Optimal approximation of analog PID controllers of complex fractional-order
Loading...
Date
2023-05-19
Authors
Mahata, Shibendu
Herencsár, Norbert
Maione, Guido
ORCID
0000-0002-9504-2275Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Altmetrics
Abstract
Complex fractional-order (CFO) transfer functions, being more generalized versions of their real-order counterparts, lend greater flexibility to system modeling. Due to the absence of commercial complex-order fractance elements, the implementation of CFO models is challenging. To alleviate this issue, a constrained optimization approach that meets the targeted frequency responses is proposed for the rational approximation of CFO systems. The technique generates stable, {minimum-phase, and real-valued coefficients based approximants}, which are not always feasible for the curve-fitting approach reported in the literature. {Stability and performance studies of the CFO proportional-integral-derivative (CFOPID) controllers for the Podlubny's, the internal model control, and the El-Khazali's forms are considered to demonstrate the feasibility of the proposed technique}. Simulation results highlight that, for a practically reasonable order, all the designs achieve good agreement with the theoretical characteristics. {Performance comparisons with the CFOPID controller approximants determined by the Oustaloup's CFO differentiator based substitution method justify the proposed approach.
Description
Citation
Fractional Calculus and Applied Analysis. 2023, vol. 26, issue 4, p. 1566-1593.
https://link.springer.com/article/10.1007/s13540-023-00168-x
https://link.springer.com/article/10.1007/s13540-023-00168-x
Document type
Peer-reviewed
Document version
Published version
Date of access to the full text
Language of document
en