu izveden je model sustava kolica na njihalu i sustava triju kolica na njihalu povezanih sustavom oprugama. Izvedeni modeli su linearizirani, a nad lineariziranim modelima provedene su sinteze različitih regulatora. Na modelu sustava kolica na njihalu istražen je utjecaj odabranih težinskih filtera na performanse sustava. Prikazani su rezultati i procedura koji mogu poslužiti za odabir težinskih filtera za sintezu regulatora i za druge sustave, ali zbog kompleksnih veza između parametara filtera i mjera performansi nije moguće dati striktne smjernice. Nadalje, na sustavu triju kolica na njihalu povezanih oprugama razmotrena je mogućnost modifikacije strukture regulatora s ciljem postizanja decentraliziranog ili distribuiranog upravljanja. Ispitane su performanse sustava s regulatorima različite strukture. Očekivano, sustav s centraliziranim upravljanjem daje najpovoljnije rezultate, a performanse sustava s distribuiranim upravljanjem blago lošije. Razmotrena je mogućnost decentraliziranog upravljanja regulatorima čija je sinteza provedena na modelu podsustava zanemarujući pritom dinamiku ostatka sustava. Pokazano je da sustav s takvim upravljanjem pokazuje lošije performanse. Upravljanje sustavom kolica na njihalu implementirano je u vidu računalnog programa i ispitano na eksperimentalnom postavu razvijenom u sklopu projekta 'Upravljanje prostorno distribuiranim dinamičkim sustavima'.

Abstract (english)

The topic of this thesis is H-infinity optimal control of unstable electromechanical system. H-infinity optimization is based on a systematic decrease of H-infinity norm, which represents the highest singular value of transfer function matrix, ie. the highest ratio of the 2-norm of the output signal and the 2-norm of the input signal in terms of signal frequency and in terms of the input signal. H-infinity optimization results with a system with nominally optimal frequency response, but does not necessary have good response in real-life conditions. By introducing the weighting filters, ie. transfer functions used for modification of input and output signals, the original transfer function matrix is being modified for H-infinity optimization purposes with the purpose of penalization of the chosen output signals caused by the chosen input signals. Precise determination of weighting filter results with both good frequency and transient response of the system. In this paper the model of seesaw-cart system is derived. The model of three elastically interconnected seesaw-cart systems is also derived. Derived models are linearised, and linearised models are used for controller synthesis. Investigation of filter parameters influence on specific performance measures of one seesaw-cart model is performed. Obtained results are presented, and can be used as guidelines for future control synthesis. Due to the nonlinear influence of filter parameters on performance measures strict and precise conclusions are impossible, but presented results could be a starting point for future investigations of filter influence on different systems performances. The model of three interconnected seesaw-cart system is used for the investigation of influence of controller's structure on system performance. The centralised controller's structure is modified so it represents set of decentralised or distributed controllers. As expected, the system with centralised control obtains best performance, while performance of the system with distributed control is slightly worse. Possibility of decentralised control with controllers synthesised on one seesaw-cart subsystem while ignoring the rest of system dynamics is considered. System with such control obtained much worse performance. The control of one seesaw-cart system is realised in terms of the computer program and tested on experimental setup developed as part of the project 'Control of spatially distributed dynamical systems'.

• Keywords: H-beskonačno optimalno upravljanje; H-beskonačno sinteza; težinski filteri; modeliranje dinamike; struktura regulatora
• Keywords (english): H-infinity optimal control; H-infinity synthesis; weighting filters; dynamics modeling; controller's structure
• Language: croatian
• URN:NBN: urn:nbn:hr:235:672265
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-07-07 08:46:33