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1

Przydatność polimerów stosowanych w technologii druku 3D do budowy modeli doświadczalnych służących do badań dynamicznych na stole wstrząsowym

Dulińska Joanna, Boroń Paweł, Tatara Tadeusz, Budzik Grzegorz, Przeszłowski Łukasz

Materiały Budowlane

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2024

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nr 1

17--22

PL

Technologia druku 3D ma coraz większe zastosowanie w budownictwie. W artykule zaprezentowano ocenę przydatności wybranych polimerów do druku modeli laboratoryjnych służących do identyfikacji częstotliwości drgań własnych obiektów na stole wstrząsowym. Wyznaczono doświadczalnie parametry fizykomechaniczne polimerów, a także obliczono skale podobieństwa w przypadku modeli wydrukowanych z analizowanych polimerów. Wskazano na parametry materiałowe polimerów warunkujące możliwość i zasadność ich stosowania w badaniach dynamicznych na stole wstrząsowym.

EN

3D printing technology is gradually becoming more employed in civil engineering. The article assesses the suitability of selected polymers for printing laboratory models used to identify the natural frequencies of structures on a shaking table. Experimental physical and mechanical parameters of the polymers were determined, and similarity scales were calculated for models printed with the analysed polymers. The material parameters of the polymers determining the possibility and validity of their use in dynamic tests on a shaking table were also indicated.

2

System wspomagania oceny stateczności przegubowych wozów wiercących

Bołoz Łukasz

Systemy Wspomagania w Inżynierii Produkcji

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2023

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Vol. 12, iss. 2

9--27

PL

Samojezdne maszyny górnicze takie jak kołowo-oponowe wozy wiercące charakteryzują się budową przegubową oraz wyposażone są w wysięgniki z organami roboczymi wysuniętymi daleko poza obrys podwozia. Taka konstrukcja powoduje, że maszyny te są podatne na utratę stateczności. Stąd też konieczne jest analizowanie rozkładu mas oraz ich szeroko pojętej stateczności podczas całego procesu projektowania, przy uwzględnienie wielu czynników wynikających ze sposoby i warunków ich pracy. Jednak brak jest odpowiednich modeli obliczeniowych pozwalających na przeprowadzenie badań analitycznych dla maszyn o takiej konstrukcji. W artykule przedstawiono autorski system wspomagający szybką ocenę stateczności jedno i dwuwysięgnikowych wozów wiercących. Model pozwala na przeprowadzenie analiz bez konieczności rozwiązywania równań różniczkowych występujących w modelach dynamicznych oraz bez stosowania badań modelowych za pomocą narzędzi CAD/CAE. Opracowany model obliczeniowy został zweryfikowany przez porównanie uzyskanych wyników z wynikami z pełnego modelu dynamicznego, z wynikami badań modelowych przeprowadzonych w programie CAD/CAE oraz z wynikami badań empirycznych nacisków kół i podpór na podłoże dla wybranego wozu wiercącego. Na podstawie weryfikacji i walidacji tego modelu stwierdzono jego pełną poprawność oraz przydatność. Model został wykorzystany do opracowania praktycznego i łatwego w obsłudze arkusza obliczeniowego. Następnie przeprowadzono badania analityczne stateczności wybranego wozu wiercącego. Model obliczeniowy jak i arkusz kalkulacyjny stanowią podręczne narzędzie wykorzystywane podczas procesu projektowania przez jedną z polskich firm produkujących wozy wiercące.

EN

Underground mining machines, such as wheel-tyre drilling rigs, are articulated and equipped with booms that project far beyond the undercarriage. Such a structure makes these machines prone to lose stability. Hence, it is necessary to analyse the distribution of masses and geometry as well as their broadly understood stability during the entire design process, taking into account many factors resulting from the manner and conditions of their operation. However, there are no ap-propriate computational models that would enable carrying out analytical tests for machines with this kind of construction. The article presents the author's support system which allows a quick assessment of the stability of single- and twin-boom drilling rigs. The model makes it possible to perform analyses without having to solve differential equations present in dynamic models or using model studies based on CAD/CAE tools. The developed computational model was verified by comparing the obtained results with the results of the full dynamic model, the results of model tests carried out in the CAD/CAE program and the results of empirical tests of wheel and jack pressures on the ground for the selected drilling rig. Based on the verification and validation of this model, it was found to be fully correct and useful. The model was used to prepare a practical and user-friendly calculation sheet. Next, analytical tests of the stability of the selected drilling rig were carried out. The computational model and the spreadsheet provide handy tools used during the design process by one of the Polish companies producing drilling rigs.

