A novel approach of fractional-order time delay system modeling based on Haar wavelet

Kajal Kothari; Utkal Mehta; Jito Vanualailai

doi:10.1016/j.isatra.2018.07.019

A novel approach of fractional-order time delay system modeling based on Haar wavelet

ISA Trans. 2018 Sep:80:371-380. doi: 10.1016/j.isatra.2018.07.019. Epub 2018 Jul 25.

Authors

Kajal Kothari¹, Utkal Mehta², Jito Vanualailai³

Affiliations

¹ School of Engineering and Physics, The University of the South Pacific, Laucala Campus, Fiji. Electronic address: s11151029@student.usp.ac.fj.
² School of Engineering and Physics, The University of the South Pacific, Laucala Campus, Fiji. Electronic address: utkal.mehta@usp.ac.fj.
³ School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Laucala Campus, Fiji. Electronic address: jito.vanualailai@usp.ac.fj.

PMID: 30055858
DOI: 10.1016/j.isatra.2018.07.019

Abstract

In this paper, fractional-order time delay system modeling is presented using Haar wavelet operational matrix of integration. Therefore, it does not require any prior knowledge of transfer function structure or partial information about fractional differentiation order. It allows the estimation of the implicit time delay parameter together with other model parameters by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition. The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. The efficacy of the approach is verified on various integer and non-integer (fractional) order systems in simulation. For realistic condition, proposed method is verified in the presence of noise in simulation and also demonstrated on the real-time process control temperature system.

Keywords: Fractional-order systems; Haar wavelet; Identification; Operational matrix; Time delays.