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Fractal Fract
Special Issues
Fractional-Order Control: Design, Stability Analysis, and Implementation
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Fractional-Order Control: Design, Stability Analysis, and Implementation

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

Deadline for manuscript submissions: closed (20 March 2023) | Viewed by 11026

Special Issue Editor

Dr. Georgios Tzounas

E-Mail Website
Guest Editor
Power Systems Laboratory, ETH Zürich, 8092 Zürich, Switzerland
Interests: power system dynamics; stability and control; singular systems; time-delay systems; fractional-order systems

Special Issue Information

Dear Colleagues,

Control systems based on fractional calculus are gaining momentum, mainly due to their ability to enhance performance and increase the stability margin of dynamical systems, as well as to provide robustness under varying operating conditions, parameter uncertainty, measurement noise, and time delays. On the other hand, despite several recent advances in the area, existing fractional-order system theory is still far from being complete and coherent, with current open research questions including, but not limited to, modelling aspects, stability, simulation, and practical realization.

This Special Issue is focused on the design, stability analysis, and implementation of fractional-order control systems for engineering applications. Potential topics that are invited for submission include the following:

  • Fractional-order control design and stability analysis;
  • Application of fractional-order control to power, energy, and other engineering systems;
  • Fractional-order control for systems of differential and difference equations;
  • Fractional-order control for singular systems;
  • Fractional-order control for time-delay systems.

Dr. Georgios Tzounas
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-order control
  • fractional calculus
  • modelling
  • stability analysis
  • control design
  • simulation
  • realization