3

Effects of plasma expansion plumes in view of pulses laser irradiating centimeter-scale spherical space debris

Fang Yingwu

Optica Applicata

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2023

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Vol. 53, nr 3

363--375

EN

The objective of this article was to investigate the dynamic evolution behaviors of plasma expansion plumes by pulses laser irradiating centimeter-scale spherical space debris. A calculated model of centimeter-scale spherical space debris irradiated by pulses laser was firstly deduced based on FEM (finite element method)/COMSOL, and the action rules of plasma expansion plumes by pulses laser-generated irradiating the debris were simulated for different laser powers and action times. The results showed that the velocity of plasma expansion plumes was increased with the increase of laser powers and action times. Especially, when the laser power was 700 kW and the action time was close to 25 μs, the maximum velocity of plasma expansion plumes approached 1.91 km/s, and the diffusion radius of plasma expansion plumes was increased by about 2.5 mm. Further, the diffusion radius was about twice that of 400 kW when the action time reached about 48 μs. As a result, by simulating the transient flow process of nanosecond pulses laser irradiating small spherical space debris, the flow field evolution information and plasma plumes evolution characteristics of centimeter-scale space debris at nanosecond time resolution were revealed.

4

Dynamic analysis of a mechatronic drive system with an induction motor

Cao Yongdi, Liu Xiaohong

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 2

245--258

EN

The paper presents research findings in the modelling and optimization of dynamic parameters of mechatronic systems with an induction motor. A mathematical model was developed to analyze currents in dynamic states of squirrel-cage rotors in the case of a line-to-line fault. The findings were verified experimentally using calculations for a 1.5 kW three-phase induction motor. The equations for a stationary 0x, 0y coordinate system relating to the stator were derived. The set of design variables selected in the optimization process contained parameters describing design features of the gear shafts and control units settings.

5

A dynamic model as a tool for design and optimization of propulsion systems of transport means

Peruń Grzegorz

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 2

183--195

EN

Designing power transmission systems is a complex and often time-consuming problem. In this task, various computational tools make it possible to speed up the process and verify a great many different solutions before the final one is developed. It is widely possible today to conduct computer simulations of the operation of various devices before the first physical prototype is built. The article presents an example of a dynamic model of power transmission systems, which has been developed to support work aimed at designing new and optimizing existing systems of that type, as well as to help diagnose them by designing diagnostic algorithms sensitive to early stages of damage development. The paper also presents sample results of tests conducted with the model, used at the gear design stage. In the presented model, the main goal is to reproduce the phenomena occurring in gears as well as possible, using numerous experiments in this direction featured in the literature. Many already historical models present different ways of modeling, but they often made significant simplifications, required by the limitations of the nature of computational capabilities. Differences also result from the purpose of the models being developed, and the analysis of these different ways of doing things makes it possible to choose the most appropriate approach.

6

Modified Hooke-Jeeves optimization of operating parameters for required slider speeds and displacements in a feeder slider-crank mechanism

Sarigecili Mehmet Ilteris, Akcali Abrahim Deniz

Archive of Mechanical Engineering

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2023

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LXX, nr 1

63--83

EN

In such applications as in the case of feeders in which a slider-crank mechanism equipped with a rotational spring on its crank is driven by a constant force and a lumped mass at the crank-connecting rod joint center, the slider is required to take on desired speeds and displacements. For this purpose, after obtaining and solving the dynamic model of the slider-crank mechanism, the output of this model is subjected to a modified Hooke-Jeeves method resulting in the development of a procedure for the optimization of selected set of operating parameters. The basic contribution involved in the so-called Hooke-Jeeves method is the procedure by which a cost-effective advancement towards a target optimum point is accomplished in a very short time. A user-friendly interface has also been constructed to support this procedure. The optimization procedure has been illustrated on a numerical example. The validation of the resulting dynamic model has also been demonstrated.

