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EN
This paper is designed to deal with the convergence and stability analysis of impulsive Caputo fractional order difference systems. Using the Lyapunov functions, the Z-transforms of Caputo difference operators, and the properties of discrete Mittag-Leffler functions, some effective criteria are derived to guarantee the global convergence and the exponential stability of the addressed systems.
2
Content available Algorithms for digital γ-ray spectroscopy
EN
The data processing in modern nuclear spectroscopy is dominated by digital methods. In this paper we present a full set of algorithms necessary for energy reconstruction, baseline restoration, trigger generation and selection of events (acceptation) which are based on digital signal processing (DSP) techniques. All algorithms were fully evaluated using mathematical apparatus of Z-transform. The energy reconstruction algorithm is based on trapezoidal shaping. The baseline restoration makes the use of a digital moving average, while trigger generation algorithm utilize a digital form of RC-CR2 filter with protection windowing. The evaluated algorithms has been implemented and used in the demonstrator build for national borders protection.
3
Content available A discrete model of the plate heat exchanger
EN
Developing numerical control methods requires precise models of technical machines. The article presents a discrete model of a plate heat exchanger. The model was worked out based on differential equations to secure high accuracy. Correctness of the model was verified using the data for the M10 – MFM cooler produced by Alfa-Laval.
4
Content available remote Non-classical operational calculus applied to certain linear discrete time-system
EN
In the paper there bas been made an advantage of the non-classical operational calculus to determination of the response of the certain discrete time-systems. The Z-transform is often used to analysis of the stationary discrete time-systems. However, the use of the Z-transform to determination of the response especially of the non-stationary discrete time-systems is doubtful or may cause complications. This method leads to differential equa-tions of n-th order of variable coefficients, whose solutions are very difficult or impossible. The non-classical operational calculus ran be used to analysis both of the stationary and non-stationary discrete time-systems. The presented method with the use of the Heaviside operator soon leads to the target without unnecessary differential equations.
5
Content available Numerical simulation of heat flow processes
EN
Numerical simulation methodis basedon mathematical models of physical processes, which describe run of a given process with a various accuracy. This paper presents a method for elaborating the computer simulation models based on differential equations. This makes it possible to obtain a high accuracy of representing dynamic features of a real process. The derived results are given in the form of numerical series. An example of modelling the dynamics of heat transfer through aflat wall is presented in the second part of the paper. Basing on the model one can simulate the process of operation of ship engine as well as such auxiliary devices as a cooler, evaporator, condenser, tank heating system etc.
PL
Przedstawiono wyniki badań, których celem było zaproponowanie pewnego uogólnienia opisu widmowego układów SC i SI. Zmodyfikowana metoda bazuje na opisie dokonywanym w dziedzinie sygnałów dyskretnych. Najistotniejszą jej nowością jest uogólnienie związku pomiędzy opisem w dziedzinie sygnałów ciągłych. Do wyrażenia tego związku wykorzystano bardziej elastyczne pojęcie funkcji interpolującej (ang. sampling function). Uzyskano dzięki temu możliwość aproksymowania sygnałów generowanych w układach SC i SI przebiegami o bardziej realistycznych kształtach, niż stosowania do tej pory funkcja schodkowa.
EN
The paper presents results of research, the objective of which was to propose certain generalisation of SC and SI circuit spectral description. The modified methods is based on description in the discrete time domain. The most essential novelty of the proposed method is generalisation of relation between description in the discrete- and continuous-time domains. A more flexible concept of sampling function was utilised to express the relation.Thanks to this a possibility of approximating signals generated in SC and SI circuits with more realistic waveforms was gained, than the staircase function used so far. As a result, better accuracy of spectrum calculation was obtained.
PL
Niniejszy artykuł ma na celu przedstawienie spostrzeżeń i uwag dotyczących zastosowania transformaty Z do identyfikacji stanów obiektów, a przede wszystkim zmian tych stanów. W diagnostyce maszyn duża rolę odgrywa analiza zachodzących zmian stanów technicznych, będąca podstawą do prognozowania. Podstawowym problemem jest sposób interpretacji parametrów modeli diagnostycznych. Dotyczy to przede wszystkim sposobu analizowania wartości tych parametrów oraz w szczególności ich zmian. Zmiany związane ze stanem obiektu, odzwierciedlają się, bowiem w zmianach parametrów fizycznych, a te z kolei w parametrach modeli. Zastosowanie płaszczyzny zespolonej Z jako płaszczyzny reprezentacji modelu diagnostycznego może być pomocna w diagnozowaniu stanu obiektu. Praca jest kontynuacją wcześniejszych doświadczeń związanych z zastosowaniem diagnozowania maszyn wirnikowych w oparciu o analizę położenia biegunów i zer na płaszczyźnie zespolonej ciągłej.
EN
The paper was devoted to present some notices and attentions in relation to application Z transform for purpose of identification of object state and most of all identification of their changes. An analysis of changes of technical states performs an elementary function in machine diagnostics and can be used in prediction. A manner of interpretation of the diagnostic model parameters is a principal problem. Most of all, it concern a way of analysis of values and changes of models parameters. Changes of object states are reflected in their physical parameters and they are next represented in model parameters. An application of complex plane Z as a plane of diagnostic model representation may be helpful in diagnosis of object states. This article is a continuance of earlier experiences connected with working out a method of diagnosing of rotating machine based on analysis of poles/zeros arrangement on the continuous complex plane
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