A digital PID controller based on Grünwald-Letnikov fractional-, variable-order operator

Piotr Oziabło , Dorota Mozyrska , Małgorzata Wyrwas


The paper presents an example of implementation of a digital PID controller with Gr¨unwald-Letnikov fractional-, variable-order summations and differences. The method of finding values of orders and parameters Kp, Ki, Kd of such controller for considered plant model is presented. Two summation performance criteria are used to evaluate the results achieved with the usage of fractional-, variable-order PID controller tuned by proposed algorithm. Mentioned criteria are integral squared time weighted error (SSTE) and integral squared time-squared weighted error (SST2E). Additionally the results are compared with the ones obtained with PID controller tuned using Ziegler- Nichols method, PID controller tuned with Matlab pidtune function and PID controller which coefficients were tuned by minimising mentioned SSTE and SST2E errors with Nelder- Mead method (implemented by Matlab fminsearch function).
Author Piotr Oziabło (FCS)
Piotr Oziabło,,
- Faculty of Computer Science
, Dorota Mozyrska (FCS / DM)
Dorota Mozyrska,,
- Department of Mathematics
, Małgorzata Wyrwas (FCS / DM)
Małgorzata Wyrwas,,
- Department of Mathematics
Publication size in sheets0.5
Book 24th International Conference on Methods and Models in Automation & Robotics: MMAR 2019, 2019, Institute of Electrical and Electronics Engineers, ISBN 978-1-7281-0932-9, 668 p.
Internal identifierROC 19-20
Languageen angielski
Score (nominal)20
Score sourcepublisherList
ScoreMinisterial score = 20.0, 26-03-2020, ChapterFromConference
Citation count*1 (2020-03-29)
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