$fractalfract-logo$

Submit to Fractal Fract Review for Fractal Fract Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Fractional Order Controllers for Non-linear Systems

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Published Papers

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

Deadline for manuscript submissions: closed (10 February 2024) | Viewed by 11049

Share This Special Issue

Special Issue Editors

Dr. Chendrayan Dineshkumar

E-Mail Website
Guest Editor

Research Center for Wind Energy Systems, Kunsan National University, Kunsan National University, 558 Daehak-ro, Gunsan-si, Jeonbuk 54150, Republic of Korea
Interests: fractional differential equations; control theory and engineering; stochastic dynamical system; wind turbine system

Dr. Velusamy Vijayakumar

E-Mail Website
Guest Editor

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, India
Interests: fractional calculus; mathematical control theory; stochastic systems; impulsive systems; neural networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

Fractional calculus serves as a valuable tool for modeling and comprehending a wide range of physical systems and engineering processes. It enables the description of real-world phenomena using fractional-order differential equations, allowing for the accurate representation of systems with memory properties. These systems find applications in advanced control methodologies. Researchers employ various modeling approaches utilizing fractional calculus to capture the dynamic properties of systems with greater accuracy. Fractional calculus makes use of integrodifferential operators such as Caputo, Riemann–Liouville, Atangana–Baleanu, or Caputo–Fabrizio. The study of fractional control theory provides a valuable framework for modeling, understanding, and controlling complex systems that exhibit memory-dependent behaviors. In comparison to traditional integer-order control approaches, fractional calculus offers increased flexibility, robustness, and improved performance. This advancement enables progress in diverse fields, including materials science, biology, energy systems, power systems, chemical control, engineering, and robotics. Within the control community, there is particular interest in the existence and stability analysis of fractional-order systems. Fractional order controllers enhance control accuracy, stability, and disturbance rejection, especially for systems with long time delays or nonlinearity. They effectively reduce oscillations and achieve faster response times compared to conventional controllers.

The focus of this Special Issue is to continue to advance research on topics relating to the fractional order systems and their multi-faceted applications.

Dr. Chendrayan Dineshkumar
Dr. Velusamy Vijayakumar
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 deterministic and stochastic systems of orders (0,1) and (1,2)
existence and controllability analysis for fractional order system
mathematical modeling and simulation of fractional order systems
dynamics and stability analysis of fractional order controllers
fractional-order neural networks and fuzzy control systems
fractal and fractional analysis in engineering problems
control engineering problems in wind turbines
fractional order controllers and its applications in wind energy systems

Published Papers (10 papers)

Download All Papers

Research

19 pages, 3797 KiB

Open AccessArticle

Modeling and Predicting Passenger Load Factor in Air Transportation: A Deep Assessment Methodology with Fractional Calculus Approach Utilizing Reservation Data

by Kevser Şimşek, Nisa Özge Önal Tuğrul, Kamil Karaçuha, Vasil Tabatadze and Ertuğrul Karaçuha

Fractal Fract. 2024, 8(4), 214; https://doi.org/10.3390/fractalfract8040214 - 7 Apr 2024

Viewed by 614

Abstract

This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample flights, we propose a novel approach combining deep assessment methodology (DAM) with fractional calculus theory. By modeling the relationship between PLF and the number of days remaining until a flight, our method yields minimal errors compared to traditional techniques. Through a continuous curve constructed using the least-squares approach, we enable the anticipation of future flight values. Our analysis demonstrates that the DAM model with a first-order derivative outperforms linear techniques and the Fractional Model-3 in both modeling capabilities and prediction accuracy. The proposed approach offers a data-driven solution for efficiently managing air transport capacity, with implications for revenue optimization. Specifically, our modeling findings indicate that the DAM wd model improves prediction accuracy by approximately 0.67 times compared to the DAM model, surpassing the fractional model and regression analysis. For the DAM wd modeling method, the lowest average mean absolute percentage error (AMAPE) value achieved is 0.571, showcasing its effectiveness in forecasting flight outcomes. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

