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Wyszukujesz frazę "fractional order systems" wg kryterium: Temat


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:
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:
Analiza sterowania ułamkowego PIλDμ mocą reaktora jądrowego
Analysis of fractional order PIλDμ power control of a nuclear reactor
Autorzy:
Puchalski, B.
Duzinkiewicz, K.
Rutkowski, T.
Powiązania:
https://bibliotekanauki.pl/articles/408118.pdf
Data publikacji:
2013
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
regulator ułamkowy
regulator PID
reaktor PWR
zaawansowane systemy sterowania
model punktowy kinetyki neutronów
fractional order control
PID controller
PWR reactor
advanced control systems
point kinetics model
Opis:
W artykule przedstawiono syntezę regulatora PIλDμ niecałkowitego rzędu dla potrzeb sterowania mocą reaktora jądrowego lekko wodnego określanego, jako typu PWR (Pressurized Water Reactor). W tym celu wykorzystano nieliniowy model matematyczny reaktora PWR o parametrach skupionych obejmujący procesy generacji i wymiany ciepła oraz termicznych efektów reaktywnościowych. Nastawy regulatora PIλDμ niecałkowitego rzędu dobrano w sposób optymalny, minimalizując klasyczne całkowe wskaźniki jakości określane na bazie odpowiedzi skokowej. Na przykładzie najpierw układu oscylacyjnego drugiego rzędu, a potem na przykładzie liniowego modelu reaktora PWR otrzymanego z linearyzacji modelu nieliniowego w określonym punkcie pracy wykazano, że proponowany ułamkowy regulator PIλDμ może stać się alternatywą dla powszechnie stosowanego klasycznego regulatora PID.
In this paper, the synthesis of fractional–order PIλDμ power controller for the PWR (Pressurized Water Reactor) nuclear reactor is presented. For this purpose the point kinetics and heat transfer nonlinear model of the PWR nuclear reactor with thermal feedback mechanisms from lumped fuel and coolant temperature was used. The parameters of the fractional-order PIλDμ controller were tuned due to optimization of the standard integral performance indexes determined on the basis of the step response. Firstly – the typical second order oscillatory dynamic system and secondly – the linear PWR nuclear reactor model derived from nonlinear model was used to show that the fractional order PIλDμ controller may become a alternative to standard PID controller.
Źródło:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2013, 4; 63-68
2083-0157
2391-6761
Pojawia się w:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
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:
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:
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:
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:
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:
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:
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:
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 algorithm for the states, parameters and order of fractional system estimation
Autorzy:
Sierociuk, D.
Dzieliński, A.
Powiązania:
https://bibliotekanauki.pl/articles/908456.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
przestrzeń fazowa
układ ułamkowy
filtr Kalmana
estymacja parametryczna
discrete fractional state-space systems
fractional Kalman filter
parameter estimation
order estimation
extended fractional Kalman filter
Opis:
This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2006, 16, 1; 129-140
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
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:
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

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