7

The use of dynamic modeling for optimization of machine design on the example of a toothed gear

Peruń Grzegorz

Vibrations in Physical Systems

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2022

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Vol. 33, nr 3

art. no. 2022322

EN

The paper presents a dynamic model of a test stand with gears operating in a circulating power system as an example of the possibility of using dynamic modeling to optimize the gear construction. The presented model is one of two advanced tools developed within the research conducted for the optimization and diagnosis of various types of gear transmission systems. Both of them were based on the assumption that simulations of system operation at variable loads and rotational speeds could be carried out and that an advanced description of gear tooth interaction could be included. The developed models, after their tuning to real objects, were used as tools for generating vibration signals for various technical states of gears. This allowed determining the influence of various constructional, technological, and operational factors on the vibroactivity of a toothed gear, which is undoubtedly helpful for designers both during the construction of new toothed gears, as well as optimization of the existing ones.

8

Development of Turboshaft Engine Adaptive Dynamic Model: Analysis of Estimation Errors

Yepifanov Sergiy, Bondarenko Oleksiy

Transactions on Aerospace Research

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2022

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Nr 4 (269)

59--71

EN

One of the most perspective directions of aircraft engine development is related to implementing adaptive automatic electronic control systems (ACS). The significant elements of these systems are algorithms of matching of mathematical models to actual performances of the engine. These adaptive models are used directly in control algorithms and are a combination of static and dynamic sub-models. This work considers the dynamic sub-models formation using the Least Square method (LSM) on a base of the engine parameters that are measured in-flight. While implementing this function in the (ACS), the problem of checking the sufficiency of the used information for ensuring the required precision of the model arises. We must do this checking a priori (to determine a set of operation modes, the shape of the engine test impact and volume of recorded information) and a posteriori. Equations of the engine models are considered. Relations are derived that determine the precision of parameters of these models’ estimation depending on the precision of measurement, the composition of the engine power ratings, and durability of observations, at a stepwise change of fuel flow. We present these relations in non-dimensional coordinates that make them universal and ready for application to any turboshaft engine.

9

Hinf-FEEDBACK/FEEDFRWORD linear control applied to the 3DOF DELTA parallel robot

Thabet Mohammed, Yssaad Benyssaad, Litime Mostafa, Benadda Abdelouahid

Przegląd Elektrotechniczny

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2022

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R. 98, nr 7

36--41

EN

In this paper we propose an implementation of a Hinf-FEEDBACK / FEEDFRWORD multivariate linear controller on a 3DOF DELTA parallel robot. First, we linearized the system around an action point by implementing the "LINMODE" function in an MATLAB environment, then we compared the result of the proposed controller with that of the Hinf controller as well as that of the classic PID controller. We have found that the Hinf controller is robust compared to the PID controller and the proposed controller is more robust compared to the Hinf controller and the classic PID controller, and it follows the trajectory very well with good precision. And so we applied these controls to a system checked out from SOLIDWORKS.

PL

W niniejszym artykule zaproponowano implementację wielowariantowego regulatora liniowego Hinf-FEEDBACK / FEEDFRWORD na robocie równoległym DELTA 3DOF. W pierwszej kolejności dokonano linearyzacji układu wokół punktu akcji poprzez implementację funkcji "LINMODE" w środowisku MATLAB, a następnie porównano wynik działania proponowanego regulatora z wynikiem działania regulatora Hinf oraz klasycznego regulatora PID. Stwierdziliśmy, że kontroler Hinf jest odporny w porównaniu do kontrolera PID, a proponowany kontroler jest bardziej odporny w porównaniu do kontrolera Hinf i klasycznego kontrolera PID, i podąża za trajektorią bardzo dobrze z dobrą precyzją. I tak zastosowaliśmy te regulatory do układu sprawdzonego z SOLIDWORKS.

