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Modelowanie systemów dynamicznych z wykorzystaniem transmitancji hybrydowych niecałkowitego rzędu

100%

Oprzędkiewicz K.

tom R. 93, nr 6

95--100

W pracy zaproponowano nowe modele transmitancyjne niecałkowitego rzedu w postaci transmitancji hybrydowych, zawierających zarówno część całkowitego, jak i niecałkowitego rzędu. Rozważono modele z opóźnieniem i bez opóźnienia. Jako przykłady rozważono doświadczalny obiekt cieplny oraz silnik indukcyjny prądu przemiennego, sterowany częstotliwościowo. Wyniki eksperymentów potwierdziły przydatność proponowanych modeli do opisu rozwązanych systemów dynamicznych.

IN the paper new, transfer function, non integer order models are proposed. The considered models have a form of hybrid transfer functions containing both integer order and non integer order parts. Models with and without delay were discussed. As examples an experimental heat plant and AC motor were tested. Results of experiments show that the proposed hybrid models are useful tool to modeling of dynamic systems.

Oustaloup parallel approximation

84%

Bauer W. , Baranowski J. , Dziwiński T. , Piątek P. , Zagórowska M.

Prace Naukowe Politechniki Śląskiej. Elektryka

2016

tom z. 3-4

59--64

This article presents Oustaloup approximation method for fractional differential systems, which has been modified by the authors. Application of this method by using numerical experiments has been shown and behavior of discrete system has been analyzed.

W artykule przedstawiono zmodyfikowaną przez autorów metodę aproksymacji Oustaloupa dla układów różniczkowych niecałkowitego rzędu. Pokazano jej wykorzystanie poprzez eksperyment numeryczny oraz przeanalizowano zachowanie systemu dyskretnego.

The positivity of the fractional order model of a two-dimensional temperature field

67%

Oprzędkiewicz K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2023

tom Vol. 71, nr 4

art. no. e145675

The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.

Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator

67%

Oprzędkiewicz K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

tom Vol. 66, nr 3

249--255

The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.