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Tytuł:
Obserwatory dodatnich liniowych układów dyskretnych ułamkowego rzędu
Observers for positive linear discrete-time fractional order systemss
Autorzy:
Kociszewski, R.
Powiązania:
https://bibliotekanauki.pl/articles/275535.pdf
Data publikacji:
2010
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
układy ułamkowego rzędu
fractional order systems
Opis:
W pracy rozpatrzono problem syntezy obserwatorów dodatnich liniowych układów dyskretnych ułamkowego rzędu. Wykorzystując podejście oparte na liniowych nierównościach macierzowych (LMI) sformułowano warunki istnienia dodatniego asymptotycznie stabilnego obserwatora. Podano warunki konieczne i wystarczające obserwowalności dodatnich dyskretnych układów ułamkowego rzędu. Rozważania zilustrowano przykładem symulacyjnym.
The paper is devoted to observer synthesis for linear positive fractional discrete-time systems. The problem of finding a nonnegative gain matrix of the observer such that the observer is positive and asymptotically stable is formulated and solved by the use of LMI method. Necessary and sufficient conditions for the observability for linear positive fractional discrete-time systems are formulated and proved. The proposed approach to computation the nonnegative gain matrix is illustrated by numerical example.
Źródło:
Pomiary Automatyka Robotyka; 2010, 14, 2; 492-500
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
Finite length triple estimation algorithm and its application to gyroscope mems noise identification
Autorzy:
Macias, Michał
Sierociuk, Dominik
Powiązania:
https://bibliotekanauki.pl/articles/2204616.pdf
Data publikacji:
2023
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional calculus
fractional Kalman filter
estimation of fractional order systems
fractional order noise
Opis:
The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from , and gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.
Źródło:
Acta Mechanica et Automatica; 2023, 17, 2; 219--229
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order, state space model of the temperature field in the pcb plate
Autorzy:
Oprzędkiewicz, Krzysztof
Mitkowski, Wojciech
Rosół, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/2204627.pdf
Data publikacji:
2023
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional order systems
fractional order state equation
temperature field
heat transfer
thermal camera
Opis:
In the paper the fractional order, state space model of a temperature field in a two-dimensional metallic surface is addressed. The proposed model is the two dimensional generalization of the one dimensional, fractional order, state space of model of the heat transfer process. It uses fractional derivatives along time and length. The proposed model assures better accuracy with lower order than models using integer order derivatives. Elementary properties of the proposed model are analysed. Theoretical results are experimentally verifed using data from industrial thermal camera.
Źródło:
Acta Mechanica et Automatica; 2023, 17, 2; 180--187
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
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:
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:
An output sensitivity problem for a class of fractional order discrete-time linear systems
Autorzy:
Benfatah, Youssef
El-Bhih, Amine
Rachik, Mostafa
Lafif, Marouane
Powiązania:
https://bibliotekanauki.pl/articles/2106242.pdf
Data publikacji:
2021
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional order systems
output sensitivity
discrete time systems
maximal output set admissible uncertainty
Opis:
Consider the linear discrete-time fractional order systems with uncertainty on the initial state {Δαxi+1=Axi+Bui, i≥0x0=τ0+τ̂0∈Rn, τ̂0∈Ωyi=Cxi, i≥0}, where A,B and C are appropriate matrices, x0 is the initial state, yi is the signal output, α the order of the derivative, τ0 and τ̂0 are the known and unknown part of x0, respectively, ui=Kxi is feedback control and Ω⊂Rn is a polytope convex of vertices w1,w2,...,wp. According to the Krein–Milman theorem, we suppose that τ̂0=Σ pj=1αjwj for some unknown coefficients α1≥0,...,αp≥0 such that Σ pj=1αj=1. In this paper, the fractional derivative is defined in the Grünwald–Letnikov sense. We investigate the charac-terisation of the set χ(τ̂0,ϵ) of all possible gain matrix K that makes the system insensitive to the unknown part τ̂0, which means χ(τ̂0,ϵ)={K∈Rm×n / ∥∂yi∂αj∥≤ϵ, ∀j=1,...,p,∀i≥0}, where the inequality ∥∂yi∂αj∥≤ϵ showing the sensitivity of yi relative-ly to uncertainties {αj}j=1p will not achieve the specified threshold ϵ>0. We establish, under certain hypothesis, the finite determination of χ(τ̂0,ϵ) and we propose an algorithmic approach to made explicit characterisation of such set.