10

Wpływ kąta rastrowania na właściwości mechaniczne polimeru PLA-IMPACT w technologii druku 3D

Boroń Paweł, Dulińska Joanna, Jurkowska Nadzieja, Tatara Tadeusz

Materiały Budowlane

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2022

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nr 4

6--10

PL

Celem pracy jest poznanie możliwości i uwarunkowań stosowania modeli wykonanych w technologii druku 3D do badań dynamicznych. Zaprezentowano metodę i wyniki badań określających parametry fizykomechaniczne polimeru PLA-IMPACT drukowanego z różnymi kątami rastrowania. Badania wykazały, że wartość modułu sprężystości polimeru nie zależy od kąta rastrowania, natomiast na granicę plastyczności ma wpływ kierunek laminacji, co wpływa w istotny sposób na realizację modeli obiektów do badań dynamicznych.

EN

The aim of the work is to identify the possibilities and conditions for the use of models made in 3D printing technology for dynamic experiments. The methodology and results of tests determining the physical and mechanical parameters of the PLA-IMPACT polymer printed with different screening angles are presented. The research showed that the value of the polymer modulus of elasticity does not depend on the rastering angle, while the yield point depends on the direction of lamination, which is of key importance in the implementation of models of objects for dynamic tests.

11

Dynamic and mathematical models of the hydroimpulsive vibro-cutting device with a pressure pulse generator bult into the ring spring

Obertyukh Roman, Slabkyі Andrii, Polishchuk Leonid, Povstianoi Oleksandr, Kumargazhanova Saule, Satymbekov Maxatbek

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2022

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T. 12, nr 3

54--58

EN

Structural calculation scheme of the hydropulse device for vibration cutting with built-in ring with pressure pulse generator (PPG) is considered. On the basis of the structural scheme and cyclogram of the working cycle of the device, its dynamic and mathematical models were developed, in whichthe hydraulic link is represented by a visco-elastic model of the working fluid (energy carrier) composed of the inertial elastic and dissipative elements (Kelvin-Foyga's body).

PL

Rozważa się schemat konstrukcyjny i projektowy hydraulicznego urządzenia impulsowego do cięcia wibracyjnego z wbudowanym generatorem impulsów ciśnieniowych ze sprężyną pierścieniową (PPG). Na podstawie schematu strukturalnego i cyklu pracy urządzenia opracowano jego modele dynamiczne i matematyczne, w których ogniwo hydrauliczne reprezentowane jest przez lepkosprężysty model cieczy roboczej (nośnika energii), złożony z bezwładnych elementów sprężystych i dyssypacyjnych (ciał Kelvina-Foiga).

12

Dynamic load analysis of the connecting bolts in a universal joint

An Yuchen, Liu Jing, Li Zengguang

Eksploatacja i Niezawodność

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2022

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Vol. 24, no. 2

211--225

EN

Dynamic loads of the connecting bolts in a universal joint can greatly affect the bolt fatigue and fracture, as well as the machinery safety and stability. But few researches focused on those. To obtain the dynamic load characteristics of the connecting bolts in a universal joint, this paper established a flexible dynamic model for the connecting bolts. A multibody dynamic model of a universal joint is developed. The dynamic loads on the connecting bolts of the universal joint are analyzed. The influences of the preloads, speeds and loads are studied. The amplitude and frequency properities are obtained. The effect of the preload is small when the preload is in the range of 80%~120% of the standard value. The load and speed have great influence on the time- and frequency-domain dynamic loads of the bolts. The flexible dynamic model of the connecting bolt is closer to the actual situation than the rigid model since it can consider the preload and deformation of the bolts. This study can provide guidance for the fatigue life prediction of the universal shaft and its bolts.

13

A comparative study between PID and PD-SMC and PD-ASMC control applied on a delta robot

Thabet Mohammed, Yssaad Benyssaad, Litime Mostafa

Przegląd Elektrotechniczny

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2021

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R. 97, nr 10

1--7

EN

This paper presents the modelling and control of a delta robot. The software SOLIDWORKS is used in this work to get a performing model that is very close to real system. The proportional integrator derivative (PID) control is used in this proposal. The results are compared with PDSliding mode (PD-SMC) and PD a robust SMC (PD-ASMC). This is an important comparative study where the advantages of each controller are presented: the PD-SMC improve the performance of the trajectory tracking, where the control signal performances and the robustness was improved by the PD-ASMC. Results presented are done with matlab-simulink and with Solidworks.

