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1
Content available Comprehensive online estimation of object signals for a control system with an adaptive approach and incomplete measurements
Kwater Tadeusz, Hawro Przemysław, Krutys Paweł, Gołębiowski Marek, Drałus Grzegorz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2024
|
Vol. 72, nr 4
art. no. e150111
EN
This paper presents the novel estimation algorithm that generates all signals of an object described by nonlinear ordinary differential equations based only on easy-to-implement measurements. Unmeasured signals are estimated by using an adaptive approach. For this purpose, a filtering equation with a continuously modified gain vector is used. Its value is determined by an incremental method, and the amount of correction depends on the current difference between the generated signal and its measured counterpart. In addition, the study takes into account the aging process of measurements and their random absence. The application of the proposed approach can be realized for any objects with a suitable mathematical description. A biochemically polluted river with an appropriate transformation of the notation of partial differential equations was chosen as an object. The results of numerical experiments are promising, and the process of obtaining them involves little computational necessity, so the approach is aimed at the needs of control implemented online.
2
Content available remote On a first-order differential system with initial and nonlocal boundary conditions
Ngoc Le Thi Phuong, Long Nguyen Thanh
Demonstratio Mathematica
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2022
|
Vol. 55, nr 1
277--296
EN
This paper is devoted to the existence of solutions and the multiplicity of positive solutions of an initial-boundary value problem for a nonlinear first-order differential system with nonlocal conditions. The main tool is the fixed-point theorem in which we construct the novel representation of the associated Green’s functions with useful properties and define a cone in the Banach space suitably. Some examples are also given to demonstrate the validity of the main results.
3
Content available remote Numerical studies for solving a free convection boundary-layer flow over a vertical plate
Othman M. I. A., Mahdy A. M. S.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 1
41--48
EN
In this paper, the aim of this study is to present a reliable combination of the shifted Legendre collocation method to approximate of the problem of free convection boundarylayer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shift Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the shifted Legendre collocation method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.
4
Content available remote A mathematical model of a synchronous drive with protrude poles, an analysis using variational methods
Rusek A., Czaban A., Lis M.
Przegląd Elektrotechniczny
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2013
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R. 89, nr 4
106-108
EN
In the paper a mathematical model of a synchronous drive with protrude poles in physical cooeridantes of magnetic couplings. The system is considered as having concentrated parameters. For formulation of differential state equations a novel interdisciplinary method based on a modification of the well-known Hamilton-Ostrogradsky principle. On the basis of the model the transient states of the drive system with synchronous motor were analyzed. The results of computer simulations were presented in the graphical form.
PL
W pracy przedstawiono model matematyczny napędu synchronicznego o biegunach jawnych w fizycznych współrzędnych sprzężeń magnetycznych. System rozpatrywany jako układ o parametrach skupionych. Dla sformułowania różniczkowych równań stanu wykorzystano nawą interdyscyplinarną metodę, która bazuje na modyfikacji znanej zasady Hamiltona-Ostrogradskiego. Na podstawie modelu poddano analizie stany nieustalone pracy układu napędowego z silnikiem synchronicznym. Wyniki symulacji komputerowej przedstawiono w postaci graficznej.
5
Solutions nonlinear differential equations with partial differentials, which describe electromagnetic and thermal process in ferromagnetic environment
Czaban Wasyl, Kycia Ewa
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2002
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z. 26 [199]
51-58
EN
In the practical tasks mathematical modeling of the physical processes if is often needed to give the common solution of both quasi stationary magnetic field -- and non stationary thermal conductivity equations. Such the equations arise in complicated problems in physics, electro mechanics, electromagnetics, automatics, electronic engineer, computer techniques. In the present paper we with examine the physical process in ferromagnetic rod steel.
6
Content available remote Dynamics of a conjugate cam mechanism driving an elastic swinging shaft
Zajączkowski J.
Zeszyty Naukowe. Włókiennictwo / Politechnika Łódzka
|
2001
|
z. 60
53-62
EN
The paper is concerned with torsional vibration of a swinging shaft driven by two conjugate cams. The dimensions of the cams for the dwell-rise-dwell-rise-return motion are determined. The set of ordinary nonlinear equations describing the motion of the system are solved numerically for various cam shaft stiffnesses. The results are shown in charts.
PL
Praca dotyczy drgań skrętnych wału oscylującego napędzanego układem krzywek sprzężonych. Określone są wymiary krzywek realizujących ruch. Układ równań różniczkowych nieliniowych opisujących ruch jest rozwiązany numeryczne dla różnych sztywności wału. Wyniki są przedstawione na wykresach.
7
Content available remote Dependence of the cam follower loading on the system elasticity
Zajączkowski J.
Zeszyty Naukowe. Włókiennictwo / Politechnika Łódzka
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2001
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z. 60
63-69
EN
The paper is concerned with the problem of dependence of the loading of the cam mechanism on the elasticity of its elements. The mechanisms with rigid elements, with spring mass system, with an elastic cam shaft and with the elastic rocker shaft are studied. The motion of the mechanism is described by nonlinear differential equations. The moment acting on the rocker is calculated and plotted.
PL
Praca dotyczy zagadnienia zależności obciążenia mechanizmu krzywkowego od sprężystości jego elementów. Badane są mechanizmy z elementami sztywnymi, ze sprężystym wałem krzywkowym, ze sprężystym wałem popychacza oraz z układem drgającym złożonym z masy i sprężyny. Ruch mechanizmu opisany jest za pomocą nieliniowych równań różniczkowych. Moment działający na popychacz, wyznaczony po rozwiązaniu równań różniczkowych, jest przedstawiony wykreślnie.
8
Content available remote Stability for certain fourth order nonlinear differential equations
Lin S., Liu Z., Yu Y.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 1
87-96
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