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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 rectangular input signal using Caputo and conformable derivative definitions
Autorzy:
Piotrowska, E.
Powiązania:
https://bibliotekanauki.pl/articles/140842.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order system
Caputo definition
conformable fractional definition
fractional electrical circuit
Opis:
An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF definitions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
Źródło:
Archives of Electrical Engineering; 2018, 67, 4; 789-802
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:
Fractional-order LTI system identification using integer order state-space model
Autorzy:
Jakowluk, Wiktor
Powiązania:
https://bibliotekanauki.pl/chapters/32083884.pdf
Data publikacji:
2021
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
fractional-order LTI system
approximating
numerical examples
Opis:
The optimal input signal design is a technique of generating an informative excitation signal to estimate the model parameters with maximum accuracy. In the paper, a novel optimal input formulation and a numerical scheme for fractional-order LTI system identification are presented. The Oustaloup recursive approximation (ORA) method is used to determine the fractional-order differentiation in an integer-order state-space form. Then, the proposed method is used to obtain an optimal input signal for fractional-order system parameter estimation from the interval 0.5 ≤ ≤ 2.0. The methodology presented in this paper has been verified using numerical examples, and the experiment results have been discussed.
Źródło:
Methods and tools in CAD – selected issues; 75-86
9788366391871
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local controllability of nonlinear discrete-time fractional order systems
Autorzy:
Mozyrska, D.
Pawłuszewicz, E.
Powiązania:
https://bibliotekanauki.pl/articles/201944.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional difference operator
fractional difference initial value problem
nonlinear fractional order system
linear approximation
controllability problem
Opis:
The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 1; 251-256
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Different fractional order models for an experimental smart beam system
Autorzy:
Markowski, K. A.
Birs, I.
Muresan, C. I.
Prodan, O.
Powiązania:
https://bibliotekanauki.pl/articles/200269.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
realization
fractional calculus
fractional order system identification
smart beam system
digraphs method
realizacja
rachunek różniczkowy
system ułamkowy
Opis:
The applicability of fractional calculus in system engineering outperforms classic identification techniques due to its ability to depict physical phenomena with increased accuracy. The present study explores the increased accuracy and flexibility of a fractional order model applied to an experimental smart beam depicting an airplane wing. The paper details the fractional order system identification of the beam and explores the possibility of realization of the model.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 485-493
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability
Autorzy:
Stanisławski, R.
Latawiec, K. J.
Powiązania:
https://bibliotekanauki.pl/articles/200600.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Grünwald-Letnikov fractional difference
discrete-time fractional order system
stability conditions
Cauchy’s argument principle
Opis:
This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I, new, general, necessary and sufficient stability conditions are introduced in a unified form for FD/FFD/NFFD-based systems. In Part II, an original, simple, analytical stability criterion is offered for FD-based systems, and the result is used to develop simple, efficient, numerical procedures for testing the asymptotic stability for FFD-based and, in particular, NFFD-based systems. Consequently, the so-called f-poles and f-zeros are introduced for FD-based system and their closed-loop stability implications are discussed.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 353-361
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional vector-order h-realisation of the impulse response function
Autorzy:
Pawłuszewicz, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/386299.pdf
Data publikacji:
2020
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
realisation
linear system
fractional vector-order system
Markov parameters
Opis:
The problem of realisation of linear control systems with the h−difference of Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type fractional vector-order operators is studied. The problem of existing minimal realisation is discussed.
Źródło:
Acta Mechanica et Automatica; 2020, 14, 2; 108-113
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional order tube model reference adaptive control for a class of fractional order linear systems
Autorzy:
Balaska, Hanane
Ladaci, Samir
Djouambi, Abdelbaki
Schulte, Horst
Bourouba, Bachir
Powiązania:
https://bibliotekanauki.pl/articles/330930.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional order system
linear system
model reference adaptive control
fractional adaptive control
performance tube
fractional order TMRAC
system ułamkowego rzędu
system liniowy
sterowanie adaptacyjne
Opis:
We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order linear systems. By considering an adaptive state feedback control configuration, the main idea is to replace the classical reference model with a single predetermined trajectory by a fractional order performance tube guidance model allowing a set of admissible trajectories. Besides, an optimization problem is formulated to compute an on-line correction control signal within specified bounds in order to update the system performance while minimizing a control cost criterion. The asymptotic stability of the closed loop fractional order control system is demonstrated using an extension of the Lyapunov direct method. The dynamical performance of the fractional order tube model reference adaptive control (FOTMRAC) is compared with the standard fractional order model reference adaptive control (FOMRAC) strategy, and the simulation results show the effectiveness of the proposed control method.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 501-515
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems
Autorzy:
Stanisławski, R.