Źródło:
Acta Mechanica et Automatica; 2021, 15, 4; 227--235
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
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:
Contribution of New Parameter Inverses to Robustification of Fractional-Order Perfect Control for LTI MIMO Discrete-Time State-Space Systems
Autorzy:
Wach, Ł.
Hunek, W. P.
Powiązania:
https://bibliotekanauki.pl/articles/385005.pdf
Data publikacji:
2016
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
LTI MIMO fractional-order systems
perfect control
inverses of nonsquare matrices
stability
Opis:
The paper presents results of application of various right inverses to fractional-order discrete-time perfect control in terms of improving its stability and robustness. For that reason the newly introduced σ-inverse and H-inverse are applied finally to obtain the mentioned above control strategy strictly dedicated to LTI MIMO nonsquare systems described by state-space framework. It is highlighted that parameter σ-inverse and H-inverse with different so called ‘degrees of freedom’ outperform the typical minimum-norm right T-inverse. Moreover, this new approach deals with the same class of problems concerning integer-order systems. The simulation studies performed in Matlab/Simulink environment confirm high potential of proposed here method.
Źródło:
Journal of Automation Mobile Robotics and Intelligent Systems; 2016, 10, 3; 29-33
1897-8649
2080-2145
Pojawia się w:
Journal of Automation Mobile Robotics and Intelligent Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Odporna stabilność rodziny wielomianów niecałkowitego stopnia o współczynnikach wieloliniowo zależnych od niepewnych parametrów
Robust stability of familly of fractional degree polynomials with coeficients multilinary dependent on uncertain parameters
Autorzy:
Kalinowski, T.
Busłowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/277397.pdf
Data publikacji:
2011
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
liniowe układy niecałkowitego rzędu
odporna stabilność
linear fractional order systems
robust stability
Opis:
W pracy rozpatrzono problem odpornej stabilności rodzin wielomianów charakterystycznych niecałkowitego stopnia, których współczynniki zależą wieloliniowo od niepewnych parametrów. Podano komputerowe metody badania odpornej stabilności. Proponowane metody bazują na warunku wykluczenia zera i na twierdzeniu o odwzorowaniu, znanych z teorii odpornej stabilności rodzin wielomianów całkowitych stopni. Rozważania zilustrowano przykładem.
The paper considers the problem of robust stability of families of fractional degree characteristic polynomials with coefficients multilinearly dependent on uncertain parameters. Computer methods for checking of robust stability are given. The methods proposed are based on the Zero Exclusion Condition and on the Mapping Theorem known from the theory of robust stability of families of natural degree polynomials. The considerations are illustrated by example.
Źródło:
Pomiary Automatyka Robotyka; 2011, 15, 2; 576-585
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Review, design, stabilization and synchronization of fractional-order energy resources demand-supply hyperchaotic systems using fractional-order PD-based feedback control scheme
Autorzy:
Soukkou, Ammar
Soukkou, Yassine
Haddad, Sofiane
Benghanem, Mohamed
Rabhi, Abdelhamid
Powiązania:
https://bibliotekanauki.pl/articles/27322620.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional-order systems
fractional-order control
Lyapunov stability theory
multiobjective optimization
artificial hummingbird algorithm
stabilization
synchronization
energy resources demand-dupply systems
Opis:
This paper introduces a fractional-order PD approach (F-oPD) designed to control a large class of dynamical systems known as fractional-order chaotic systems (F-oCSs). The design process involves formulating an optimization problem to determine the parameters of the developed controller while satisfying the desired performance criteria. The stability of the control loop is initially assessed using the Lyapunov’s direct method and the latest stability assumptions for fractional-order systems. Additionally, an optimization algorithm inspired by the flight skills and foraging behavior of hummingbirds, known as the Artificial Hummingbird Algorithm (AHA), is employed as a tool for optimization. To evaluate the effectiveness of the proposed design approach, the fractional-order energy resources demand-supply (Fo-ERDS) hyperchaotic system is utilized as an illustrative example.
