Recent Research in Fractional-Order Controllers and Their Applications

Dear Colleagues,

Mathematical modeling serves as a means to elucidate various facets of the real world, capturing reciprocal interactions and their dynamics through mathematical representation. Mathematical models have the ability to encompass universal concepts, allowing for the mechanization and automation of intellectual processes.

Fractional calculus (FC) has emerged as a burgeoning field in mathematical modeling, namely within system identification and control engineering. Fractional-order models are believed to be better suited for accurately characterizing intricate physical phenomena, including viscoelasticity, diffusion in porous media, and various biomedical processes. From a control perspective, FC extends the conventional Proportional Integral Derivative (PID) controller, popular in control systems, into a more versatile Fractional-Order Proportional Integral Derivative controller (FOPID). This extension incorporates two additional parameters into the controller's transfer function, featuring arbitrary, non-integer orders of integration and differentiation. The two latter parameters empower the FOPID controller to meet a more stringent set of specifications compared to the traditional PID controller. This leads to enhanced degrees of freedom, improved stability, and superior performance in a closed-loop system. Additionally, a significant advantage lies in the ability to directly impose robustness requirements, typically achieved through the isodamping property, during the tuning process. Beyond the FOPID controller, other control strategies have also been extended using FC, showing promising outcomes.

This Special Issue is dedicated to the exploration of design methodologies for FOPID and their diverse applications. The primary objective is to showcase the latest developments in the theory, design, execution, and verification of various FO control strategies, catering to both integer and FO processes. Areas of interest for submission encompass, but are not limited to:

• Theoretical insights and design strategies of FOPID.
• Approximation of fractional-order elements in digital and analog domains.
• Real-world implementation of FOPID.
• Empirical validation through experimental implementations.
• The challenges of integration of FOPID in the context of Industry 4.0.
• Comparative analysis between FOPID and PIDs.
• Wide-ranging applications of fractional-order control strategies.

The published papers will be selected from submissions to the ICMASC'24—International Conference on Mathematical Analysis and Applications in Science and Engineering—which will be held in the beautiful city of Porto, Portugal, on June 20th–June 22nd 2024. This conference is dedicated to the memory of Prof. JA Tenreiro Machado, who passed away in October 2021.

Dr. Carla M. A. Pinto
Dr. Cristina I. Muresan
Dr. Dana Copot
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.