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Wyświetlanie 1-15 z 19
Tytuł:
Fractional order model of measured quantity errors
Autorzy:
Cioć, R.
Chrzan, M.
Powiązania:
https://bibliotekanauki.pl/articles/200953.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
data processing
measured quantities errors
jitter
Opis:
The paper presents an interpretation of fractional calculus for positive and negative orders of functions based on sampled measured quantities and their errors connected with digital signal processing. The derivatives as a function limit and the Grunwald-Letnikov differintegral are shown in chapter 1 due to the similarity of the presented definition. Notation of fractional calculus based on the gradient vector of measured quantities and its geometrical and physical interpretation of positive and negative orders are shown in chapter 2 and 3.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 6; 1023-1030
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional calculus for continuum mechanics – anisotropic non-locality
Autorzy:
Sumelka, W.
Powiązania:
https://bibliotekanauki.pl/articles/201244.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non-local kinematics
fractional calculus
anisotropy
kinematyka
rachunek ułamkowy
anizotropia
Opis:
In this paper, a generalisation of previous author’s formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 361-372
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Economic growth in the European Union modelled with fractional derivatives: first results
Autorzy:
Tejado, I.
Pérez, E.
Valério, D.
Powiązania:
https://bibliotekanauki.pl/articles/201418.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
economic growth
Europe
fractional calculus
wzrost gospodarczy
Europa
rachunek różniczkowy
Opis:
This paper presents models of economic growth for all states of the European Union (EU), since either 1970 or the year of accession to the EU. Both integer and fractional order models are obtained, where the gross domestic product (GDP) is a function of the country’s land area, gross capital formation (GCF), exports of goods and services, and average years of school attendance.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 455-465
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional discrete model of an electrical drive with brushless micro-motor
Autorzy:
Matusiak, M.
Bąkała, M.
Wojciechowski, R.
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/200454.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
system modeling
system identification
fractional order calculus
Opis:
The use of fractional-order calculus for system modeling is a good alternative to well-known classic integer-order methods, primarily due to the precision with which the modeled object may be mapped. In this study, we created integer and fractional discrete models of a real object – a highspeed brushless micro-motor. The accuracy of the models was verified and compared.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 3; 421-427
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Duality of variable fractional order difference operators and its application in identification
Autorzy:
Sierociuk, D.
Twardy, M.
Powiązania:
https://bibliotekanauki.pl/articles/201717.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
variable order fractional calculus
duality
identification
rachunek z ułamkową zmienną
dualizm
identyfikacja
Opis:
The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 809-815
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description
Autorzy:
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/200397.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
discrete-time system response
ułamkowy rachunek różniczkowy
czas reakcji
system dyskretny
Opis:
In this paper three simplified forms of the fractional-order (FO) backward difference (BD) are proposed and analysed. Due to time and frequency characteristics criteria parameters of simplified forms of the FOBDs are chosen. Applications of the simplified forms of the FOBDs diminish a number of multiplications and additions needed to evaluate the FOBD. This is very important in real-time microprocessor calculations. It is proved that in a discrete state-space description of a fractional-order system one should correct the input matrix with simplified forms of the FOBD. Investigations are supported by two numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 2; 457-464
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability conditions for fractional-order linear equations with delays
Autorzy:
Mozyrska, D.
Ostalczyk, P.
Wyrwas, M.
Powiązania:
https://bibliotekanauki.pl/articles/201130.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
discrete-time models with delays
stability
rachunek różniczkowy
model dyskretny
stabilność
Opis:
The problem of stability of the Gr¨unwald-Letnikov-type linear fractional-order discrete-time systems with delays is discussed. For the stability analysis of the considered systems the Z -transform is used. The sufficient conditions for the asymptotic stability of the considered systems are presented. Using conditions related to eigenvalues of the matrices defining the linear difference systems, one can determine the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems. Some of these regions are illustrated with relevant examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 449-454
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional variable order anti-windup control strategy
Autorzy:
Sierociuk, D.
Malesza, W.
Powiązania:
https://bibliotekanauki.pl/articles/200019.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
variable order
PID control
anti-windup
rachunek różniczkowy
sterowanie PID
przebieg zmienności
Opis:
In this paper, a novel anti-windup strategy is presented. It is based on using fractional variable order integrator instead of integer order one in PID controller. It is shown that among four different types of variable order derivative definitions, only one gives satisfactory results – comparable, and even slightly better than the classical back-calculation anti-windup algorithm. Results are also presented in the form of simulation plots.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 427-432
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Different fractional order models for an experimental smart beam system
Autorzy:
Markowski, K. A.
Birs, I.
Muresan, C. I.
Prodan, O.
