Robustnost regulátorů
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B
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Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií
Abstract
Táto práca sa zaoberá skúmaním pojmu robustnosť regulátorov. Jej ciežom je porovnať robustnosť diskrétnych PID regulátorov (Discrete Equivalent Continuous Controller, Discrete Impulse Area Invariant, Takahashi, Feed-Forward), adaptívnych diskrétnych PID regulátorov (Discrete Impulse Area Invariant, Takahashi, Feed- Forward), optimálnych (kvadratický optimálny) a adaptívnych optimálnych regulátorov (kvadratický optimálny) na zvolených prenosových funkciách a tiež má byť preverený vplyv A/D a D/A prevodníkov. Na začiatku textu sú vytýčené ciele, ktoré majú byť dosiahnuté a je vysvetlený pojem robustnosť. Nasleduje popísanie a priblíženie jednotlivých vybraných druhov regulátorov a použitých identifikačných metód (pre adaptívne regulátory bola použitá rekurzívna metóda najmenších štvorcov). Je spravený rozbor vybranej prenosovej funkcie pomocou Kharitonovho teorému. Ďalej nasleduje popis metód, ktorými sa bude overovať robustnosť vybraných regulátorov. Prvou z metód sú integrálne kritériá, konkrétne kritérium ITAE a kvadratické kritérium. Druhou metódou je vyšetrenie zásoby stability v module v komplexnej rovine. Za týmto nasleduje zobrazenie dosiahnutých výsledkov a komentár k nim. Získané výsledky sú graficky zobrazené a sú pomocou nich vzájomne porovnané jednotlivé typy regulátorov. Všetky simulácie a dosiahnuté výsledky boli získané pomocou programu MATLAB – Simulink. V závere práce je celkové zhodnotenie.
This thesis tries to research the term “robust controllers”. Its aim is to compare the robustness of discrete PID controllers (Discrete Equivalent Continuous Controller, Discrete Impulse Area Invariant, Takahashi, Feed-Forward), adaptive discrete PID controllers (Discrete Impulse Area Invariant, Takahashi, Feed-Forward), optimal controllers (quadratic optimal), and adaptive optimal controllers (quadratic optimal) on chosen transfer functions. Its aim is also to check the influence of A/D and D/A converters. The aims to obtain are demarked at the beginning of the text and also there is an explanation of the term “robustness.” Later on there is a description and an approximation to each of the chosen kinds of controllers and the identification methods used in the thesis (for adaptive controllers the method of recursive least-squares was used). The Kharitonov's Theorem are made on the chosen transfer function. Next there is a description of the methods with which the robustness of the controllers will be tested. The first method is the integral criteria, particular ITAE criterion and quadratic criterion. The second one is the analysis of the generalised circle criterion. Furthermore there are various displays of the results obtained and their corresponding comments. The results obtained are graphically displayed and by means of these schemes the particular types of controllers are compared. All of the simulations and results obtained were acquired through the use of the program MATLAB- Simulink. In the end of the thesis there is an overall evaluation.
This thesis tries to research the term “robust controllers”. Its aim is to compare the robustness of discrete PID controllers (Discrete Equivalent Continuous Controller, Discrete Impulse Area Invariant, Takahashi, Feed-Forward), adaptive discrete PID controllers (Discrete Impulse Area Invariant, Takahashi, Feed-Forward), optimal controllers (quadratic optimal), and adaptive optimal controllers (quadratic optimal) on chosen transfer functions. Its aim is also to check the influence of A/D and D/A converters. The aims to obtain are demarked at the beginning of the text and also there is an explanation of the term “robustness.” Later on there is a description and an approximation to each of the chosen kinds of controllers and the identification methods used in the thesis (for adaptive controllers the method of recursive least-squares was used). The Kharitonov's Theorem are made on the chosen transfer function. Next there is a description of the methods with which the robustness of the controllers will be tested. The first method is the integral criteria, particular ITAE criterion and quadratic criterion. The second one is the analysis of the generalised circle criterion. Furthermore there are various displays of the results obtained and their corresponding comments. The results obtained are graphically displayed and by means of these schemes the particular types of controllers are compared. All of the simulations and results obtained were acquired through the use of the program MATLAB- Simulink. In the end of the thesis there is an overall evaluation.
Description
Citation
DOBIAS, M. Robustnost regulátorů [online]. Brno: Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. 2009.
Document type
Document version
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Language of document
sk
Study field
Kybernetika, automatizace a měření
Comittee
doc. Ing. Eduard Janeček, CSc. (předseda)
prof. Ing. Petr Pivoňka, CSc. (místopředseda)
doc. Ing. Petr Blaha, Ph.D. (člen)
doc. Ing. Zdeněk Bradáč, Ph.D. (člen)
Ing. Ilona Janáková, Ph.D. (člen)
Ing. Stanislav Klusáček, Ph.D. (člen)
Date of acceptance
2009-06-10
Defence
Student obhájil diplomovou práci.
Result of defence
práce byla úspěšně obhájena
Document licence
Standardní licenční smlouva - přístup k plnému textu bez omezení