Step Response-Based Identification of Fractional Order Time Delay Models

  • Salim AhmedEmail author


An identification method for fractional order models with time delay is presented. The proposed method, based on the output error optimization, simultaneously estimates model orders, coefficients and time delay from a single noisy step response. Analytical expressions for logarithmic derivatives of the step input are derived to evaluate the Jacobian and the Hessian required for the Newton’s algorithm for optimization. A simplified initialization procedure is also outlined that assumes an integral initial order and uses estimated coefficients as the initial guess. Simulation results are presented to demonstrate the efficacy of the proposed approach. Convergence of the Newton’s method and the Gauss–Newton scheme are also studied in simulation. Identification results from noisy step response data for time delay models with different structures are presented.


Step response Fractional order Parameter estimation Time delay Optimization 



The author acknowledges the financial supports from Research and Development Corporation (RDC) of Newfoundland and Labrador and Natural Sciences and Engineering Research Council (NSERC) of Canada.

Compliance with Ethical Standards

Conflicts of interest

The author declares that there is no conflict of interest.

Human Participants

The study does not involve any human participants and/or animal. The manuscript has not been published previously (partly or in full).


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Authors and Affiliations

  1. 1.Centre for Risk, Integrity and safety Engineering (C-RISE), Department of Process EngineeringMemorial UniversitySt. John’sCanada

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