Metoda IRKA za optimalno redukcijo modela : magistrsko delo

Peterlin, Jakob (author), Plestenjak, Bor (mentor)

V delu je predstavljena metoda IRKA, ki je namenjena redukciji oziroma aproksimaciji sistemov upravljanja glede na ${\cal H}_2$-normo. Najprej so predstavljene osnovne definicije iz teorije sistemov upravljanja. Predstavljena je osnovna ideja aproksimacije sistemov s pomočjo projekcij. Predstavljena in dokazana je povezava med projekcijo in interpolacijo prenosnih funkcij sistemov upravljanja. Nato je predstavljena ${\cal H}_2$-norma. Izpeljanih je več rezultatov povezanih s ${\cal H}_2$-normo, med drugim Meier-Luenbergovi pogoji za ${\cal H}_2$ optimalno aproksimacijo sistema. Ti aproksimacijo sistema povežejo z interpolacijo prenosnih funkcij. Nato je predstavljena metoda IRKA in dokaz, da v primeru stabilnih SSS siste- mov konvergira. Na koncu je predstavljenih še nekaj praktičnih primerov uporabe metode IRKA.

• Language: Slovenian
• Keywords: metoda IRKA, aproksimacija sistema upravljanja, ${\cal H}_2$-norma, SSS sistemi
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-103308
• UDC: 517.9
• COBISS.SI-ID: 18436185
• Publication date in RUL: 16.09.2018

Secondary language

• Language: English
• Title: Method IRKA for optimal model reduction

Abstract

This work presents the IRKA method for reduction or approximation of control systems according to the ${\cal H}_2$ norm. The basic definitions of control system theory are presented first, followed by the basic idea of system projection methods. Next, the connection between projection and interpolation of transfer function is proven and presented. Then the ${\cal H}_2$ norm is presented. Several results associated with the ${\cal H}_2$ norm, including Meier-Luenber conditions for ${\cal H}_2$ optimal approximation of the system are presented. These conditions are a link between the approximation of systems and the interpolation of transfer functions. Finally the IRKA method and the proof of convergence in the case of stable SSS systems are presented. In the end, several examples of using the IRKA method in practice are shown.

• Keywords: method IRKA, approximation of control systems, ${\cal H}_2$-norm, SSS systems