Źródło:
Archives of Control Sciences; 2023, 33, 3; 539--563
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Microcontroller Implementation of the Basic Fractional-Order Element
Implementacja podstawowego elementu ułamkowego na mikrokontrolerze
Autorzy:
Oprzędkiewicz, Krzysztof
Rosół, Maciej
Żegleń-Włodarczyk, Jakub
Powiązania:
https://bibliotekanauki.pl/articles/2068657.pdf
Data publikacji:
2020
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
fractional-order systems
microcontroller
STM32
FOBD
CFE approximation
układy ułamkowe
mikrokontroler
aproksymacja CFE
Opis:
The paper presents the implementation of the basic fractional order element sγ, γ ∈ R on the STM32 microcontroller platform. The implementation employs the typical CFE and FOBD approximations, the accuracy of approximation as well as duration of calculations are experimentally tested. Microcontroller implementation of fractional order elements is known; however, real-time tests of such implementations have been not presented yet. Results of experiments show that both methods can be implemented at the considered platform. The FOBD approximation is more accurate, but the CFE one is faster. The presented experimental results prove that the STM32F7 family processor could be used to develop the embedded fractional-order control systems for a broad class of linear and nonlinear dynamic systems. This is crucial during the implementation of the fractional-order control in the hard real-time or embedded systems.
W pracy przedstawiono implementację podstawowego układu ułamkowego rzędu sγ, γ ∈ R na platformie mikrokontrolera STM32. Implementacja wykorzystuje typowe aproksymacje CFE oraz FOBD. Dokładność aproksymacji oraz czas trwania obliczeń testowane są eksperymentalnie. Implementacja układów ułamkowych na mikrokontroler jest znana, jednak ich testy w czasie rzeczywistym nie były jak dotąd omawiane w literaturze. Wyniki wskazują, że obie metody można wdrożyć na rozważanej platformie. Aproksymacja FOBD jest dokładniejsza, z kolei CFE jest szybsza. Przedstawione rezultaty eksperymentów dowodzą, że procesor z rodziny STM32F7 może zostać wykorzystany do opracowania wbudowanych ułamkowych układów sterowania dla szerokiej klasy liniowych i nieliniowych układów dynamicznych. Zaprezentowane wyniki są istotne z punktu widzenia implementacji algorytmów ułamkowych w twardych systemach czasu rzeczywistego lub w systemach wbudowanych.
Źródło:
Pomiary Automatyka Robotyka; 2020, 24, 4; 19--26
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
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:
Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems
Autorzy:
Basdouri, Imed
Kasmi, Souad
Lerbet, Jean
Powiązania:
https://bibliotekanauki.pl/articles/27312007.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
fractional-order systems
Caputo derivative
quasi-one-sided Lipschitz condition
nonlinear systems
observer design
output feedback stabilization
separation principle
Opis:
This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 55--70
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of unknown input fractional-order observers for fractional-order systems
Autorzy:
N’Doye, I.
Darouach, M.
Voos, H.
Zasadzinski, M.
Powiązania:
https://bibliotekanauki.pl/articles/330946.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional calculus
fractional order systems
fractional order observers
existence condition
linear matrix inequality
unknown input
stability
ułamkowy rachunek różniczkowy
układ ułamkowego rzędu
liniowa nierówność macierzowa
Opis:
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 3; 491-500
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Autorzy:
Beata, Sikora
Powiązania:
https://bibliotekanauki.pl/articles/27311455.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
descriptor systems
fractional-order systems
Caputo derivative
Drazin inverse
controllability
pochodna Caputo
odwrotność Drazina
sterowalność
system deskryptorowy
system ułamkowego rzędu
Opis:
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical 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:
Fractional Kalman Filter algorithms for correlated system and measurement noises
Autorzy:
Sierociuk, D.
Powiązania:
https://bibliotekanauki.pl/articles/206137.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional order calculus
discrete fractional state-space systems
fractional Kalman filter
Opis:
The paper presents a generalization of the Fractional Kalman Filter to a case when correlated system and measurement noises appear. The algorithm proposed is derived in detail for a linear generalized discrete fractional order state-space system for both constant and variable order cases. In order to present the efficiency of the proposed algorithm, results of numerical simulations are presented. Results of numerical experiments are compared with the effect of estimation obtained when using the traditional Fractional Kalman Filter algorithm.
Źródło:
Control and Cybernetics; 2013, 42, 2; 471-490
0324-8569
Pojawia się w:
Control and Cybernetics
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:
Monotone method for Riemann-Liouville multi-order fractional differential systems
Autorzy:
Denton, Z.
Powiązania:
https://bibliotekanauki.pl/articles/254754.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
multi-order systems
lower and upper solutions
monotone method
Opis:
In this paper we develop the monotone method for nonlinear multi-order N-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders qi where 0 < qi < 1. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
Źródło:
Opuscula Mathematica; 2016, 36, 2; 189-206
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-25 z 38

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