Fractional derivatives and the laws of electrical engineering

Sikora, R.; Pawłowski, Stanisław

doi:10.1108/compel-08-2017-0347

Cited by 16 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Literature items (Sikora et al, 2018;Piotrowska, 2018Piotrowska, , 2020 are my own or co-authored works. In the current list of literature, I have listed them respectively under the numbers (Sikora, 2017b;Sikora and Pawłowski, 2018a;Sikora and Pawłowski, 2018b). Do such citations meet AEE's scientific integrity requirements?…”

Section: Free Discussionmentioning

confidence: 99%

“…I have published alone or with co-authors several works (Sikora, 2016;Sikora, 2017;Sikora and Pawłowski, 2018c;Sikora, 2017bSikora, , 2018Sikora and Pawłowski, 2018a;Sikora and Pawłowski, 2018b;Sikora et al, 2018), having the subject related to the use of fractional derivatives in electrical engineering. In my opinion, misuse of fractional derivatives causes damage in two ways, material and mental.…”

Section: Problem Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Can science exist without free discussion?

Sikora

2023

COMPEL

Self Cite

View full text Add to dashboard Cite

Purpose The aim of this article is to draw attention to the importance of open discussion for the proper development of science. Design/methodology/approach In the phase of the developed market economy we are currently in, the evaluation of each human activity, including scientific work, which is based on an evaluation of the value of the profit it brings. Unfortunately, it does not always work correctly. Findings The problem will be analyzed using as an example the erroneous (according to the author) use of fractional derivatives in electrical engineering. Originality/value To the best of the author’s knowledge, this is the author's original point of view on the problem of improper use of fractional derivatives in electrical engineering.

show abstract

Section: Free Discussionmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

Can science exist without free discussion?

Sikora

2023

COMPEL

Self Cite

View full text Add to dashboard Cite

show abstract

“…Unfortunately, although several attempts have been made [6][7][8][9], it is not clear which definition of the FO derivative should be used in electrical sciences. Recent discussion in literature [10] suggests that pointing out which definition of the FO derivative can be applied in electrical sciences is of the utmost importance. Therefore, in this paper, we employ a very general definition of the FO derivative, i.e., the two-sided Ortigueira-Machado derivative [6,11], which unites the ideas of forward and backward differentiations, and employs two parameters, i.e., the derivative order and the asymmetry parameter.…”

Section: Introductionmentioning

confidence: 99%

Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative

2021

View full text Add to dashboard Cite

In this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality of the system is investigated; its output is an electromagnetic signal propagating in media described by the time-domain two-sided fractional derivative. It is demonstrated that, for the derivative order in the range [1,+∞), the transfer function describing attenuated signal propagation is not causal for any value of the asymmetry parameter of the derivative. On the other hand, it is shown that, for derivative orders in the range (0,1), the transfer function is causal if and only if the asymmetry parameter is equal to certain specific values corresponding to the left-sided Grünwald–Letnikov derivative. The results are illustrated by numerical simulations and analyses. Some comments on the Kramers–Krönig relations for logarithm of the transfer function are presented as well.

show abstract

“…As an extension of integral calculus, fractional calculus has developed for more than 300 years. Fractional calculus theory has been widely applied in electrical engineering (Sikora and Pawlowski, 2018), physics and control theory (Kumar and Baleanu, 2019; Li et al, 2017b; Zhang and Zhang, 2020), viscoelastic dynamics, and other fields (Alotta et al, 2018; Bazhlekova and Bazhlekov, 2014); Ma et al (2019); (Tarasov and Tarasova, 2018). The dynamic characteristics of generators, metal materials, and Newtonian fluid all possess fractional-order characteristics along with memory features on a large time scale.…”

Section: Introductionmentioning

confidence: 99%

Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

Chen

Wang

Tian

et al. 2021

Journal of Vibration and Control

View full text Add to dashboard Cite

This article mainly studies the Mittag–Leffler stability and finite-time control of a time-delay fractional-order hydraulic turbine governing system. First, properties of the Riemann–Liouville derivative and some important lemmas are introduced. Second, considering the mechanical time delay of the main servomotor, the mathematical model of a fractional-order hydraulic turbine governing system with mechanical time delay is presented. Then, based on Mittag–Leffler stability theorem, a suitable sliding surface and finite-time controller are designed for the hydraulic turbine governing system. The system stability is confirmed, and the stability condition is given in the form of linear matrix inequalities. Finally, the traditional proportional–integral–derivative control method and an existing sliding mode control method are selected to verify the effectiveness and robustness of the proposed method. This study also provides a new approach for the stability analysis of the time-delay fractional-order hydraulic turbine governing system.

show abstract

Fractional derivatives and the laws of electrical engineering

Cited by 16 publications

References 12 publications

Can science exist without free discussion?

Can science exist without free discussion?

Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative

Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

Contact Info

Product

Resources

About