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Optimal input signal design for fractional-order system identification

Jakowluk W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 1

37--44

The optimal design of excitation signal is a procedure of generating an informative input signal to extract the model parameters with maximum pertinence during the identification process. The fractional calculus provides many new possibilities for system modeling based on the definition of a derivative of noninteger-order. A novel optimal input design methodology for fractional-order systems identification is presented in the paper. The Oustaloup recursive approximation (ORA) method is used to obtain the fractional-order differentiation in an integer order state-space representation. Then, the presented methodology is utilized to solve optimal input design problem for fractional-order system identification. The fundamental objective of this approach is to design an input signal that yields maximum information on the value of the fractional-order model parameters to be estimated. The method described in this paper was verified using a numerical example, and the computational results were discussed.

Oustaloup parallel approximation

Bauer W., Baranowski J., Dziwiński T., Piątek P., Zagórowska M.

Prace Naukowe Politechniki Śląskiej. Elektryka

2016

z. 3-4

59--64

This article presents Oustaloup approximation method for fractional differential systems, which has been modified by the authors. Application of this method by using numerical experiments has been shown and behavior of discrete system has been analyzed.

W artykule przedstawiono zmodyfikowaną przez autorów metodę aproksymacji Oustaloupa dla układów różniczkowych niecałkowitego rzędu. Pokazano jej wykorzystanie poprzez eksperyment numeryczny oraz przeanalizowano zachowanie systemu dyskretnego.