Fractional-Order Controllers in Electronics and Automation Engineering, 2nd Edition

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

Deadline for manuscript submissions: 30 August 2026 | Viewed by 1084

Editors


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Guest Editor
CONAHCYT-Instituto Tecnológico de Celaya, Celaya 38010, Mexico
Interests: fractional-order control; power electronic converters; E-mobility; non-linear systems; synchronization; complex networks
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Guest Editor
Applied Physics Division, Center for Scientific Research and Higher Education at Ensenada, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico
Interests: robust control; chaotic dynamics; fractional calculus; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus has been considered as an alternative to improve the modeling, performance, and efficiency of dynamic systems. Numerous linear and nonlinear control approaches have been proposed and adapted to integrate fractional-order derivative and integral definitions to their control objective to effectively regulate systems' output, focusing on transient and permanent responses, as well as the velocity of regulation and robustness.

Fractional-order control was successfully incorporated into well-known control strategies such as the PID structure, which has been combined with more sophisticated approaches to validate effectiveness and feasibility of noninteger-order techniques. To date, some theory and practical results have been reported, but a systematic procedure to integrate a fractional-order approach into a control strategy and its implementation are not clear enough.

Therefore, this Special Issue is represents an invitation for researchers to explore the potential of fractional-order theory through visionary, radical, and innovative control proposals to help expand the application areas, exploit the advantages, determine the limitations, and above all, clarify the bridges that connect the theory with its implementation. Thus, the aim of this Special Issue is to motivate the development of advanced research on the theory, design, and experimental validation of fractional-order control strategies.

Thus, the topics of interest include, but are not limited to, the following:

  • Fractional-order control strategies for energy harvesting/management.
  • Batteries fractional-order modeling.
  • Analog and digital implementation of fractional-order controllers.
  • Fractional-order control strategies developed for electromobility.
  • Applications of fractal-order control strategies in biomedicine.
  • Fractional-order circuit theory.
  • Applications for fractional-order calculus.
  • The implementation of fractional-order approximations through circuitry.
  • Stability of systems regulated with fractional-order controllers.

Dr. Allan G.S. Sánchez
Dr. Joaquin Alvarez
Guest Editors

Manuscript Submission Information

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Keywords

  • fractional-order calculus
  • fractional-order control
  • fractional-order approximations
  • fractional-order implementation
  • tuning of fractional-order controllers

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Published Papers (2 papers)

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Research

24 pages, 21878 KB  
Article
Fractional-Order Quasi-Resonant Extended State Observer for Position Error Compensation in PMSM Sensorless Control
by Xiaohong Wang, Zhaoqi Zhou, Likai Zheng and Ying Luo
Fractal Fract. 2026, 10(7), 491; https://doi.org/10.3390/fractalfract10070491 - 20 Jul 2026
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Abstract
Flux linkage observers have been widely employed in permanent magnet synchronous motor (PMSM) sensorless drives, and the back electromotive force (BEMF) estimated by an extended state observer (ESO) can be used to compensate for the position estimation error of the flux linkage observer. [...] Read more.
Flux linkage observers have been widely employed in permanent magnet synchronous motor (PMSM) sensorless drives, and the back electromotive force (BEMF) estimated by an extended state observer (ESO) can be used to compensate for the position estimation error of the flux linkage observer. However, inverter dead time introduces periodic disturbances into the estimated synchronous reference frame, thereby contaminating the BEMF estimation and degrading the accuracy of position compensation. To this end, a position estimation error compensation strategy based on a fractional-order quasi-resonant extended state observer (FOQR-ESO) is proposed. First, a PMSM voltage model incorporating the inverter dead-time effect is established, and the resulting sixth-order harmonic component in the estimated synchronous reference frame is analyzed. Then, a fractional-order quasi-resonant element is embedded into the ESO to enhance its capability to estimate harmonic components. The proposed FOQR-ESO separates the BEMF-related component from the sixth-order harmonic disturbance, while the fractional-order parameter provides an additional degree of freedom for shaping the observer frequency response. Simulation and experimental results demonstrate that the proposed FOQR-ESO effectively suppresses the sixth-order harmonic disturbance and achieves higher rotor position estimation accuracy than the conventional ESO and the integer-order quasi-resonant extended state observer (IOQR-ESO). Full article
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24 pages, 8464 KB  
Article
A Control Method for Three-Phase Inverters Based on Adaptive Parameters of Fractional-Order QPCIs
by Mingyuan Hu, Bo Gao, Ying-Ren Chien, Lei Zhang, Qimeng Sun, Yang Liu and Jingwen Liu
Fractal Fract. 2026, 10(7), 480; https://doi.org/10.3390/fractalfract10070480 - 15 Jul 2026
Viewed by 337
Abstract
In order to improve the performance of three-phase NPC inverters under unbalanced working conditions, a quasi-proportional complex integral controller (QPCI) three-phase inverter control method based on an adaptive fractional-order algorithm is proposed. Firstly, the reasons for the poor performance of conventional control methods [...] Read more.
In order to improve the performance of three-phase NPC inverters under unbalanced working conditions, a quasi-proportional complex integral controller (QPCI) three-phase inverter control method based on an adaptive fractional-order algorithm is proposed. Firstly, the reasons for the poor performance of conventional control methods under unbalanced load conditions are analyzed. Subsequently, a fractional-order quasi-proportional complex integral (FO-QPCI) controller is proposed, and the effects of its control parameters, including proportional gain (KP), integral gain (KI), resonant frequency (ωc), and fractional order (μ), are systematically investigated. Furthermore, the optimal control parameter dataset is utilized to train a Generalized Regression Neural Network (GRNN), through which an adaptive parameter-tuning model is established. As a result, the proposed FO-QPCI controller can dynamically adjust its control parameters according to different voltage references and load unbalanced levels. Finally, to verify the effectiveness of the proposed control strategy, both simulation models and an experimental platform based on a three-level inverter are developed. The results show that the proposed control method has good control ability for the output voltage and harmonics under unbalanced working conditions. Full article
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