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Wyświetlanie 1-15 z 49
Tytuł:
Remarks on five equivalent forms of the fractional – order backward – difference
Autorzy:
Ostalczyk, P.
Powiązania:
https://bibliotekanauki.pl/articles/202441.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
discrete systems
fractional order backward difference
fractional - order backward sum
Opis:
In this paper a fractional-order backward-difference/sum (FOBD/S) equivalent formulae are considered. From the Gr¨unwald- Letnikov (GL - FOBD) definition formula and its Horner equivalent form one derives the Riemann-Liouville FOBD (RL - FOBD). Also the Caputo and polynomial-like forms are defined. All forms may be useful in real-time calculations (in the evaluation of digital control strategies) due to the reduction of fractional orders. The investigations are illustrated by a numerical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 2; 271-278
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator
Autorzy:
Oprzędkiewicz, K.
Dziedzic, K.
Więckowski, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/200257.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non integer order systems
heat transfer
fractional order state equation
fractional order backward difference
Grünwald-Letnikov operator
convergence
Opis:
The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 5; 905-914
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:
Robustness of adaptive discrete-time LQG control for first-order systems
Autorzy:
Królikowski, A.
Horla, D.
Powiązania:
https://bibliotekanauki.pl/articles/199940.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
first order system
adaptive LQG control
robustness
Opis:
The discrete-time adaptive LQG control of first-order systems is considered from robustness point of view. Both stability and performance robustness are analyzed for different control system structures. A case of amplitude-constrained control is presented, and application of certainty equivalence for self-tuning implementation is also discussed.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2010, 58, 1; 89-97
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive linear systems with different fractional orders
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/200652.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
positive
fractional order
linear
solution electrical circuit
Opis:
A new class of positive linear systems with different fractional orders is introduced. A solution to the set of linear differential equations with different fractional orders is derived Necessary and sufficient conditions for the positivity of the fractional systems are established. It is shown that the linear electrical circuits composed of resistors, supercondensators, coils and voltage (current) sources are positive systems with different fractional orders.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2010, 58, 3; 453-458
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global stability of positive standard and fractional nonlinear feedback systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/200986.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
global stability
fractional order
positive
nonlinear system
Opis:
The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 2; 285-288
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimized fractional low and highpass filters of (1 + α) order on FPAA
Autorzy:
Singh, N.
Mehta, U.
Kothari, K.
Cirrincione, M.
Powiązania:
https://bibliotekanauki.pl/articles/200342.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional-order filter
FPAA
realization
robustness
bilevel optimization
Opis:
This work proposes an optimum design and implementation of fractional-order Butterworth filter of order (1 + α), with the help of analog reconfigurable field-programmable analog array (FPAA). The designed filter coefficients are obtained after dual constraint optimization to balance the tradeoffs between magnitude error and stability margin together. The resulting filter ensures better robustness with less sensitivity to parameter variation and minimum least square error (LSE) in magnitude responses, passband and stopband errors as well as a better –3 dB normalized frequency approximation at 1 rad/s and a stability margin. Finally, experimental results have shown both lowpass and highpass fractional step values. The FPAA-configured outputs represent the possibility to implement the real-time fractional filter behavior with close approximation to the theoretical design.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 3; 635-644
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional-order models of the supercapacitors in the form of RC ladder networks
Autorzy:
Mitkowski, W.
Skruch, P.
Powiązania:
https://bibliotekanauki.pl/articles/202034.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional-order model
electrical ladder network
supercapacitor
identification
Opis:
In the paper, mathematical models of the supercapacitors are investigated. The models are based on electrical circuits in the form of RC ladder networks. The elementary cell of the network may consist of resistances and capacitances that are connected in series or parallel. The dynamic behavior of the circuit is described using fractional-order differential equations and its properties are analyzed. The identification procedure with quadratic performance index is performed in time domain to identify the parameters of the supercapacitor models. The results of numerical simulations are compared with the results measured experimentally in the physical system. In addition, an example from the automotive industry is used for an experimental evaluation of the theoretical analysis and to present a perspective on the applicability of the approach for other industrial projects.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 3; 581-587
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation
Autorzy:
Oprzędkiewicz, K.
Stanisławski, R.
Gawin, E.
Mitkowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/199796.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order calculus
discrete-time noninteger-order state equation
continuous fraction expansion
Al-Alaoui operator
równanie dyskretne
aproksymacja Al-Alaoui
CFE
Opis:
In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the operator expressed by a discrete transfer function, e.g. CFE-based Al-Alaoui approximation. A simulation example confirms the usefulness of the method.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 4; 429-437
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variable order 3D models of bone remodelling
Autorzy:
Valério, D.
Neto, J.
Vinga, S.
Powiązania:
https://bibliotekanauki.pl/articles/202197.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
variable-order derivative
bone remodelling
cancer
przebudowa kości
rak
Opis:
This paper presents simulations of a three-dimensional model of the bone remodelling process. The model consists of a set of variable order partial differential equations, in which the varying order depends on the presence of tumour cells. The simulations are of a two-dimensional bone, to make visualisation simpler. They show that this model corresponds to the known evolution of bone remodelling, and is simpler than integer order models found in the literature.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 3; 501-508
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonadaptive estimation of the rotor speed in an adaptive full order observer of induction machine
Autorzy:
Morawiec, M.
Kroplewski, P.
Powiązania:
https://bibliotekanauki.pl/articles/202062.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
observers
induction machines
speed estimation
adaptive full order observer
Opis:
The article proposes a new method of reproducing the angular speed of the rotor of a cage induction machine designed for speed observers based on the adaptive method. In the proposed solution, the value of the angular speed of the rotor is not determined by the classical law of adaptation using the integrator only by an algebraic relationship. Theoretical considerations were confirmed by simulation and experimental tests.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 5; 973--981
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non integer order, state space model of heat transfer process using Atangana-Baleanu operator
Autorzy:
Oprzędkiewicz, K.
Powiązania:
https://bibliotekanauki.pl/articles/202078.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non integer order systems
heat transfer equation
infinite dimensional systems
fractional order state equation
Riesz operator
Caputo operator
Atangana-Baleanu operator
Opis:
In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 1; 43-50
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
Autorzy:
Oprzędkiewicz, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/2173561.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
heat transfer equation
fractional order state equation
fractional order backward difference
Grünwald-Letnikov operator
practical stability
systemy ułamkowego rzędu
równanie wymiany ciepła
równanie stanu rzędu ułamkowego
różnica wsteczna rzędu ułamkowego
operator Grünwalda-Letnikowa
stabilność praktyczna
Opis:
In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; art. no. e135843
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
Autorzy:
Oprzędkiewicz, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/2090693.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
heat transfer equation
fractional order state equation
fractional order backward difference
Grünwald-Letnikov operator
practical stability
systemy ułamkowego rzędu
równanie wymiany ciepła
równanie stanu rzędu ułamkowego
różnica wsteczna rzędu ułamkowego
operator Grünwalda-Letnikowa
stabilność praktyczna
Opis:
In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; e135843, 1--10
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Descriptor fractional discrete-time linear system with two different fractional orders and its solution
Autorzy:
Sajewski, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/201410.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional
different order
descriptor
solution
układ nieliniowy
deskryptor
rozwiązanie
systemy liniowe
Opis:
Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 1; 15-20
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 49

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