22 pages, 528 KiB

Open AccessArticle

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

by Miglena N. Koleva and Lubin G. Vulkov

Fractal Fract. 2024, 8(4), 196; https://doi.org/10.3390/fractalfract8040196 - 28 Mar 2024

Viewed by 638

Abstract

This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a quadratic functional, to compute the values of the unknown parameter vector. Numerical algorithm combining the method with appropriate fractional derivative approximation on graded mesh is applied to SIS and SEIR problems to illustrate the efficiency and accuracy. Tikhonov regularization is implemented to improve the convergence. Results from computations, both with noisy-free and noisy data, are provided and discussed. Simulations with real data are also performed. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

22 pages, 7686 KiB

Open AccessArticle

Investigation of the Robust Fractional Order Control Approach Associated with the Online Analytic Unity Magnitude Shaper: The Case of Wind Energy Systems

by Amina Mseddi, Ahmed Abid, Omar Naifar, Mohamed Rhaima, Abdellatif Ben Makhlouf and Lassaad Mchiri

Fractal Fract. 2024, 8(4), 187; https://doi.org/10.3390/fractalfract8040187 - 25 Mar 2024

Cited by 1 | Viewed by 859

Abstract

This paper investigates the development of a novel analytic approach for computing Unity Magnitude (UM) shapers that deviates from established numerical methodologies. The experimental validation on a test bench confirms the practicality and benefits of the suggested UM shaper technique. The study extends the use of UM shapers to improve the control of wind conversion systems (WCSs), particularly those including hybrid excitation synchronous generators (HESGs), demonstrating their adaptability and versatility. Experimental validation guarantees real-world application, confirming the suggested UM shapers’ trustworthiness. Strict management is still required to assure the system’s efficiency and dependability. In reality, the dynamic equations of a turbine, as well as those of an HESG, are substantially nonlinear; most system parameters are very uncertain; and, finally, a WCS is always impacted by disturbance sources such as load variations, harmonics, and mechanical vibrations. Robust control measures must be used to overcome these issues. A CRONE controller (Robust Fractional Order Control) of the second generation is created. A comparative study performed on the Simulink platform reveals substantial gains brought about by UM shapers in real-world circumstances. The study demonstrates the effectiveness of UM-shaped inputs in mechanical stabilization and Maximum Power Point Tracking (MPPT), emphasizing both theoretical soundness and practical advantages. The analytic equations for UM shapers in undamped and damped systems, offered together with a real-time algorithm, contribute to the optimization of wind conversion systems. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

15 pages, 1459 KiB

Open AccessArticle

Event-Triggered Adaptive Fuzzy Control for Strict-Feedback Nonlinear FOSs Subjected to Finite-Time Full-State Constraints

by Changhui Wang, Wencheng Li and Mei Liang

Fractal Fract. 2024, 8(3), 160; https://doi.org/10.3390/fractalfract8030160 - 12 Mar 2024

Viewed by 881

Abstract

In this article, an event-triggered adaptive fuzzy finite-time dynamic surface control (DSC) is presented for a class of strict-feedback nonlinear fractional-order systems (FOSs) with full-state constraints. The fuzzy logic systems (FLSs) are employed to approximate uncertain nonlinear functions in the backstepping process, the dynamic surface method is applied to overcome the inherent computational complexity from the virtual controller and its fractional-order derivative, and the barrier Lyapunov function (BLF) is used to handle the full-state constraints. By introducing the finite-time stability criteria from fractional-order Lyapunov method, it is verified that the tracking error converges to a small neighborhood near the zero and the full-state constraints are satisfied within a predetermined finite time. Moreover, reducing the communication burden can be guaranteed without the occurrence of Zeno behavior, and the example is given to demonstrate the effectiveness of the proposed controller. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

22 pages, 12543 KiB

Open AccessFeature PaperArticle

Power Quality Conditioners-Based Fractional-Order PID Controllers Using Hybrid Jellyfish Search and Particle Swarm Algorithm for Power Quality Enhancement

by Abdallah Aldosary

Fractal Fract. 2024, 8(3), 140; https://doi.org/10.3390/fractalfract8030140 - 28 Feb 2024

Viewed by 979

Abstract

Power quality (PQ) is a major issue in today’s electrical system that affects both utilities and customers. The proliferation of power electronics devices, smart grid technology, and renewable energy sources (RES) have all contributed to the emergence of PQ concerns in today’s power system. The Unified Power Quality Conditioner (UPQC) is a versatile tool that can be used to fix distribution grid issues caused by irregular voltage, current, or frequency. Several tuning parameters, however, restrict the effectiveness of the Fractional-Order Proportional Integral Derivative (FOPID) control technique, which is proposed to improve UPQC performance. To move beyond these restrictions and find the optimal solution for the FOPID controller problem, a hybrid optimization strategy called the Hybrid Jellyfish Search Optimizer and Particle Swarm Optimizer (HJSPSO) is employed. To meet the load requirement during PQ issue periods, the suggested model incorporates a renewable energy source into the grid system. Whether the load is linear or non-linear, the design maintains PQ problems to a minimum. Furthermore, the FOPID control technique is compared with other controllers. Results show that grid-connected RES systems using the proposed FOPID control approach for UPQC have fewer PQ problems. The presented UPQC with HJSPSO strategy significantly outperformed, with the shortest computing time of 127.474 s and an objective function value of 1.423. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

23 pages, 4340 KiB

Open AccessArticle

Enhancing Microgrid Inverter-Integrated Charging Station Performance through Optimization of Fractional-Order PI Controller Using the One-to-One Sine Cosine Algorithm

by Abdallah Aldosary

Fractal Fract. 2024, 8(3), 139; https://doi.org/10.3390/fractalfract8030139 - 28 Feb 2024

Viewed by 945

Abstract

This paper is dedicated to optimizing the functionality of Microgrid-Integrated Charging Stations (MICCS) through the implementation of a new control strategy, specifically the fractional-order proportional-integral (FPI) controller, aided by a hybrid optimization algorithm. The primary goal is to elevate the efficiency and stability of the MICCS-integrated inverter, ensuring its seamless integration into modern energy ecosystems. The MICCS system considered here comprises a PV array as the primary electrical power source, complemented by a proton exchange membrane fuel cell as a supporting power resource. Additionally, it includes a battery system and an electric vehicle charging station. The optimization model is formulated with the objective of minimizing the integral of square errors in both the DC-link voltage and grid current while also reducing total harmonic distortion. To enhance the precision of control parameter estimation, a hybrid of the one-to-one optimizer and sine cosine algorithm (HOOBSCA) is introduced. This hybrid approach improves the exploitation and exploration characteristics of individual algorithms. Different meta-heuristic algorithms are tested against HOOBSCA in different case studies to see how well it tunes FPI settings. Findings demonstrate that the suggested method improves the integrated inverters’ transient and steady-state performance, confirming its improved performance in generating high-quality solutions. The best fitness value achieved by the proposed optimizer was 3.9109, outperforming the other algorithms investigated in this paper. The HOOBSCA-based FPI successfully improved the response of the DC-link voltage, with a maximum overshooting not exceeding 8.5% compared to the other algorithms employed in this study. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

19 pages, 14874 KiB

Open AccessArticle

Fractional-Order Load Frequency Control of an Interconnected Power System with a Hydrogen Energy-Storage Unit

by Ping Wang, Xi Chen, Yunning Zhang, Lei Zhang and Yuehua Huang

Fractal Fract. 2024, 8(3), 126; https://doi.org/10.3390/fractalfract8030126 - 21 Feb 2024

Viewed by 1080

Abstract

Modern power systems are confronted with widespread concern on the frequency stability issue due to the widespread integration of randomly fluctuating renewable resources. To address the above concern, this work introduces a load-frequency-control (LFC) scheme based on a parameter tuning strategy for fractional-order proportional–integral–derivative (FOPID) controller. Firstly, a two-area interconnected power system (IPS) model, including thermal, hydro, solar, wind, and gas power generator and a hydrogen-based energy-storage unit, is established. Then, a FOPID controller is designed for this IPS model, and an improved gradient-based optimizer (IGBO) is developed to adaptively regulate the parameters of the FOPID controllers. Finally, the effectiveness of the offered LFC scheme is tested through load disturbance and renewable energy fluctuations test scenarios and provides a comparison and robustness analysis among different schemes. The test results validated that the offered LFC scheme can effectively suppress the frequency fluctuations of the IPS and has excellent robustness. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

16 pages, 1764 KiB

Open AccessArticle

Controllability of Fractional Complex Networks

by Xionggai Bao, Weiyuan Ma and Xin Li

Fractal Fract. 2024, 8(1), 43; https://doi.org/10.3390/fractalfract8010043 - 11 Jan 2024

Cited by 1 | Viewed by 926

Abstract

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

21 pages, 4767 KiB

Open AccessArticle

Optimal Design of Fractional-Order PID Controllers for a Nonlinear AWS Wave Energy Converter Using Hybrid Jellyfish Search and Particle Swarm Optimization

by Ziad M. Ali, Ahmed Mahdy Ahmed, Hany M. Hasanien and Shady H. E. Abdel Aleem

Fractal Fract. 2024, 8(1), 6; https://doi.org/10.3390/fractalfract8010006 - 20 Dec 2023

Cited by 2 | Viewed by 1228

Abstract

In this study, a nonlinear Archimedes wave swing (AWS) energy conversion system was employed to enable the use of irregular sea waves to provide useful electricity. Instead of the conventional PI controllers used in prior research, this study employed fractional-order PID (FOPID) controllers to control the back-to-back configuration of AWS. The aim was to maximize the energy yield from waves and maintain the grid voltage and the capacitor DC link voltage at predetermined values. In this study, six FOPID controllers were used to accomplish the control goals, leading to an array of thirty parameters required to be fine-tuned. In this regard, a hybrid jellyfish search optimizer and particle swarm optimization (HJSPSO) algorithm was adopted to select the optimal control gains. Verification of the performance of the proposed FOPID control system was achieved by comparing the system results to two conventional PID controllers and one FOPID controller. The conventional PID controllers were tuned using a recently presented metaheuristic algorithm called the Coot optimization algorithm (COOT) and the classical particle swarm optimization algorithm (PSO). Moreover, the FOPID was also tuned using the well-known genetic algorithm (GA). The system investigated in this study was subjected to various unsymmetrical and symmetrical fault disturbances. When compared with the standard COOT-PID, PSO-PID, and GA-FOPID controllers, the HJSPSO-FOPID results show a significant improvement in terms of performance and preserving control goals during system instability Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

22 pages, 9676 KiB

Open AccessArticle

Disturbance Rejection-Based Optimal PID Controllers for New 6ISO AVR Systems

by Muhyaddin Rawa, Sultan Alghamdi, Martin Calasan, Obaid Aldosari, Ziad M. Ali, Salem Alkhalaf, Mihailo Micev and Shady H. E. Abdel Aleem

Fractal Fract. 2023, 7(10), 765; https://doi.org/10.3390/fractalfract7100765 - 18 Oct 2023

Cited by 1 | Viewed by 1172

Abstract

In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated. Full article

(This article belongs to the Special Issue Fractional Order Controllers for Non-linear Systems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Fractional Order Controllers for Non-linear Systems

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (10 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI