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

Modelling of real physical systems having long memory transients and infinite dimensional structures using fractional-order dynamic models has significantly attracted interest over the last few years. For this reason, many identification techniques both in the frequency domain and time domain have been developed to model these fractional-order systems. However, in many processes time delays are also present and estimation of time delays along with continuous-time fractional-order model parameters have not been addressed anywhere. This study deals with the continuous-time model identification of fractional-order system models with time delays. In this study, a new linear filter is introduced for simultaneous estimation of all model parameters for commensurate fractional-order system models with time delays. The proposed method simultaneously estimates time delays 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 optimisation 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 by simulations on a fractional-order system model by doing Monte Carlo simulation analysis in the presence of white noise. The proposed algorithm has also been applied to identify a process of thermal diffusion in a wall in simulation, which are characterised by fractional-order behaviour.