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Fractional order model identification using the sinusoidal input.

Shaikh M Fahim1, Salim Ahmed1, Syed A Imtiaz1

  • 1Centre for Risk, Integrity and Safety Engineering (C-RISE), Department of Process Engineering, Memorial University, St. John's, NL, Canada.

ISA Transactions
|September 24, 2018
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Summary

This study introduces an optimization method for identifying fractional order models using multi-frequency sinusoids. The approach analytically calculates derivatives, improving accuracy and efficiency in model parameter estimation.

Keywords:
Fractional orderGauss–NewtonIdentificationLogarithmic derivativeOptimization

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Area of Science:

  • Control Systems Engineering
  • Applied Mathematics
  • Signal Processing

Background:

  • Fractional order models offer enhanced system representation compared to integer order models.
  • Accurate identification of fractional order models is crucial for control system design.
  • Existing methods for fractional order model identification face challenges in calculating Jacobian matrices due to logarithmic derivatives.

Purpose of the Study:

  • To propose an output error optimization approach for identifying parsimonious fractional order models.
  • To develop a method that simultaneously estimates orders, parameters, and delays of fractional order models.
  • To address the computational difficulties in evaluating sensitivity functions for fractional order model identification.

Main Methods:

  • Utilizing multi-frequency sinusoids as input signals for model identification.
  • Employing the Gauss-Newton optimization approach for parameter estimation.
  • Deriving and applying analytical expressions for logarithmic derivatives of input signals to compute the Jacobian matrix.

Main Results:

  • Demonstrated the efficacy of the proposed method through simulations, analyzing the effects of noise, input frequency, and sampling intervals.
  • Successfully estimated orders, parameters, and delays of fractional order models.
  • Showcased the convergence and robustness of the developed optimization approach.

Conclusions:

  • The proposed analytical method for Jacobian evaluation significantly improves fractional order model identification.
  • The approach is theoretically applicable to models with extensive parameter sets, though optimization convergence requires further investigation.
  • This work provides a more efficient and accurate tool for fractional order system identification.