Non-Linear Fractional-Order PID Controller

Provides an equation of the non-linear fractional-order PID controller for given parameters.


Updated 30 Mar 2022

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Non-Linear Fractional-Order PID Controller of the form:
u(t)=f(e(t))*(Kp*e(t) + Ti*D^-lambda e(t) + Td*D^delta e(t)),
where f(e(t)) is nonlinear function: f(e(t))=K0+(1-K0)*|e(t)|.
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For more information and description see articles:
[1] Ivo Petráš: Fractional-order nonlinear controllers: Design and implementation notes,
In: Proc. of the IEEE 17th International Carpathian Control Conference (ICCC2016),
pp. 579-583, DOI: 10.1109/CarpathianCC.2016.7501163
[2] Ivo Petráš; Miroslav Köver-Dorčo: An effective algorithm for implementation of non-linear fractional-order controller on PLC,
In: Proc. of the IEEE 17th International Carpathian Control Conference (ICCC2016),
pp. 584-589, DOI: 10.1109/CarpathianCC.2016.7501164
[3] Ivo Petráš: A note on fractional-order non-linear controller: Possible neural network approach to design,
In: Proc. of the World Congress on Computational Intelligence (WCCI2016), IEEE Conference IJCNN 2016,
pp. 603-608, DOI: 10.1109/IJCNN.2016.7727255
[4] Ivo Petráš: Tuning of the non-linear fractional-order controller, In: Proc. of the IEEE 20th International Carpathian Control Conference (ICCC2019), DOI: 10.1109/CarpathianCC.2019.8765988
[5] Ivo Petráš: Fractional-order control: New control techniques, In: Fractional Order Systems. An Overview of Mathematics, Design, and Applications for Engineers. Volume 1 in Emerging Methodologies and Applications in Modelling, 2022, pp. 71-106, DOI:

Cite As

Ivo Petras (2023). Non-Linear Fractional-Order PID Controller (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010b
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