o:32996 Условна оптимизација дискретних система аутоматског управљања применом потпуне преносне функције докторска дисертација Conditional optimization of discrete-time control systems using the full transfer function : doctoral dissertation sr U okviru doktorske disertacije istrauje se sinteza upravljaqkog sistemaproporcionalno-diferencno-sumarnog (PDS) tipa na osnovu karakteristiqnogpolinoma potpune prenosne funkcije. Potpuna prenosna funkcija omoguava dase dobiju taqni rezultati u pogledu skraivanja jednakih nula i polova, do-bijanja karakteristiqnog polinoma i odreivanja potpunog odziva sistema. Napoqetku se odreuje oblast relativne stabilnosti u prostoru podexljivih para-metara upravljaqkog sistema tako da stepen priguxenja ζ ima unapred zahtevanuvrednost. To je uraeno u sluqaju dva podexljiva parametra na primerima PDi PS upravljaqkih sistema. Osim toga, pronaena je oblast relativne stabilno-sti u sluqaju tri podexljiva parametra PDS upravljaqkog sistema. U narednomkoraku se sprovodi metoda uslovne optimizacije pri qemu se koristi izraz zagrexku izlazne veliqine koji uzima u obzir istovremeno dejstvo nenultih poqe-tnih uslova i spoljaxnjeg ulaza, a xto je omogueno primenom potpune prenosnefunkcije. Na taj naqin se pronalaze optimalni parametri linearnih upravlja-qkih sistema PDS tipa za koje indeks performanse, u obliku sume kvadrata gre-xaka, ima minimalnu vrednost.U drugom delu disertacije prethodno razvijena metoda uslovne optimizacijelinearnih diskretnih sistema se proxiruje i primenjuje na klasu nelinearnihdiskretnih sistema, u obliku Takagi-Sugeno (TS) fazi sistema. U tu svrhuje iskorixena osobina TS fazi sistema da se dinamika nelinearnog sistemamoe izraziti pomou nekoliko linearnih (linearizovanih) sistema. Neline-arni Takagi-Sugeno fazi model, koji verodostojno opisuje ponaxanje sistema nacelom prostoru izlaza, se dobija interpolacijom nekoliko linearnih matemati-qkih modela. Izvrxena je sinteza upravljaqkog sistema tipa paralelno raspode-ljenog upravljanja (PDC) koji koristi iste funkcije pripadnosti kao i nelinearniTakagi-Sugeno model objekta. Ovakav upravljaqki sistem interpolira nekolikolokalnih linearnih upravljaqkih sistema. Zahvaljujui teoriji potpune preno-sne funkcije, razmatra se najopxtiji i najrealistiqniji sluqaj uslovne opti-mizacije lokalnih linearnih upravljaqkih sistema, pri qemu je grexka rezultatistovremenog delovanja nenultih poqetnih uslova i spoljaxnjeg ulaza. Odreenisu optimalni parametri za tri linearna proporcionalno-sumarna (PS) kontro-lera pri nultim i nenultim poqetnim uslovima, uvaavajui zahtev da svi po-jedinaqni zatvoreni sistemi imaju zahtevani stepen priguxenja ζ. Uraena jesinteza PDC kontrolera koji koristi iste funkcije pripadnosti kao i fazi TSmodel objekta, u dva sluqaja. U prvom sluqaju, PDC kontroler je sastavljen odtri lokalna linearna PS kontrolera qiji su parametri odreeni pri nultimpoqetnim uslovima. U drugom sluqaju, PDC kontroler qine linearni kontroleriqiji su parametri odreeni pri nenultim poqetnim uslovima. The doctoral dissertation investigates the synthesis of a proportional-difference-sum (PDS)type control system based on the characteristic polynomial of the full transfer function. The fulltransfer function makes it possible to obtain accurate results in terms of cancellation of equalzeros and poles, obtaining the characteristic polynomial and determining the full response ofthe system. At the beginning, the relative stability area in the space of adjustable parametersof the control system is determined so that damping coefficient ζ has the value required inadvance. This was done in the case of two adjustable parameters using the examples of PDand PS control systems. In addition, an area of relative stability was found in the case ofthree adjustable parameters of the PDS control system. In the next step, the method ofconditional optimization is implemented using an expression for the output error that includesthe simultaneous influence of nonzero initial conditions and the external output, which is madepossible by applying a full transfer function. Thus, the optimal parameters of the PDS typelinear control systems are found for which the performance index, in the form of the sum ofsquared errors, has a minimum value.In the second part of the dissertation, the previously developed method of conditionaloptimization of linear discrete systems is extended and applied to the class of nonlinear discretesystems, in the form of Takagi-Sugeno (TS) fuzzy systems. For this purpose, the property ofthe TS fuzzy system was used that the dynamics of a nonlinear system can be expressed usingseveral linear (linearized) systems. The nonlinear Takagi-Sugeno fuzzy model, which crediblydescribes the behavior of the system over the entire output space, is obtained by interpolatingseveral linear mathematical models. A synthesis of a PDC (parallel distributed compensation)control system using the same membership functions as the nonlinear Takagi-Sugeno fuzzymodel of the plant was performed. Such control system interpolates several local linear controlsystems. Thanks to the theory of the complete transfer function, the most general and realisticcase of conditional optimization of the local linear control systems is considered, where theoutput error is the result of the simultaneous action of nonzero initial conditions and externalinput. The optimal parameters for three local linear proportional-sum (PS) controllers at zeroand nonzero initial conditions were determined, considering the requirement that all individualclosed systems have the required damping coefficient ζ. Synthesis of a PDC controller that usesthe same membership functions as the fuzzy TS plant model is made in two cases. In the firstcase, the PDC controller is composed of three local linear PS controllers whose parameters aredetermined at zero initial conditions. In the second case, the PDC controller consists of linearcontrollers whose parameters are determined at nonzero initial conditions. Mašinstvo -Automatsko upravljanje /Mechanical engineering - Control engineering Datum odbrane: 24.01.2023. iskretni sistemi automatskog upravljanja, sinteza u trodi- menzionom prostoru, relativna stabilnost, potpuna prenosna funkcija, uslovna stabilizacija i optimizacija, Takagi-Sugeno, fazi upravljanje, paralelno raspo- deljeno upravljanje Discrete-time control systems, three parameters synthesis, relative stability, full transfer function, conditional stabilization and optimization, Takagi-Sugeno, fuzzy control, parallel distributed compensation 91552100 112025865 91552101 9564 2024-03-05T15:10:26.053Z 45 no 46 Vladimir, 1990- Zarić 18831975 2022 63 mentor Radiša Ž., 1969- Jovanović 18897767 2022 63 član komisije Dragan, 1961- Lazić 12572263 2022 63 član komisije Milan, 1972- Ristanović 12846695 2022 63 član komisije Srđan, 1959- Ribar 12533863 2022 63 član komisije Dragan, 1962- Pršić 13613415 2022 116 стр. 3533858 http://phaidrabg.bg.ac.rs/o:32996 no yes 12 2024-03-05T15:10:26.320Z 70 11 1066609 1066643 11 1067197 1067219 diskretni sistemi automatskog upravljanja, sinteza u trodi-menzionom prostoru, relativna stabilnost, potpuna prenosna funkcija, uslovnastabilizacija i optimizacija, Takagi-Sugeno, fazi upravljanje, paralelno raspo-deljeno upravljanje Discrete-time control systems, three parameters synthesis, relative stability,full transfer function, conditional stabilization and optimization, Takagi-Sugeno, fuzzy control,parallel distributed compensation 681.511:519.718(043.3) 1738 11A30 2022