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Wyświetlanie 1-15 z 16
Tytuł:
Approximation method for a fractional order transfer function with zero and pole
Autorzy:
Oprzędkiewicz, K.
Powiązania:
https://bibliotekanauki.pl/articles/229961.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
fractional order transfer function
Charef approximation
Opis:
The paper presents an approximation method for elementary fractional order transfer function containing both pole and zero. This class of transfer functions can be applied for example to build model - based special control algorithms. The proposed method bases on Charef approximation. The problem of cancelation pole by zero with useful conditions was considered, the accuracy discussion with the use of interval approach was done also. Results were depicted by examples.
Źródło:
Archives of Control Sciences; 2014, 24, 4; 447-463
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case
Autorzy:
Dzieliński, A.
Czyronis, P. M.
Powiązania:
https://bibliotekanauki.pl/articles/201358.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
discrete-time systems
optimal control
linear quadratic performance index
Opis:
The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 3; 681-690
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller
Autorzy:
Yaghoubi, Zahra
Talebi, Heidar Ali
Powiązania:
https://bibliotekanauki.pl/articles/230002.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear multi agent systems
cluster consensus
fractional-order systems
adaptive sliding mode controller
Opis:
In this paper cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics via adaptive sliding mode controller. First, cluster consensus for fractional-order nonlinear multi agent systems with general form is investigated. Then, cluster consensus for the fractional-order nonlinear multi agent systems with first-order and general form dynamics is investigated by using adaptive sliding mode controller. Sufficient conditions for achieving cluster consensus for general fractional-order nonlinear multi agent systems are proved based on algebraic graph theory, Lyapunov stability theorem and Mittag-Leffler function. Finally, simulation examples are presented for first-order and general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.
Źródło:
Archives of Control Sciences; 2019, 29, 4; 643-665
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of linear convex combination of linear discrete-time fractional systems
Autorzy:
Kaczorek, Tadeusz
Klamka, Jerzy
Dzieliński, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2173704.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
controllability
linear convex combination
system ułamkowego rzędu
sterowność
kombinacja wypukła liniowa
Opis:
In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 5; art. no. e143102
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Lepschy stability test and its application to fractional-order systems
Autorzy:
Casagrande, Daniele
Krajewski, Wiesław
Viaro, Umberto
Powiązania:
https://bibliotekanauki.pl/articles/1409108.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional-order systems
D-stability
recursive algorithms
complex polynomials
root locus
symmetries
control-theory didactics
Opis:
It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students.
Źródło:
Archives of Control Sciences; 2021, 31, 1; 145-163
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process
Autorzy:
Oprzędkiewicz, K.
Mitkowski, W.
Gawin, E.
Dziedzic, K.
Powiązania:
https://bibliotekanauki.pl/articles/200001.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order systems
Caputo operator
Caputo-Fabrizio operator
non singular kernel operator
heat transfer
simplex method
transfer ciepła
metoda simplex
system ułamkowy
pochodna Caputo
Opis:
In the paper two non-integer order, state space models of heat transfer process are compared. The first uses a known Caputo operator and the second – a new operator proposed by Caputo and Fabrizio in 2015. Both discussed models are modifications of a known, integer order, state space, semigroup model of heat transfer process. Parameters of both models were identified by means of optimization of MSE cost function with the use of simplex method, available in MATLAB. Both proposed models have been compared in the aspect of accuracy and convergence. Analytical and numerical results show that the Caputo-Fabrizio model is faster convergent and easier to implement than the Caputo model. However, its accuracy in the sense of MSE cost function is worse.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 501-507
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:
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:
Fractional descriptor observers for fractional descriptor continuous-time linear system
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/229221.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional descriptor linear systems
design
full-order
fractional
observer
Opis:
Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.
Źródło:
Archives of Control Sciences; 2014, 24, 1; 27-37
1230-2384
Pojawia się w:
Archives of Control 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:
Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201870.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional descriptor linear systems
design
reduced order
descriptor
fractional
observer
redukcja rzędu
projekt
deskryptor
obserwator
Opis:
Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 4; 889-895
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical 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 comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems
Autorzy:
Bingi, K.
Ibrahim, R.
Karsiti, M. N.
Hassan, S. M.
Harindran, V. R.
Powiązania:
https://bibliotekanauki.pl/articles/229519.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order controller
set-point weighting
2DOF PID
process control
unstable systems
Opis:
The proportional-integral-derivative (PID) controllers have experienced series of structural modifications and improvements. Example of such modifications are set-point weighting and fractional ordering. While the former is to achieve two-degree-of-freedom (2DOF) ability of set-point tracking and disturbance rejection, the latter is to ensure smooth control action. Therefore, this paper reviews various forms of PID controllers and provides a comparative analysis of 2DOF PID and 2DOF fractional order PID (FOPID) controllers. The paper also discusses the conversion of one PID form to another. For the comparative analysis of the various controllers, a class of unstable systems are considered. Simulation result shows that in most cases the conversion from one form to another does not significantly affect the performance of the system. It is also observed that the 2DOF controllers (2DOF PID and 2DOF FOPID) improved significantly the performance of the ordinary PID controllers.
Źródło:
Archives of Control Sciences; 2018, 28, 4; 635-682
1230-2384
Pojawia się w:
Archives of Control 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
Wyświetlanie 1-15 z 16

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