Continuous-time model identification of fractional order models with time delays

Abstract

This paper deals with the continuous-time model identification (CMI) of fractional order systems with time delays. In this paper, a new linear filter is introduced for simultaneous estimation of all model parameters for commensurate fractional order systems with time delays (CFOTDS) based on step response data. The proposed method simultaneously estimates the time delay along with other model parameters in an iterative manner by solving simple linear regression equations. For the case when the fractional order is unknown, we also propose a nested loop optimization method where the time delay along with other model parameters are estimated iteratively in the inner loop and the fractional order is estimated in the non-linear outer loop. The applicability of the developed procedure is demonstrated on two fractal systems by doing Monte Carlo simulation analysis in the presence of white noise.