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Fractal Fract
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Fractional Calculus in Control and Modelling
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Fractional Calculus in Control and Modelling

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 12016

Special Issue Editor

Dr. Riccardo Caponetto

E-Mail Website
Guest Editor
Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, 95125 Catania, Italy
Interests: systems modeling and control; fractional order systems; soft computing techniques
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The main aim of this Special Issue is to present control algorithms and models based on the framework of the fractional calculus. Furthermore, the Special Issue aims at proposing practical applications of fractional calculus. Digital and analogue implementations of fractional order controllers are all welcome as a possible market application of fractional calculus.
We are inviting the submission of papers describing original research work that reflects both recent theoretical advances and experimental results as well as opens new avenues for research.

Prof. Dr. Riccardo Caponetto
Guest Editor

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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind 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.

Keywords

  • fractional dynamics
  • chaos
  • fractals
  • neural systems
  • information and computation theory
  • random walks and their applications
  • signal processing
  • economy and finance
  • thermal engineering
  • mechanics mechatronics
  • biology, biophysics, biomathematics
  • bioengineering
  • anomalous diffusion
  • wave propagation
  • artificial life
  • numerical algorithms

Published Papers (5 papers)

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Research

11 pages, 4362 KiB  
Article
Design of Fractional-Order Lead Compensator for a Car Suspension System Based on Curve-Fitting Approximation
by Evisa Memlikai, Stavroula Kapoulea, Costas Psychalinos, Jerzy Baranowski, Waldemar Bauer, Andrzej Tutaj and Paweł Piątek
Fractal Fract. 2021, 5(2), 46; https://doi.org/10.3390/fractalfract5020046 - 15 May 2021
Cited by 5 | Viewed by 2356
Abstract
An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved accuracy compared to the Oustaloup and Padé methods. As a design example, [...] Read more.
An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved accuracy compared to the Oustaloup and Padé methods. As a design example, a lead compensator intended for usage in car suspension systems is realized. The open-loop and closed-loop behavior of the system is evaluated by post-layout simulation results obtained using the Cadence IC design suite and the Metal Oxide Semiconductor (MOS) transistor models provided by the Austria Mikro Systeme 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process. The derived results verify the efficient performance of the introduced implementation. Full article
(This article belongs to the Special Issue Fractional Calculus in Control and Modelling)
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22 pages, 4334 KiB  
Article
Fuel Cell Fractional-Order Model via Electrochemical Impedance Spectroscopy
by Riccardo Caponetto, Fabio Matera, Emanuele Murgano, Emanuela Privitera and Maria Gabriella Xibilia
Fractal Fract. 2021, 5(1), 21; https://doi.org/10.3390/fractalfract5010021 - 06 Mar 2021
Cited by 7 | Viewed by 1980
Abstract
The knowledge of the electrochemical processes inside a Fuel Cell (FC) is useful for improving FC diagnostics, and Electrochemical Impedance Spectroscopy (EIS) is one of the most used techniques for electrochemical characterization. This paper aims to propose the identification of a Fractional-Order Transfer [...] Read more.
The knowledge of the electrochemical processes inside a Fuel Cell (FC) is useful for improving FC diagnostics, and Electrochemical Impedance Spectroscopy (EIS) is one of the most used techniques for electrochemical characterization. This paper aims to propose the identification of a Fractional-Order Transfer Function (FOTF) able to represent the FC behavior in a set of working points. The model was identified by using a data-driven approach. Experimental data were obtained testing a Proton Exchange Membrane Fuel Cell (PEMFC) to measure the cell impedance. A genetic algorithm was firstly used to determine the sets of fractional-order impedance model parameters that best fit the input data in each analyzed working point. Then, a method was proposed to select a single set of parameters, which can represent the system behavior in all the considered working conditions. The comparison with an equivalent circuit model taken from the literature is reported, showing the advantages of the proposed approach. Full article
(This article belongs to the Special Issue Fractional Calculus in Control and Modelling)
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20 pages, 947 KiB  
Article
Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags
by Guido Maione
Fractal Fract. 2020, 4(3), 37; https://doi.org/10.3390/fractalfract4030037 - 27 Jul 2020
Cited by 6 | Viewed by 2134
Abstract
This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the [...] Read more.
This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the simple elements of the cascade can be easily realized by rational transfer functions. On this basis, a method is proposed in order to design a robust controller for a class of benchmark plants that are difficult to compensate due to monotonically increasing lags. The simulation experiments show the efficiency, performance and robustness of the approach. Full article
(This article belongs to the Special Issue Fractional Calculus in Control and Modelling)
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11 pages, 1131 KiB  
Article
Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor
by Dina A. John, Saket Sehgal and Karabi Biswas
Fractal Fract. 2020, 4(3), 34; https://doi.org/10.3390/fractalfract4030034 - 15 Jul 2020
Cited by 5 | Viewed by 2800
Abstract
In this paper, the performance of an analog PI λ D μ controller is done for speed regulation of a DC motor. The circuits for the fractional integrator and differentiator of PI λ D μ controller are designed by optimal pole-zero interlacing algorithm. [...] Read more.
In this paper, the performance of an analog PI λ D μ controller is done for speed regulation of a DC motor. The circuits for the fractional integrator and differentiator of PI λ D μ controller are designed by optimal pole-zero interlacing algorithm. The performance of the controller is compared with another PI λ D μ controller—in which the fractional integrator circuit employs a solid-state fractional capacitor. It can be verified from the results that using PI λ D μ controllers, the speed response of the DC motor has improved with reduction in settling time ( T s ), steady state error (SS error) and % overshoot (% M p ). Full article
(This article belongs to the Special Issue Fractional Calculus in Control and Modelling)
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14 pages, 1429 KiB  
Article
Fractional State Space Description: A Particular Case of the Volterra Equations
by Jocelyn Sabatier
Fractal Fract. 2020, 4(2), 23; https://doi.org/10.3390/fractalfract4020023 - 22 May 2020
Cited by 11 | Viewed by 2005
Abstract
To tackle several limitations recently highlighted in the field of fractional differentiation and fractional models, some authors have proposed new kernels for the definition of fractional integration/differentiation operators. Some limitations still remain, however, with these kernels, whereas solutions prior to the introduction of [...] Read more.
To tackle several limitations recently highlighted in the field of fractional differentiation and fractional models, some authors have proposed new kernels for the definition of fractional integration/differentiation operators. Some limitations still remain, however, with these kernels, whereas solutions prior to the introduction of fractional models exist in the literature. This paper shows that the fractional pseudo state space description, a fractional model widely used in the literature, is a special case of the Volterra equations, equations introduced nearly a century ago. Volterra equations can thus be viewed as a serious alternative to fractional pseudo state space descriptions for modelling power law type long memory behaviours. This paper thus presents a new class of model involving a Volterra equation and several kernels associated with this equation capable of generating power law behaviours of various kinds. One is particularly interesting as it permits a power law behaviour in a given frequency band and, thus, a limited memory effect on a given time range (as the memory length is finite, the description does not exhibit infinitely slow and infinitely fast time constants as for pseudo state space descriptions). Full article
(This article belongs to the Special Issue Fractional Calculus in Control and Modelling)
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