Frakcionalni račun i primjena na realizaciju elementa s konstantnom fazom

undergraduate thesis

• Title (english): Fractional Calculus and Application to the Realization of a Constant Phase Element
• Author: Mislav Rendulić
• Mentor: Dražen Jurišić (mentor)
• Committee member: Dražen Jurišić (predsjednik povjerenstva)
• Committee member: Marko Šprem (član povjerenstva)
• Committee member: Edi Emanović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2022-09-05, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Frakcionalni račun je grana matematike koja se bavi diferenciranjem i integriranjem necjelobrojnog reda. Koncepti frakcionalnog računa su našli primjenu i u inženjerstvu. U ovom radu smo usporedili razne definicije frakcionalne derivacije. Frakcionalni račun smo primjenili na realizaciju elementa s konstantnom fazom (CPE). Realizirani CPE smo opisali pomoću Cole-Cole modela. Simulirani element CPE upotrijebili smo na primjeru frakcionalnog Tow-Thomas filtra. Opisali smo dobivanje frakcionalne eksponencijale. Pomoću programa Matlab simulirali smo odziv necjelobrojnog sustava, odnosno frakcionalog Tow-Thomas filtra.

Abstract (english)

Fractional calculus is a branch of mathematics that deals with the differentiation and integration of an integer order. The concepts of fractional calculus have also found application in engineering. In this paper, we have compared various definitions of fractional derivation. We applied the fractional calculus to the realization of the constant phase element (CPE). We described the realized CPU using the Cole-Cole model. We used the simulated CPE element on the example of a fractional Tow-Thomas filter. We have described obtaining a fractional exponential. Using the Matlab program, we simulated the response of a non-integer system, ie. a fractional Tow-Thomas filter.

• Keywords: Frakcionalna derivacija; sustav necjelobrojnog reda; element s konstantnom fazom (CPE); frakcionalna eksponencijala; frakcionalni Tow-Thomas filtar
• Keywords (english): Fractional derivative; fractional-order system; constant phase element (CPE); fractional exponential; fractional Tow-Thomas filter.
• Language: croatian
• URN:NBN: urn:nbn:hr:168:381477
• Study programme: Title: Electrical Engineering and Information Technology; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-13 16:02:52