Wyniki wyszukiwania - BazTech

1

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

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

|

2018

|

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.

3

On reconstructing unknown characteristics of a nonlinear system of differential equations

Kuklin A., Maksimov V., Nikulina N.

Archives of Control Sciences

|

2015

|

Vol. 25, no. 2

163--176

EN

Problems of dynamical reconstruction of unknown characteristics for nonlinear equations described the process of diffusion of innovations through results of observations of phase states are considered. Solving algorithms, which are stable with respect to informational noises and computational errors, are designed. The algorithms are based on the principle of auxiliary models with adaptive controls.

4

A mathematical model of a synchronous drive with protrude poles, an analysis using variational methods

Rusek A., Czaban A., Lis M.

Przegląd Elektrotechniczny

|

2013

|

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

Linearization of the ship equations of motion

Mielewczyk A.

Journal of KONES

|

2013

|

Vol. 20, No. 2

269--275

EN

In real systems are non-linear mathematical description. The exact solution can not be determined, and then look for approximate methods. Important is the type of nonlinearity, solutions and error method approximation. Linearization is an essential part of creating a model of the selected process. Ship resistance is a function of power with exponent two and higher. Model motion of the ship must have a solution in terms of maneuverability speed and speed of the sea. The solution must be well reproduce the actual path of the transition and the transition time of the ship. Nonlinear solution method determines the accuracy of the answers. Has presented the revised approach to solve the nonlinear differential equation of parabolic function. Linearization has been made in the selected range, and not where you want it to work and solve the error estimate. Range of solutions selected by external priorities adopted. Before the solution is estimated response error. The error value determines whether the selected interval will apply. If the problem solution is unacceptable, it will increase the accuracy of the result of the narrow scope of the work. The new scope of work should also be reassessed a solution error. This type of approach correlates with fuzzy logic, where we use the value of the Boolean variable with the function of belonging. The combination of classical methods of solving differential equations of the theory of fuzzy sets can bring new benefits. Such a solution must have the function of the accuracy of the answers. The linearization method meets this requirement.

6

Identification and identifiability of models of cell signalling pathways

Fujarewicz K., Kimmel M., Świerniak A.

Przegląd Elektrotechniczny

|

2008

|

R. 84, nr 5

91-94

EN

The dynamical behaviour of a cell signalling pathway may be described by means of a set of nonlinear ordinary differential equations. The data for parameter estimation are collected only at discrete time moments that are relatively rare. We show a gradient-based algorithm for parameter estimation. We also present some considerations about identifiability of cell signalling pathways. The approach is illustrated on a model of NF?B transcription factor pathway.

PL

Dynamiczne zachowanie komórkowych szlaków sygnałowych może być modelowane za pomocą nieliniowych równań różniczkowych zwyczajnych. Dane potrzebne do identyfikacji zbierane są w nielicznych, dyskretnych chwilach czasu. W artykule zamieszczamy gradientową metodę identyfikacji parametrów oraz przedstawiamy rozważania dotyczące identyfikowalności parametrów. Podejście jest zilustrowane na przykładzie modelu szlaku sygnałowego czynnika transkrypcyjnego NF?B.

7

On theorems for weak solutions of nonlinear differential equations with and without delay in Banach spaces

Gomaa A,M

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2007

|

Vol. 47, [Z] 2

179-191

EN

In the present work we give an existence theorem for bounded weak solution of the differential equation.......[formuła matematyczna]

8

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

|

2002

|

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.

9

Remarks on recent fixed pont theorems and applications to integral equations

Mishra S., Singh S.

Demonstratio Mathematica

|

2001

|

Vol. 34, nr 4

847-857

EN

Coincidence and fixed point theorems for a quadruple of maps on an arbitrary set with values in a metric space and with minimal commutavity conditions have been studied. Applications to nonlinear integral equations are also given.

10

Comparison of the behavior of exact and approximate modelling of a nonlinear oscilator with one degree-of-freedom

Mesnier V., Lamarque C., Malasoma J., Awrejcewicz J.

Journal of Technical Physics

|

1999

|

Vol. 40, no 1

101-108

EN

We consider a nonlinear mechanical system with one degree of freedom described by an exact model and then by a piecewise linear approximations of this model. We compare the global dynamic behavior of the exact model with that of the approximate model. An example shows that it is possible to describe complex behaviors with a rather reasonable accuracy.

11

On bounded pseudo and weak solutions of a nonlinear differential equation in Banach spaces

Krzyśka S., Kubiaczyk I.

Demonstratio Mathematica

|

1999

|

Vol. 32, nr 2

323-330

EN

In this paper, we prove an existence theorem for bounded pseudo and weak solution of the differential equation . XI(t) = A(t)x(t) + f(t, X(t)) where f(., X(.) ) is Pettis- integrable for each strongly absolutely continuous function X and f(t,.) is weakly-weakly sequentially continuous. We also assume some condition expressed in terms of De Blasi's measure of weak noncompactness.