Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition

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

Deadline for manuscript submissions: 10 April 2024 | Viewed by 1432

Special Issue Editors

Conservatoire National des Arts et Métiers (CNAM), Cedric-Laetitia, 292 Rue St-Martin, 75141 Paris CEDEX 03, France
Interests: state estimation; interval observer; robust control; output feedback; positive fractional-order systems
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Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, India
Interests: stability and stabilization of fractional order systems; sliding mode control; nonlinear observers; contraction analysis
Special Issues, Collections and Topics in MDPI journals
Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
Interests: fractional differential equations; fractional variational problems; applications of fractional calculus in image processing; computational methods
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Department of Electrical Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342 037, India
Interests: fractional-order systems; large scale systems; sliding mode control; large size nuclear reactor modelling and control
School of Mechanical and Electrical Engineering, Soochow University, Suzhou 215137, China
Interests: nonlinear systems and control; stochastic systems; multi-agent systems; fault diagnosis and reliable control; interval observer design
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the last two decades, (fractional) differential equations have become more common in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry, and many other fields, allowing for a new and more realistic way to capture memory-dependent phenomena and irregularities within systems through more sophisticated mathematical analysis. As a result of its growing applications, the study of the stability of (fractional) differential equations has received significant attention. Furthermore, in recent years, interest in fractional- and integer-order controllers has grown. Examples of these are optimal control, CRONE controllers, fractional PID controllers, lead–lag compensators, and sliding mode control. 

The purpose of this Special Issue is to disseminate research on fractional-/integer-order control theory and its applications in practical systems modeled using fractional-/integer-order differential equations. These include the design, implementation, and application of fractional-/integer-order control to electrical circuits and systems, mechanical systems, chemical systems, biological systems, finance systems, and so on.

Submissions are welcome on, but not limited to, the following topics:

  • Control theory for fractional- and integer-order systems;
  • Lyapunov-based stability and stabilization of fractional- and integer-order systems;
  • Feedback linearization-based controller and observer design for fractional- and integer-order systems;
  • Digital implementation of fractional- and integer-order control;
  • Sliding mode control of fractional- and integer-order systems;
  • Finite-, fixed-, and predefined-time stability and stabilization of fractional- and integer-order systems;
  • Set-membership design for fractional- and integer-order systems;
  • High-gain based observers and differentiator design for fractional- and integer-order systems;
  • Event-based control of fractional- and integer-order systems;
  • Incremental stability of fractional- and integer-order systems;
  • Control of non-minimum phase systems using fractional- and integer-order theory;
  • New physical interpretation of fractional- and integer-order operators and their relationship to control design;
  • Design and development of efficient battery management and state of health estimation using fractional- and integer-order calculus;
  • Applications of fractional- and integer-order control to electrical, mechanical, chemical, financial, and biological systems;
  • Verification and reachability analysis of fractional- and integer-order differential equations.

Dr. Thach Ngoc Dinh
Dr. Shyam Kamal
Dr. Rajesh Kumar Pandey
Prof. Dr. Bijnan Bandyopadhyay
Prof. Dr. Jun Huang
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.

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Research

21 pages, 5607 KiB  
Article
An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer
by Ali Yüce
Fractal Fract. 2023, 7(6), 460; https://doi.org/10.3390/fractalfract7060460 - 03 Jun 2023
Viewed by 1127
Abstract
System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical [...] Read more.
System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model. Full article
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