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Wyświetlanie 1-15 z 19
Tytuł:
Equivalent diagrams of fractional order elements
Autorzy:
Różowicz, Sebastian
Włodarczyk, Maciej
Zawadzki, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/27324011.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional order derivative
Laplace transform for fractional order systems
CFE method
circuit synthesis
numerical experiments
Opis:
This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: sαL,sub>α and 1/sαCsub>α, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy – the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.
Źródło:
Archives of Control Sciences; 2023, 33, 4; 801--827
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems
Autorzy:
Balochian, S.
Powiązania:
https://bibliotekanauki.pl/articles/200478.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear time invariant fractional order derivative
switching systems
linear matrix inequality
LMI
Opis:
In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 495-503
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders
Autorzy:
Zhang, X.
Liang, S.
Shao, S.
Yu, J.
Powiązania:
https://bibliotekanauki.pl/articles/38615994.pdf
Data publikacji:
2021
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
guided wave
fractional order derivative
anisotropic viscoelastic hollow cylinder
quadrature-free Legendre polynomial approach
dispersion
attenuation
Opis:
Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.
Źródło:
Archives of Mechanics; 2021, 73, 2; 121-152
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order impulsive partial hyperbolic differential inclusions with variable times
Autorzy:
Abbas, Saïd
Benchohra, Mouffak
Górniewicz, Lech
Powiązania:
https://bibliotekanauki.pl/articles/729238.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive functional differential inclusions
fractional order
solution
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
variable times
fixed point
Opis:
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 91-114
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay
Autorzy:
Benchohra, Mouffak
Boutefal, Zohra
Powiązania:
https://bibliotekanauki.pl/articles/746465.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
impulsive partial hyperbolic differential equations,
fractional order, solution
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
finite delay
fixed point
Opis:
This paper deals with the existence of solutions to impulsive partial hyperbolic differential equations with finite delay, involving the Caputo fractional derivative. Our results will be obtained using Krasnoselskii fixed point theorem.
Źródło:
Commentationes Mathematicae; 2014, 54, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses
Autorzy:
Abbas, Saïd
Benchohra, Mouffak
Powiązania:
https://bibliotekanauki.pl/articles/729279.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive hyperbolic differential inclusion
fractional order
upper solution
lower solution
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
fixed point
Opis:
In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 141-161
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modelowanie procesów ładowania i rozładowania superkondensatora
Modelling of supercapacitor charging and discharging processes
Autorzy:
Zawadzki, A.
Włodarczyk, M.
Powiązania:
https://bibliotekanauki.pl/articles/153328.pdf
Data publikacji:
2010
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
stan nieustalony w obwodach elektrycznych
superkondensator
pochodna ułamkowego rzędu
transient state in electrical circuit
double-layer capacitor (supercapacitor)
fractional order derivative
Opis:
W artykule przedstawiono zastosowanie rachunku różniczkowego ułamkowego rzędu do analizy stanu nieustalonego: ładowania i rozładowania superkondensatora w układzie RC. Obiektem badań był superkondensator wykorzystywany w elektronice, trakcji i różnych gałęziach przemysłu jako dodatkowe źródło o dużej pojemności pełniące funkcję zaawansowanego magazynu energii. Pokazano wyniki badań eksperymentalnych i symulacyjnych. Badania eksperymentalne przeprowadzono w różnych temperaturach pracy w celu analizy wpływu środowiska na parametry superkondensatorów. W badaniach symulacyjnych wykonano obliczenia dla klasycznego układu RC oraz dokonano wyboru rzędu pochodnej ułamkowej, dla której otrzymuje się najlepsze przybliżenia w stosunku do danych pomiarowych.
In the paper there is presented use of differential calculus of fractional grade for analysis of transient state of charging and discharging supercapacitor in the RC system. The research object was a supercapacitor used in electronic, traction and other industry branches as an additional source of large capacity functioning as the energy store. The results of experimental and simulation research are given. In order to analyse the environmental influence on supercapacitor parameters, experimental investigations were carried out in different work temperatures for analysis. In simulation research there were carried out calculations for the classic RC system and there was determined the order of fractional derivative which gives the best closeness to the measurement data. In the figures placed in the paper the simulation and experiments results are shown. From the performed investigations it follows that the classical theory gives better approximation of charging and uncharging current, altough for time instants, where the current changes more slowly, fractional derivatives give better approximations.
Źródło:
Pomiary Automatyka Kontrola; 2010, R. 56, nr 12, 12; 1413-1415
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses
Autorzy:
Abbas, Saïd
Benchohra, Mouffak
Abdalla Darwish, Mohamed
Powiązania:
https://bibliotekanauki.pl/articles/729578.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
fractional differential inclusion
left-sided mixed Riemann-Liouville integral
Caputo fractional order derivative
upper solution
lower solution
extremal solution
fixed point
Banach algebras
not instantaneous impulses
Opis:
In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 155-179
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some new existence results and stability concepts for fractional partial random differential equations
Autorzy:
Abbas, S.
Benchohra, M.
Darwish, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/357770.pdf
Data publikacji:
2016
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
random differential equations
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
Banach space
Darboux problem
Ulam stability
równanie różniczkowe
pochodna Caputo
przestrzeń Banacha
problem Darbouxa
Opis:
In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.
Źródło:
Journal of Mathematics and Applications; 2016, 39; 5-22
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The wave transformer – analysis and application of time digital filters and the integral-derivative operators of ½ order
Autorzy:
Siwczyński, M.
Drwal, A.
Żaba, S.
