1. Fractional Calculus and Application to the Realization of a Constant Phase Element
- Author
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Rendulić, Mislav and Jurišić, Dražen
- Subjects
element s konstantnom fazom (CPE) ,TEHNIČKE ZNANOSTI. Računarstvo ,TEHNIČKE ZNANOSTI. Elektrotehnika ,Frakcionalna derivacija ,Fractional derivative ,fractional-order system ,sustav necjelobrojnog reda ,frakcionalni Tow-Thomas filtar ,fractional exponential ,TECHNICAL SCIENCES. Electrical Engineering ,TECHNICAL SCIENCES. Computing ,frakcionalna eksponencijala ,constant phase element (CPE) ,fractional Tow-Thomas filter - 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. 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.
- Published
- 2022