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Fractal Fract
Special Issues
Fractional-Order Approaches in Automation: Models and Algorithms
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Fractional-Order Approaches in Automation: Models and Algorithms

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

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 2990

Special Issue Editors

Dr. Abraham Efraim Rodriguez Mata

E-Mail Website
Guest Editor
División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México, Instituto Tecnológico de Chihuahua, Chihuahua 31310, Mexico
Interests: nonlinear control; high-gain observer; fractional calculus and biological applications
Dr. Jesús Alfonso Medrano-Hermosillo

E-Mail Website
Guest Editor
División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México, Instituto Tecnológico de Chihuahua, Chihuahua 31310, Mexico
Interests: nonlinear systems; robotics; geometric methods; AI
Dr. Pablo Antonio López-Pérez

E-Mail Website
Guest Editor
Escuela Superior de Apan, Universidad Autónoma del Estado de Hidalgo, Pachuca, Mexico
Interests: bioreactors; controller design; bioprocess; cadmium bioprocess; engineering and fermentation technology; industrial biotechnology; control theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus is a relatively new field of mathematics that deals with derivatives and integrals of non-integer orders. In recent years, there has been an increase in the popularity of this mathematical tool due to its ability to model and analyze complex physical systems that are difficult to describe using classical calculus. Fractional calculus has a wide range of applications, from control theory and signal processing to image analysis and finance. In this Special Issue of the journal Fractal and Fractional, we will explore the latest developments and applications of fractional calculus in various fields. These include, but are not limited to, biomedicine, materials science, and engineering. We will also showcase the latest advances in numerical methods and algorithms for solving fractional-order differential equations, which are the cornerstone of many applications in the field. Overall, this Special Issue aims to provide readers with a comprehensive overview of the current state of the art in fractional calculus and its applications.

In the realm of current automated control, fractional-order approximation has countless uses, including state estimating, controller design for linear and nonlinear systems, and the development of more precise mathematical models.

With this Special Issue, we hope to delve more deeply into the theory, design, implementation, and use of fractional-order approaches in the modeling and automation of dynamic systems across a variety of fields.

Topics of interest include, but are not limited to:

  • Design of fractional-order control systems for high-power electrical systems.
  • Modeling, control, and stability of fractional-order systems.
  • Fractional-order chaotic systems.
  • Control of fractional-order chaotic systems.
  • Applications of fractional-order systems in engineering.
  • Fractional impulsive systems.
  • Deterministic and stochastic fractional-order nonlinear systems.
  • Filters, observers, and approximations of nonlinear systems using fractional derivatives.
  • Fractional sliding mode control.
  • Geometric control for fractional systems.

Dr. Abraham Efraim Rodriguez Mata
Dr. Jesús Alfonso Medrano-Hermosillo
Dr. Pablo Antonio López-Pérez
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 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-order systems
  • fractional-order control systems
  • fractional filtering
  • geometric interpretation of fractional-order calculus
  • system identifications
  • fractional derivatives
  • neural networks using fractional-order calculus

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Published Papers (2 papers)

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20 pages, 2094 KiB  
Article
Fractional Calculus Applied to the Generalized Model and Control of an Electrohydraulic System
by Edgar Hiram Robles, Felipe J. Torres, Antonio J. Balvantín-García, Israel Martínez-Ramírez, Gustavo Capilla and Juan-Pablo Ramírez-Paredes
Fractal Fract. 2024, 8(12), 679; https://doi.org/10.3390/fractalfract8120679 - 21 Nov 2024
Cited by 1 | Viewed by 874
Abstract
In this paper, fractional calculus is used to develop a generalized fractional dynamic model of an electrohydraulic system composed of a servo valve and a hydraulic cylinder, where a fractional position controller PIγDμ is proposed for minimizing the performance [...] Read more.
In this paper, fractional calculus is used to develop a generalized fractional dynamic model of an electrohydraulic system composed of a servo valve and a hydraulic cylinder, where a fractional position controller PIγDμ is proposed for minimizing the performance index according to the integral of the time-weighted absolute error (ITAE). First, the general mathematical equations of the cylinder and servo valve are used to obtain the transfer functions in fractional order by applying Caputo’s definition and a Laplace transform. Then, through a block diagram of the closed-loop system without a controller, the fractional model is validated by comparing its performance concerning the integer-order electrohydraulic system model reported in the literature. Subsequently, a fractional PID controller is designed to control the cylinder position. This controller is included in the closed-loop system to determine the fractional exponents of the transfer functions of the servo valve, cylinder, and control, as well as to tune the controller gains, by using the ITAE objective function, with a comparison of the following: (1) the electrohydraulic system model in integer order and the controller in fractional order; (2) the electrohydraulic system model in fractional order and the controller in integer order; and (3) both the system model and the controller in fractional order. For each of the above alternatives, numerical simulations were carried out using MATLAB®/Simulink® R2023b and adding white noise as a perturbation. The results show that strategy (3), where electrohydraulic system and controller model are given in fractional order, develops the best performance because it generates the minimum value of ITAE. Full article
(This article belongs to the Special Issue Fractional-Order Approaches in Automation: Models and Algorithms)
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25 pages, 2842 KiB  
Article
A Novel Fractional High-Order Sliding Mode Control for Enhanced Bioreactor Performance
by Abraham E. Rodríguez-Mata, Jesús A. Medrano-Hermosillo, Pablo A. López-Pérez, Victor A. Gonzalez-Huitron, Rafael Castro-Linares and Jorge Said Cervantes-Rojas
Fractal Fract. 2024, 8(10), 607; https://doi.org/10.3390/fractalfract8100607 - 18 Oct 2024
Cited by 3 | Viewed by 985
Abstract
This research introduces a fractional high-order sliding mode control (FHOSMC) method that utilises an inverse integral fractional order, 0<β<1, as the high order on the FHOSMC reaching law, exhibiting a novel contribution in the related field of study. [...] Read more.
This research introduces a fractional high-order sliding mode control (FHOSMC) method that utilises an inverse integral fractional order, 0<β<1, as the high order on the FHOSMC reaching law, exhibiting a novel contribution in the related field of study. The application of the proposed approach into a bioreactor system via diffeomorphism operations demonstrates a notable improvement in the management of the bioreactor dynamics versus classic controllers. The numerical findings highlight an improved precision in tracking reference signals and an enhanced plant stability compared to proportional–integral–derivative (PID) controller implementations within challenging disturbance scenarios. The FHOSMC effectively maintains the biomass concentration at desired levels, reducing the wear of the system as well as implementation expenses. Furthermore, the theoretical analysis of the convergence within time indicates substantial potential for further enhancements. Subsequent studies might focus on extending this control approach to bioreactor systems that integrate sensor technologies and the formulation of adaptive algorithms for real-time adjustments of β-type fractional-orders. Full article
(This article belongs to the Special Issue Fractional-Order Approaches in Automation: Models and Algorithms)
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