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

17 pages, 1049 KiB  
Article
Improved Particle Swarm Optimization Fractional-System Identification Algorithm for Electro-Optical Tracking System
by Tong Guo, Jiuqiang Deng, Yao Mao and Xi Zhou
Fractal Fract. 2023, 7(3), 264; https://doi.org/10.3390/fractalfract7030264 - 16 Mar 2023
Cited by 3 | Viewed by 1729
Abstract
When an electro-optical tracking system (ETS) needs higher control precision, system identification can be considered to improve the accuracy of the system, so as to improve its control effect. The fractional system model of ETS can describe the characteristics of the system better [...] Read more.
When an electro-optical tracking system (ETS) needs higher control precision, system identification can be considered to improve the accuracy of the system, so as to improve its control effect. The fractional system model of ETS can describe the characteristics of the system better and improve the accuracy of the system model. Therefore, this paper presents a fractional system identification algorithm for ETS that is based on an improved particle swarm optimization algorithm. The existence of the fractional order system of ETS was verified by identification experiments, and the fractional order system model was obtained. Under the same conditions, PI controllers were designed based on a fractional order system and an integer order system, respectively. The results verify the superiority of fractional order system in ETS. Full article
(This article belongs to the Special Issue Fractional-Order Control: Design, Stability Analysis, and Implementation)
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13 pages, 9444 KiB  
Article
Attitude Control of the Quadrotor UAV with Mismatched Disturbances Based on the Fractional-Order Sliding Mode and Backstepping Control Subject to Actuator Faults
by Hui Sun, Jinming Li, Rui Wang and Kaixin Yang
Fractal Fract. 2023, 7(3), 227; https://doi.org/10.3390/fractalfract7030227 - 3 Mar 2023
Cited by 6 | Viewed by 2103
Abstract
Considering mismatched disturbances, aerodynamic interference, chattering, and actuator failure in the attitude control of the quadrotor unmanned aerial vehicle (UAV), this paper establishes a new quadrotor UAV model with mismatched disturbances, based on quaternion, and designs a fault tolerant controller. First, in order [...] Read more.
Considering mismatched disturbances, aerodynamic interference, chattering, and actuator failure in the attitude control of the quadrotor unmanned aerial vehicle (UAV), this paper establishes a new quadrotor UAV model with mismatched disturbances, based on quaternion, and designs a fault tolerant controller. First, in order to reduce the chattering of the traditional reaching law, a new reaching law based on the sigmoid function is introduced into the design. Second, the sliding mode control and backstepping control methods are adopted, based on the new fractional-order sliding mode surface when the faults occur in quadrotor UAV actuators, and parameters in the sliding mode control are adaptively adjusted. The simulation results show that the fault tolerant control method can control the attitude of UAV quickly and achieve good robustness. Full article
(This article belongs to the Special Issue Fractional-Order Control: Design, Stability Analysis, and Implementation)
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38 pages, 33028 KiB  
Article
A New Method for Controlling Fractional Linear Systems
by Subramanian V. Shastri, Kumpati S. Narendra and Lihao Zheng
Fractal Fract. 2023, 7(1), 50; https://doi.org/10.3390/fractalfract7010050 - 31 Dec 2022
Cited by 1 | Viewed by 1751
Abstract
The study of fractional linear time-invariant (LTI) systems has been an area of active research over the past thirty years. Results indicate that such systems are becoming important in the representation of certain types of dynamical behavior in biology and engineering. Several methods [...] Read more.
The study of fractional linear time-invariant (LTI) systems has been an area of active research over the past thirty years. Results indicate that such systems are becoming important in the representation of certain types of dynamical behavior in biology and engineering. Several methods have been developed for the representation, identification, and control of fractional LTI systems. The primary purpose of this paper is to introduce a new approach to their control. Its principal contribution is the transformation of a fractional LTI system into one without fractional terms (standard LTI system) using feedback and feedforward compensation. While the former may be quite difficult to control, tools widely available in linear systems theory may be used to control the latter. Transformation of a fractional system into a standard one requires compensators with fractional transfer functions. It is shown, using research results from the past two decades, that such functions can be realized using hardware and software subsystems. The authors demonstrate, using an example, that better control performance is possible with the new method when compared to current ones that are most common in the research literature. Robustness in the presence of noise and model uncertainties is also studied for the new method and currently available ones. Simulation results presented illustrate improvements achievable in control robustness with the new method. Full article
(This article belongs to the Special Issue Fractional-Order Control: Design, Stability Analysis, and Implementation)
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17 pages, 3282 KiB  
Article
High-Tracking-Precision Sensorless Control of PMSM System Based on Fractional Order Model Reference Adaptation
by Hongjie Niu, Ling Liu, Dongsong Jin and Siyuan Liu
Fractal Fract. 2023, 7(1), 21; https://doi.org/10.3390/fractalfract7010021 - 26 Dec 2022
Cited by 10 | Viewed by 2312
Abstract
In order to solve parameter fluctuations and disturbances, a novel fractional order model reference adaptive speed observer that estimates the rotor position and the angular velocity from the stator currents is proposed for sensorless control of permanent-magnet synchronous motors (PMSM). Firstly, a novel [...] Read more.
In order to solve parameter fluctuations and disturbances, a novel fractional order model reference adaptive speed observer that estimates the rotor position and the angular velocity from the stator currents is proposed for sensorless control of permanent-magnet synchronous motors (PMSM). Firstly, a novel fractional order model reference adaptive controller (FOMRAC) for adaptive identification is designed to achieve fast response and high precise identification of load torque in the full speed range when the motor is running at variable-speed or variable-load. Additionally, an appropriate adjustable matrix P is chosen to make the convergence of the adaptive law meet the requirements. Next, an improved model reference adaptive observer (MRAO) is proposed to suppress the serious chattering and compensate rotor position error, which can stabilize the system. The validity of the proposed fractional order model reference adaptive sensorless control strategy for PMSM is demonstrated with simulations. Full article
(This article belongs to the Special Issue Fractional-Order Control: Design, Stability Analysis, and Implementation)
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35 pages, 7779 KiB  
Article
Distributed Optimization for Fractional-Order Multi-Agent Systems Based on Adaptive Backstepping Dynamic Surface Control Technology
by Xiaole Yang, Weiming Zhao, Jiaxin Yuan, Tao Chen, Chen Zhang and Liangquan Wang
Fractal Fract. 2022, 6(11), 642; https://doi.org/10.3390/fractalfract6110642 - 3 Nov 2022
Cited by 11 | Viewed by 2177
Abstract
In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurable states and a local objective function described by a quadratic [...] Read more.
In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurable states and a local objective function described by a quadratic polynomial function. A penalty function is constructed by a sum of local objective functions and integrating consensus conditions of the MASs. Radial basis function Neural-networks (RBFNNs) and Neural networks (NN) state observer are applied to approximate the unknown nonlinear dynamics and estimate unmeasured states, respectively. By combining the NN state observer and the penalty function, and the stability theory of the Lyapunov function, the distributed observer-based adaptive optimized backstepping dynamic surface control protocol is proposed to ensure the outputs of all agents asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme. Full article
(This article belongs to the Special Issue Fractional-Order Control: Design, Stability Analysis, and Implementation)
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