COMPARATIVE ANALYSIS OF THE METHODS FOR IMPLEMENTING FRACTIONAL-ORDER INTEGRATOR-DIFFERENTIATOR CONTROLLERS
DOI:
https://doi.org/10.32718/agroengineering2025.29.112-116Keywords:
models, Laplace transform, Oustaloup transform, fractional order transfer function, fractional order controllersAbstract
At the present stage, the NINTEGER package is used for modeling fractional differential and integral elements in electromechanical systems. The application of the specially developed NINTEGER package as an add-on for the MATLAB Simulink package has enabled the first studies in the field of using fractional-order controllers in fractional-order automatic control systems. However, it has certain drawbacks: the NINTEGER package works exclusively in the MATLAB Simulink environment and cannot be used outside this package. The literature does not clarify the accuracy of representing fractional elements and fractional-order PID controllers in this package.
The work presents a comparative analysis of mathematical models based on the well-known Oustaloup transformation in the MATLAB programming environment with the possibility of its use in MATLAB Simulink instead of the NINTEGER application. In addition, a study was conducted on the accuracy of integral and differential regulators of fractional order represented in the Oustaloup, Riemann, Riemann-Liouville, and Grünwald-Letnikov forms compared to the model obtained through the Laplace transformation as a benchmark. Based on the conducted analysis, it is concluded that the models built on the Oustaloup transformation are the most promising for the implementation of regulators. Oustaloup models allow replacing fractional order transfer functions with equivalent transfer functions of integer order. This provides significantly higher performance in processing control influences compared to Grünwald-Letnikov models. Regarding accuracy, it is somewhat worse, but this drawback is compensated for by the simplicity of the computational procedure.
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