Latawiec, K. J.
Powiązania:
https://bibliotekanauki.pl/articles/200325.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Grünwald-Letnikov fractional difference
discrete-time fractional order system
stability criterion
non-minimum phase system
closed loop stability
Opis:
This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I of the paper, new necessary and sufficient stability conditions have been given in a unified form for FD, FFD and NFFD-based systems. Part II offers a new, simple, ultimate stability criterion for FD-based systems. This gives rise to the introduction of new definitions of the so-called f-poles and f-zeros for FD-based systems, which are used in the closed-loop stability analysis for FD-based systems and, approximately, for FFD/NFFD-based ones.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 363-370
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Autorzy:
Grzymkowski, Łukasz
Trofimowicz, Damian
Stefański, Tomasz P.
Powiązania:
https://bibliotekanauki.pl/articles/1838161.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stability analysis
discrete time system
fractional order system
analiza stabilności
układ czasu dyskretnego
układ rzędu ułamkowego
Opis:
In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 649-658
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques
Autorzy:
Kumar, Sanjay
Singh, Chaman
Prasad, Sada Nand
Shekhar, Chandra
Aggarwal, Rajiv
Powiązania:
https://bibliotekanauki.pl/articles/229902.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional-order chaotic system
chaos synchronization
Rabinovich-Fabrikant system
Lyapunov exponents
Opis:
In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.
Źródło:
Archives of Control Sciences; 2019, 29, 2; 307-322
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Full-order observers for linear fractional multi-order difference systems
Autorzy:
Wyrwas, M.
Powiązania:
https://bibliotekanauki.pl/articles/199928.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
difference operators
fractional order difference system
observer
operator różniczkowy
obserwator
system różniczkowy
Opis:
The paper is devoted to the construction of observers for linear fractional multi–order difference systems with Riemann–Liouville– and Grünwald–Letnikov–type operators. Basing on the Z-transform method the sufficient condition for the existence of the presented observers is established. The behaviour of the constructed observer is demonstrated in numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 6; 891-989
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Realizacje dodatnie dyskretnych liniowych układów niecałkowitego rzędu w oparciu o odpowiedź impulsową
Positive realisation of linear discrete-time fractional-order systems based on impulse response
Autorzy:
Sajewski, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/157129.pdf
Data publikacji:
2010
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
realizacja dodatnia
układy dyskretne
układy niecałkowitego rzędu
charakterystyka impulsowa
positive realisation
discrete-time fractional order system
impulse response
Opis:
Podane zostaną warunki zewnętrznej i wewnętrznej dodatniości dyskretnych liniowych układów niecałkowitego rzędu. Sformułowany zostanie problem realizacji dodatniej dla dyskretnych liniowych układów niecałkowitego rzędu. Podana zostanie metoda wyznaczania realizacji dodatniej na podstawie zadanej transmitancji operatorowej w oparciu o charakterystykę impulsową układu dyskretnego. Rozpatrzone zostaną dwa przypadki transmitancji operatorowej opisującej układ dyskretny niecałkowitego rzędu. Metoda zobrazowana zilustrowana przykładami numerycznymi.
Linear discrete-time fractional-order systems are dealt with in the paper. Conditions for external and internal positivity of linear discrete-time fractional-order systems with single-input and single-output (SISO) are presented. A positive realisation problem for linear discrete-time fractional systems is formulated. The method for finding positive realisation based on the impulse response for the known transfer function is given. There are considered two cases of the linear discrete-time fractional system transfer function. The considerations are illustrated by examples. In Section 2 of the paper there are presented the fundamentals of linear discrete-time fractional systems and the conditions for internal and external positivity are given. This section also contains formulation of the positive realisation problem for the class of linear discrete-time fractional systems. The main results and the procedure for computation of the positive realisation for the known linear discrete-time fractional system transfer function are given in Section 3. This section also contains some examples illustrating the method proposed. There are concluding remarks in Section 4.
Źródło:
Pomiary Automatyka Kontrola; 2010, R. 56, nr 5, 5; 404-408
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 50

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