Powiązania:
https://bibliotekanauki.pl/articles/200269.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
realization
fractional calculus
fractional order system identification
smart beam system
digraphs method
realizacja
rachunek różniczkowy
system ułamkowy
Opis:
The applicability of fractional calculus in system engineering outperforms classic identification techniques due to its ability to depict physical phenomena with increased accuracy. The present study explores the increased accuracy and flexibility of a fractional order model applied to an experimental smart beam depicting an airplane wing. The paper details the fractional order system identification of the beam and explores the possibility of realization of the model.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 485-493
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order based velocity control system for a nanorobot in non-Newtonian fluids
Autorzy:
Muresan, C. I.
Birs, I. R.
Folea, S.
Ionescu, C.
Powiązania:
https://bibliotekanauki.pl/articles/200089.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non-Newtonian fluids
drag force
velocity control
fractional calculus
płyny nienewtonowskie
kontrola prędkości
rachunek ułamkowy
Opis:
Customized patient drug delivery overcomes classic medicine setbacks such as side effects, improper drug absorption or slow action. Nanorobots can be successfully used for targeted patient-specific drug administration, but they must be reliable in the entire circulatory system environment. This paper analyzes the possibility of fractional order control applied to the nanomedicine field. The parameters of a fractional order proportional integral controller are determined with the purpose of controlling the velocity of the nanorobot in non-Newtonian fluids envisioning the blood flow in the circulatory system.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 6; 991-997
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional-order models: The case study of the supercapacitor capacitance measurement
Autorzy:
Lewandowski, M.
Orzyłowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/200370.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
supercapacitor model
capacitance measurement
IEC standard
rachunek różniczkowy
model superkondensatora
pomiar pojemności
norma IEC
Opis:
At the beginning of the paper, the fractional calculus is briefly presented. Then, the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model, a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as a basis for the analysis of their dynamics. An example of the fractional dynamic model application was used for the critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations, which probably result from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper indicate that the models of fractional-order dynamics may be useful not only for the control purposes but also in other domains.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 4; 449-457
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical solution of fractional variable order linear control system in state-space form
Autorzy:
Malesza, W.
Macias, M.
Powiązania:
https://bibliotekanauki.pl/articles/201996.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
variable order fractional calculus
differential equations
analog modeling
równania różniczkowe
modelowanie analogowe
rachunek różniczkowy ułamkowego rzędu
Opis:
The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 5; 715-724
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability and robustness analysis of discrete-time fractional-piecewise-constant-order PID controller
Autorzy:
Oziablo, Piotr
Mozyrska, Dorota
Wyrwas, Malgorzata
Powiązania:
https://bibliotekanauki.pl/articles/2086870.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
stability analysis
fractional calculus
control systems
digital control
analiza stabilności
rachunek ułamkowy
systemy kontrolne
sterowanie cyfrowe
Opis:
In the paper we propose a fractional-piecewise-constant-order PID controller and discuss the stability and robustness of a closed loop system. In stability analysis we use the transform method and include the Nyquist-like criteria. Simulations for designed controllers are performed for the second-order plant with a delay.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 5; e137937, 1--10
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matrix Mittag‑Leffler function in fractional systems and its computation
Autorzy:
Matychyn, I.
Onyshchenko, V.
Powiązania:
https://bibliotekanauki.pl/articles/200538.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
matrix Mittag‑Leffler function
Jordan canonical form
fractional calculus
fractional differential equation
równanie różniczkowe cząstkowe
funkcja Mittag-Lefflera
rozkład Jordana
Opis:
Matrix Mittag‑Leffler functions play a key role in numerous applications related to systems with fractional dynamics. That is why the methods for computing the matrix Mittag‑Leffler function are so important. The matrix Mittag‑Leffler function is a generalization of matrix exponential function. This implies that some of numerous existing methods for computing the matrix exponential can be adapted for matrix Mittag‑Leffler functions as well. Unfortunately, the technique of scaling and squaring, widely used in computing of the matrix exponential, cannot be applied to matrix Mittag‑Leffler functions, as the latter do not possess the semigroup property. Here we describe a method of computing the matrix Mittag‑Leffler function based on the Jordan canonical form representation. This method is implemented with Matlab code [1].
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 495-500
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A local truncation error estimation for a SubIval solver
Autorzy:
Sowa, M.
Powiązania:
https://bibliotekanauki.pl/articles/202058.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional calculus
numerical method
adaptive step size
local truncation error
circuit analysis
rachunek różniczkowy
metoda numeryczna
analiza obwodów
Opis:
The paper concerns an analysis for SubIval (the subinterval-based method for fractional derivative computations in initial value problems). A time step size adaptive solver is discussed, for which the formula of a local truncation error is derived. A general form for a system of linear equations is given for the considered class of problems (for which the analysis is performed in the paper). Two circuit examples are introduced to display the usefulness of the SubIval solver. For the examples that have been chosen it is possible to obtain referential solutions through completely different methods. The results obtained through the numerical solver are compared with evaluations of the referential solutions. The error estimation results obtained for the time steps of the SubIval solver are compared with the actual errors, being the differences between the numerical solutions and the referential solutions. The paper also contains a comparison of the accuracy of results obtained through the SubIval solver with the accuracies of other solvers.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 475-484
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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