Perturbacijska metoda homotopije u teoriji upravljanja hamiltonskih sustava

master's thesis

• Title (english): Homotopy perturbation method in control theory of Hamiltonian systems
• Author: Matko Tomić
• Mentor: Josip Kasać (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2017-12-07, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Zadnjih dvadesetak godina, pojavila se nova paradigma u teoriji upravljanja dinamičkih sustava, zasnovana na reprezentaciji dinamike sustava u obliku kanonskih Hamiltonskih diferencijalnih jednadžbi. Totalni Hamiltonijan sustava je ujedno i Lyapunovljeva funkcija sustava, što omogućuje trivijalnu analizu stabilnosti, bez obzira na kompleksnost sustava. Sinteza regulatora se svodi na problem definiranja uvjeta Hamiltonske strukture zatvorenog regulacijskog kruga. U ovom radu primjenjena je navedena upravljačka metoda na problem stabilizacije sinkronog generatora. Kako bismo odredili upravljačku varijablu koja će stabilizirati nelinearni model sinkronog generatora, potrebno je riješiti odgovaraju ́cu parcijalnu diferencijalnu jednadžbu. Za rješavanje navedene jednadže, primjenjena je perturbacijska metoda homotopije. Predložena je nova konveksna homotopija, za rješavanje parcijalnih diferencijalnih jednadžbi bez poznatih početnih i rubnih uvjeta. Provedena je usporedba simulacijskih rezultata konvencionalnog i predloženog upravljačkog algoritma.

Abstract (english)

In the last twenty years, there has been a new paradigm in control theory of dynamical systems. Representation of dynamical system is based on the canonical Hamilton’s equations. Total Hamiltonian function of the system is also Lyapunov function of the system, which allows trivial stability analysis, regardless of complexity and nonlinearity of the system. Synthesis of control algorithm is based on defining closed loop port-controlled Hamiltonian structure. In this thesis, proposed control algorithm for stabilization of nonlinear model of synchronous generator was used. To determine control variable for nolinear model of synchronous generator, we must solve corresponding partial differential equation. Proposed method for solving partial differential equation is homotopy perturbation method. New convex homotopy has been proposed for solving partial differential equations without known initial and boundary conditions. A comparison between the conventional and proposed control algorithm was performed.

• Keywords: Perturbacijska metoda homotopije; Lyapunovljeva analiza stabilonosti; Hamiltonski sustavi; nelinearni sustavi; parcijalne diferencijalne jednadžbe; disipativnost i pasivnost dinamičkih sustava
• Keywords (english): Homotopy perturbation method; Lyapunov stability analysis; port-controlled Hamiltonian systems; nonlinear systems; partial differential equations; dissipativity and passivity theory for dynamical systems.
• Language: croatian
• URN:NBN: urn:nbn:hr:235:555022
• 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: 2019-05-22 21:03:03