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17 pages, 654 KiB

Open AccessArticle

Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks

by Zhenduo Sun, Nengneng Qing and Xiangzhi Kong

Mathematics 2023, 11(13), 2905; https://doi.org/10.3390/math11132905 - 28 Jun 2023

Viewed by 517

Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more susceptible to changes over time. Therefore, it is essential to [...] Read more.

Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more susceptible to changes over time. Therefore, it is essential to incorporate variable-order fractional calculus into the asymptotic hybrid projection lag synchronization of complex networks. Firstly, this approach considers nonidentical models with variable-order fractional characteristics, which is more general. Secondly, a class of variable-order fractional sliding mode surfaces is designed, and an accurate formula for calculating finite arriving time is provided, in contrast to traditional sliding mode control methods that use an inequality-based range. Thirdly, sufficient conditions for achieving asymptotic hybrid projection lag synchronization of nonidentical variable-order fractional complex networks are derived. Lastly, the feasibility and effectiveness of our approach are demonstrated through two illustrative examples. Full article

(This article belongs to the Special Issue Fractional Calculus and Its Application on Control and Decision)

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17 pages, 3048 KiB

Open AccessArticle

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data

by Cristina I. Muresan, Iulia Bunescu, Isabela Birs and Robin De Keyser

Mathematics 2023, 11(5), 1097; https://doi.org/10.3390/math11051097 - 22 Feb 2023

Viewed by 953

Abstract

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm [...] Read more.

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability. Full article

(This article belongs to the Special Issue Fractional Calculus and Its Application on Control and Decision)

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20 pages, 3602 KiB

Open AccessArticle

Knacks of Fractional Order Swarming Intelligence for Parameter Estimation of Harmonics in Electrical Systems

by Naveed Ahmed Malik, Ching-Lung Chang, Naveed Ishtiaq Chaudhary, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema, Chi-Min Shu and Sultan S. Alshamrani

Mathematics 2022, 10(9), 1570; https://doi.org/10.3390/math10091570 - 06 May 2022

Cited by 14 | Viewed by 1610

Abstract

The efficient parameter estimation of harmonics is required to effectively design filters to mitigate their adverse effects on the power quality of electrical systems. In this study, a fractional order swarming optimization technique is proposed for the parameter estimation of harmonics normally present [...] Read more.

The efficient parameter estimation of harmonics is required to effectively design filters to mitigate their adverse effects on the power quality of electrical systems. In this study, a fractional order swarming optimization technique is proposed for the parameter estimation of harmonics normally present in industrial loads. The proposed fractional order particle swarm optimization (FOPSO) effectively estimates the amplitude and phase parameters corresponding to the first, third, fifth, seventh and eleventh harmonics. The performance of the FOPSO was evaluated for ten fractional orders with noiseless and noisy scenarios. The robustness efficiency of the proposed FOPSO was analyzed by considering different levels of additive white Gaussian noise in the harmonic signal. Monte Carlo simulations confirmed the reliability of the FOPSO for a lower fractional order (