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Discrete Fractional-Order PID Controller

version (4.13 KB) by Ivo Petras
Provides a transfer function of the fractional-order PID controller for given parameters.


Updated 13 Nov 2011

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Digital version of Fractional-Order PID Controller (DFOC) of the form:
C(s) = K + Ti/s^m + Td*s^d for given sampling period Ts [sec].

For more details and help write:
>> help DFOC

It is based on:

See also books:

[1] Ivo Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Series: Nonlinear Physical Science, 2011, ISBN 978-3-642-18100-9.

[2] Riccardo Caponetto, Giovanni Dongola, Luigi Fortuna and Ivo Petras, Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010, ISBN 978-9-814-30419-1.

[3] Ivo Petras, Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab, chapter 10, in: Engineering Education and Research Using MATLAB, Ali H. Assi (Ed.), InTech, ISBN 978-953-307-656-0.

Cite As

Ivo Petras (2020). Discrete Fractional-Order PID Controller (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (12)

sha yet

Can you help me to implement this, in simulink? I use the PI Fractional Block and Transfer Function Block, but it's not enough.


how to use it ?



can you help me to write code program for digital fraction order PID controller in MATLAB or C++

thank you
can you help me using Al-Alaoui method in function "DFOC"



thank you a lot :) this is really helpful thing



MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux