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Fractal Fract
Special Issues
Applications of Fractional-Order Systems to Automatic Control
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Applications of Fractional-Order Systems to Automatic Control

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

Deadline for manuscript submissions: 15 August 2024 | Viewed by 6157

Special Issue Editors

Dr. Germán Ardúl Muñoz Hernández

E-Mail Website
Guest Editor
Instituto Tecnológico de Puebla, Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
Interests: modeling and control of hydropower systems; predictive control; fractional-order control; power electronics
Prof. Dr. Fermi Guerrero-Castellanos

E-Mail Website
Guest Editor
Facultad de Ciencias de la Electrónica, Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
Interests: modeling and control of mechatronics and unmanned vehicles; inertial navigation systems; event-based control; multi-agent systems; active-disturbance rejection control; renewable energy applications

Special Issue Information

Dear Colleagues,

Fractional-order systems have been applied in diverse areas of science and engineering. Fractional-order calculus is a generalization of the integration and differentiation operators to non-integer order. Factional order provides additional flexibility and adjustments to operation specifications. In automatic control, fractional systems allow forms of response that are impossible to achieve with classical control, e.g., improvement in noise measurement attenuation without unnecessarily deteriorating the disturbance rejection properties and, consequently, the time response of the closed-loop system.

The focus of this Special Issue is to showcase advances in research on topics related to the theory, design, implementation and application of fractional order systems in automatic control. Topics expected to be submitted include (but are not limited to):

  • Fractional-order control design and stability analysis;
  • Applications of fractional-order control for unmanned vehicles;
  • Applications of fractional-order control for renewable energy systems;
  • Fractional-order control applied to electric power systems;
  • Fractional-order control applied to manufacturing systems;
  • Fractional-order control applied to robotic systems;
  • Fractional-order control applied to automotive control systems;
  • Fractional-order modelling and control of time-delay systems;
  • Fractional-order modeling and control of complex systems.

Dr. Germán Ardúl Muñoz Hernández
Prof. Dr. Fermi Guerrero-Castellanos
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

  • unmanned vehicles
  • renewable energy
  • electric power
  • manufacturing
  • robotics
  • automotive control systems
  • time-delay systems
  • modeling and control of complex systems

Published Papers (6 papers)

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Research

17 pages, 8493 KiB  
Article
Robust Fractional-Order PI/PD Controllers for a Cascade Control Structure of Servo Systems
by Vo Lam Chuong, Ngo Hong Nam, Le Hieu Giang and Truong Nguyen Luan Vu
Fractal Fract. 2024, 8(4), 244; https://doi.org/10.3390/fractalfract8040244 - 22 Apr 2024
Viewed by 402
Abstract
In this paper, a cascade control structure is suggested to control servo systems that normally include a servo motor in coupling with two kinds of mechanism elements, a translational or rotational movement. These kinds of systems have high demands for performance in terms [...] Read more.
In this paper, a cascade control structure is suggested to control servo systems that normally include a servo motor in coupling with two kinds of mechanism elements, a translational or rotational movement. These kinds of systems have high demands for performance in terms of fastest response and no overshoot/oscillation to a ramp function input. The fractional-order proportional integral (FOPI) and proportional derivative (FOPD) controllers are addressed to deal with those control problems due to their flexibility in tuning rules and robustness. The tuning rules are designed in the frequency domain based on the concept of the direct synthesis method and also ensure the robust stability of controlled systems by using the maximum sensitivity function. The M-Δ structure, using multiplicative output uncertainties for both control loops simultaneously, is addressed to justify the robustness of the controlled systems. Simulation studies are considered for two kinds of plants that prove the effectiveness of the proposed method, with good tracking of the ramp function input under the effects of the disturbances. In addition, the robustness of the controlled system is illustrated by a structured singular value (µ) plot in which its value is less than 1 over the frequency range. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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17 pages, 3893 KiB  
Article
Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm
by Guangxin Jiao, Zhengcai An, Shuyi Shao and Dong Sun
Fractal Fract. 2024, 8(2), 99; https://doi.org/10.3390/fractalfract8020099 - 6 Feb 2024
Viewed by 1083
Abstract
In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system [...] Read more.
In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system uncertainties in the system. Then, a fractional-order sliding-mode controller is constructed to control the system, and the parameters of the controller are tuned using the TD3 algorithm, which can optimize the control effect. The results show that the fractional-order control method based on the TD3 algorithm can not only improve the closed-loop system performance under different operating conditions but also enhance the signal tracking capability. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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20 pages, 2743 KiB  
Article
A Fractional-Order ADRC Architecture for a PMSM Position Servo System with Improved Disturbance Rejection
by Shaohua Wang, He Gan, Ying Luo, Xin Luo and Yangquan Chen
Fractal Fract. 2024, 8(1), 54; https://doi.org/10.3390/fractalfract8010054 - 14 Jan 2024
Cited by 1 | Viewed by 1115
Abstract
This paper proposes an active disturbance rejection control (ADRC) architecture for a permanent magnet synchronous motor (PMSM) position servo system. The presented method achieved enhanced tracking and disturbance rejection performance with a limited observer bandwidth. The model-aided extended state observer (MESO)-based ADRC was [...] Read more.
This paper proposes an active disturbance rejection control (ADRC) architecture for a permanent magnet synchronous motor (PMSM) position servo system. The presented method achieved enhanced tracking and disturbance rejection performance with a limited observer bandwidth. The model-aided extended state observer (MESO)-based ADRC was designed for the current, speed, and position loops of the PMSM position servo system. By integrating known plant information, the MESO improved disturbance estimation with a limited observer bandwidth without amplifying the noise. Additionally, a fractional-order proportional-derivative (FOPD) controller was designed as the feedback controller for the speed loop to further enhance the disturbance rejection. A simulation and experimental tests were conducted on a PMSM servo platform. The results demonstrate not only that the proposed method achieved superior tracking performance but also that the position error of the proposed strategy decreases to 2.25% when the constant disturbance was input, significantly improving the disturbance rejection performance. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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21 pages, 3222 KiB  
Article
Fractional-Order Phase Lead Compensation Multirate Repetitive Control for Grid-Tied Inverters
by Fen Liang, Ho-Joon Lee and Hongwei Zhang
Fractal Fract. 2023, 7(12), 848; https://doi.org/10.3390/fractalfract7120848 - 29 Nov 2023
Viewed by 826
Abstract
To reduce computational load and memory consumption, multirate repetitive control (MRC) with downsampling rates provides a flexible and efficient design for proportional-integral multi-resonant repetitive control (PIMR-RC) systems for grid-tied inverters. However, in MRC systems, repetitive controllers with low sampling rates produce low delay [...] Read more.
To reduce computational load and memory consumption, multirate repetitive control (MRC) with downsampling rates provides a flexible and efficient design for proportional-integral multi-resonant repetitive control (PIMR-RC) systems for grid-tied inverters. However, in MRC systems, repetitive controllers with low sampling rates produce low delay periods, and integer-order phase lead compensation may cause undercompensation or overcompensation. These imprecise linear phase lead compensations may result in deteriorated control performance. To address these problems, based on an infinite impulse response (IIR) filter, a fractional-order phase lead proportional-integral multi-resonant multirate repetitive control (FPL-PIMR-MRC) is proposed for grid-tied inverters in this paper. The proposed method can provide a suitable fractional phase lead step to achieve a wide stability region, minor tracking errors, and low hardware costs. The IIR fractional-order lead filter design, stability analysis, and the step-by-step parameter tuning of the FPL-PIMR-MRC system are derived in detail. Finally, simulation performed confirms the feasibility and effectiveness of the proposed scheme. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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19 pages, 4831 KiB  
Article
Optimal Fractional-Order Controller for the Voltage Stability of a DC Microgrid Feeding an Electric Vehicle Charging Station
by Sherif A. Zaid, Abualkasim Bakeer, Hani Albalawi, Aadel M. Alatwi, Hossam AbdelMeguid and Ahmed M. Kassem
Fractal Fract. 2023, 7(9), 677; https://doi.org/10.3390/fractalfract7090677 - 9 Sep 2023
Cited by 2 | Viewed by 1062
Abstract
Charging stations are regarded as the cornerstone of electric vehicle (EV) development and utilization. Electric vehicle charging stations (EVCSs) are now energized via standalone microgrids that utilize renewable energy sources and reduce the stress on the utility grid. However, the control and energy [...] Read more.
Charging stations are regarded as the cornerstone of electric vehicle (EV) development and utilization. Electric vehicle charging stations (EVCSs) are now energized via standalone microgrids that utilize renewable energy sources and reduce the stress on the utility grid. However, the control and energy management of EVCSs are challenging tasks because they are nonlinear and time-varying. This study suggests a fractional-order proportional integral (FOPI) controller to improve the performance and energy management of a standalone EVCS microgrid. The microgrid is supplied mainly by photovoltaic (PV) energy and utilizes a battery as an energy storage system (ESS). The FOPI’s settings are best created utilizing the grey wolf optimization (GWO) method to attain the highest performance possible. The grey wolf is run for 100 iterations using 20 wolves. In addition, after 80 iterations for the specified goal function, the GWO algorithm almost discovers the ideal values. For changes in solar insolation, the performance of the proposed FOPI controller is compared with that of a traditional PI controller. The Matlab/Simulink platform models and simulates the EVCS’s microgrid. The results demonstrate that the suggested FOPI controller significantly improves the transient responsiveness of the EVCS performance compared to the standard PI controller. Despite all PV insolation disruptions, the EV battery continues to charge while the ESS battery precisely stores and balances PV energy changes. The results support the suggested FOPI control’s robustness to parameter mismatches. The microgrid’s efficiency fluctuations with the insolation level and state of charge of the EV battery are discussed. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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24 pages, 6969 KiB  
Article
Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link
by Saddam Gharab and Vicente Feliu Batlle
Fractal Fract. 2023, 7(9), 646; https://doi.org/10.3390/fractalfract7090646 - 24 Aug 2023
Cited by 1 | Viewed by 889
Abstract
This work addresses the robust control of processes of the form G(s)=K·e−τ·s/(1+T·sλ) with 1<λ≤2. A new method for [...] Read more.
This work addresses the robust control of processes of the form G(s)=K·e−τ·s/(1+T·sλ) with 1<λ≤2. A new method for tuning fractional-order PI and PD controllers is developed. The stability is assessed based on the frequency domain tuning of the regulators to control such delayed fractional-order underdamped processes. In order to analyze the closed-loop stability and robustness, the new concept of Robust High-Frequency Condition is introduced. The analysis based on that demonstrates that each controller has a different region of feasible frequency specifications, and, in all cases, they depend on their fractional integral or derivative actions. Finally, an application example, the position control of a teleoperated manipulator with a flexible link, is presented. Simulations and experiments illustrate that the region of feasible frequency specifications defined at low and high frequencies allows us to obtain robust controllers that fulfill frequency requirements. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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