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Hardware Implementation of Fractional-Order Calculus in Control Systems Cover

Hardware Implementation of Fractional-Order Calculus in Control Systems

Open Access
|Jun 2025

Figures & Tables

Fig. 3.1.

General structure of FOPID Controller

Fig. 3.2.

The FOPID controller plane

Fig. 3.3.

Stability region of fractional order system

Fig. 4.1.

Example of universal blocks from FOMCON toolbox

Fig. 4.2.

Example of universal blocks from FOTF toolbox

Fig. 4.3.

Example of universal blocks from Ninteger toolbox

Fig. 5.1.

Distribution of potentials and currents in the ladder system [34]

Fig. 6.1.

Domino ladder system created in Simulink for α= 0.60

Fig. 6.2.

Comparison of the responses of the considered fractional-order models

Fig. 6.3.

Relative error of the considered fractional-order models

Fig. 6.4.

Comparison of the response of the system with a FOPID controller tuned by considering different integral indices

Fig. 7.1.

Example of QUARC blocks for real-time implementation

Fig. 7.2.

A flow chart of the procedure for implementing the control algorithm

Fig. 7.3.

Comparison of the simulation and real control plant responses for PID and FOPID controller

Fig. 7.4.

Comparison of control signals from PID and FOPID controller from the experiment

Controller parameters and cost function for the system

PID ControllerFOPID Controller
Kp1,89022,5043
Ki0,47850,6644
λ1,00001,0060
Kd0,43700,7156
μ1,00000,5027
CF_ESIM12,43898,0557
CF_EREAL11,04357,5231
CF_USIM318,4723300,3850
CF_UREAL328,7697306,1467
RMSE0,79480,6858
DOI: https://doi.org/10.2478/ama-2025-0031 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 250 - 257
Submitted on: Sep 10, 2024
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Accepted on: May 2, 2025
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Published on: Jun 26, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Paweł KIECZMERSKI, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.