Powiązania:
https://bibliotekanauki.pl/articles/141515.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
wave transformer
integral-derivative operators of fractional order
convolution operators
time domain
digital filters
Opis:
In this paper the way of modeling phenomena occurring during the voltage and current waves passing through a point connection of two lines, with different wave impedance operators, is presented. This connection point is called „the wave transformer”. The analyzes and the resulting formulas concern not the frequency domain, but the time domain. The appropriate transition matrices of waves through the wave transformer are defined. This matrices are the convolution integral-derivative operators of fractional order (the digital filters). For a lossless line the wave transition matrices through the wave transformer become number type instead of operator type. All matrix multiplications occurring in the formulas should be understood in convolution way.
Źródło:
Archives of Electrical Engineering; 2013, 62, 3; 497-504
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo
Autorzy:
Piotrowska, E.
Powiązania:
https://bibliotekanauki.pl/articles/141097.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
conformable fractional derivative
fractional electrical circuit
different fractional order system
Opis:
The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
Źródło:
Archives of Electrical Engineering; 2018, 67, 3; 629--639
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions
Autorzy:
Piotrowska, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/378130.pdf
Data publikacji:
2019
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
fractional order system
Sinusoidal Signals
Caputo definition
conformable fractional derivative definition
fractional electrical circuit
Opis:
This paper presents the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo definition and the conformable fractional derivative definition are given the solutions in the case of: 1) control in the form of sine function at zero initial states 2) control in the form of cosine function at zero initial states 3) control in the form of the sine function with phase shift at zero initial states. The solutions are shown for capacitor voltages for fractional derivative orders of 0.7; 0.8; 1.0. The results were compared using graphs.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2019, 97; 155-167
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Problems with modeling of fractional electrical circuits containing supercapacitors
Autorzy:
Piotrowska, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/378115.pdf
Data publikacji:
2020
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
fractional order system
electrical circuits containing supercapacitors
Caputo definition
Conformable Fractional Derivative definition
Opis:
For proper operation, diagnostics or control, it is required to know the parameters of the supercapacitor replacement model (relationship between current and voltage at the terminals). The paper describe the bahavior of the eletrical circuit (RC) containing the supercapacitor were used the fractional derivatives of Caputo definiton and Conformable Fractional Derivative definition. Verification of the correctness of the suggested electrical circuit models was carried out a series of measurements of the system response to the given control signal. The measurement data were compared by fractionalorder derivatives: classical case, Caputo definition and CFD definition. Conducting a series of experiments with charging a supercapacitor in an RC circuit, constant control voltage from 2 V to 5 V with an exchanged external resistor, it was shown that none of the three mathematical models reflects the real behavior of the supercapacitor. It has been shown that the behavior of supercapacitor requires the use of different mathematical than fractional derivatives.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2020, 104; 65-74
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On LQ optimization problem subject to fractional order irregular singular systems
Autorzy:
Muhafzan, -
Nazra, Admi
Yulianti, Lyra
Zulakmal, -
Revina, Refi
Powiązania:
https://bibliotekanauki.pl/articles/1409212.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear quadratic optimization
fractional order
irregular singular system
Caputo fractional derivative
Mittag-Leffler function
Opis:
In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.
Źródło:
Archives of Control Sciences; 2020, 30, 4; 745-756
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Influence of Grünwald-Letnikow time and space temperature derivative on heat distribution
Wpływ zastosowania definicji pochodnej temperatury Grünwalda-Letnikova w czasie i w przestrzeni na rozkład ciepła
Autorzy:
Raszkowski, Tomasz
Raszkowska, Agnieszka
Zubert, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/1837637.pdf
Data publikacji:
2021-08-12
Wydawca:
Łódzkie Towarzystwo Naukowe
Tematy:
Dual-Phase-Lag model
Grünwald-Letnikov derivative
heat transfer approximation
Fourier-Kirchhoff modification
fractional order time derivative
model Dual-Phase-Lag
pochodna temperatury Grünvalda-Letnikova
aproksymacja rozkładu ciepła
modyfikacja modelu Fouriera-Kirchhoffa
niecałkowity rząd pochodnej temperatury w czasie i przestrzeni
Opis:
In this paper the new thermal model called Dual-Phase-Lag model has been investigated. This method is reasonable for nanometric structures which are more and more popular nowadays. However, during its numerical implementation, some problems can occur. Moreover, the simulation process can take a long period of time. Thus, it is needed to find some approximation scheme of the Dual-Phase-Lag model, which provides highly accurate results and simultaneously reduces time of simulation. Due to these reasons, investigation presented in this paper focuses on the determination of the approximation of the Dual-Phase-Lag model based on the Grünwald-Letnikov derivative definition. Moreover, this approximation takes into consideration the time and space derivative at the same time
W pracy wykorzystano nowy model termiczny o nazwie Dual-Phase-Lag. Model ten jest odpowiedni dla struktur nanometrycznych, które obecnie są coraz bardziej. Jednakże, podczas numerycznej impementacji tego modelu mogą pojawić się pewne problemy numeryczne, zaś czas symulacji może być znacznie wydłużony w stosunku do zastosowania klasycznego modelu przepływu ciep la Fouriera-Kirchhoffa. Z tego powodu, rozważania przedstawione w pracy dotyczą wyznaczenia schematu aproksymacyjnego modelu Dual-Phase-Lag opartego na zastosowaniu definicji pochodnej temperatury Grünvalda-Letnikowa, jednocześnie w czasie i w przestrzeni
Źródło:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2020, 70, 1; 97-113
1895-7838
2450-9329
Pojawia się w:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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