PL

Atykuł przedstawia modelowanie i sterowanie robotem delta. Oprogramowanie SOLIDWORKS jest używane w tej pracy do uzyskania wydajnego modelu, który jest bardzo bliski rzeczywistemu systemowi. tak jak będziemy wyniki porównywane pomiędzy kontrolerami PID i (PD-SMC) i (PD-ASMC). Jest to ważne badanie porównawcze, w którym przedstawione są zalety każdego sterownika: PD-SMC poprawia wydajność śledzenia trajektorii, gdzie wydajność sygnału sterującego i odporność zostały ulepszone przez PD-ASMC. Przedstawione wyniki zostały wykonane za pomocą matlab-simulink oraz Solidworks.

14

Algorytmiczna optymalizacja pasma przenoszenia anemometru z grzanym włóknem

Ligęza Paweł

Prace Instytutu Mechaniki Górotworu PAN

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2021

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T. 23, nr 1-4

3--9

PL

Optymalizacja pasma przenoszenia anemometrów z grzanym włóknem stanowi jedno z wyzwań metrologii przepływów turbulentnych i pulsacyjnych. W tym celu stosowana jest miniaturyzacja czujników zmniejszająca inercję termiczną elementu pomiarowego, struktura układu elektronicznego i parametry jego elementów podlegają optymalizacji, rozwijane są metody i algorytmy przetwarzania sygnału wyjściowego. W typowych anemometrach z grzanym włóknem wyjściowy sygnał napięciowy przetwarzany jest na sygnał mierzonej prędkości z zastosowaniem statycznej funkcji wzorcowania. W artykule opisano algorytm pomiarowy wykorzystującą równocześnie dwa sygnały pomiarowe z anemometru. Są to sygnały proporcjonalne do napięcia i prądu czujnika. Na podstawie tych sygnałów i dynamicznego modelu czujnika z parametrami wzorcowania odtwarzany jest przebieg mierzonej prędkości przepływu.

EN

One of the challenges of turbulent and pulsed flow metrology is the optimization of the bandwidth of hot- -wire anemometers. The miniaturization of sensors is used there, which reduces the thermal inertia of the measuring element, the structure of the electronic system and parameters of its elements are optimized, methods and algorithms for processing the output signal are developed. In typical hot-wire anemometers, the output voltage signal is converted into the measured velocity signal using a static calibration function. The article describes a measurement algorithm that simultaneously uses two measurement signals from an anemometer. These are signals proportional to the sensor voltage and current. Based on these signals and the dynamic calibration function, the measured flow velocity is calculated using a dynamic sensor model.

15

A mathematical model of two-stage Solid Oxide Fuel Cell, SOFC, stacks for dynamic simulation of Combined Heat and Power system fed by natural gas

Palus Mateusz, Pianko-Oprych Paulina

Polish Journal of Chemical Technology

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2021

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Vol. 23, nr 2

1--11

EN

Zero-dimensional two-stage SOFC stacks dynamic model was developed to investigate the effect of operating parameters on stacks performance. The model resolves spatially thermal and thermo-electrochemical behaviour for electrochemical reactions, Catalytic Partial Oxidation and Steam Reforming processes. Design variables and thermo-electrochemical properties were obtained from in-house-fabricated SOFCs carried out by project partners. The completed SOFCs based Combined Heat and Power, CHP, system model was validated by data18 and numerical results obtained at steady-state mode showing its high-fidelity. A parametric study with respect to key operating parameters including changes in fuel utilization, lambda number and current density values was conducted. The global CHP system dynamic response, in term of the current/voltage delivered by two-stage SOFC stacks, under a fi xed fuel utilization, has been determined resulting in greater variations in the voltage of a single cell in the first stack in comparison to the corresponding values in the second stack.

16

Comparison of the Vibration Response of a Rotary Dobby with Cam-Link and Cam-Slider Modulators

Yu Hongbin, Yin Honghuan, Peng Junqiang, Wang Lei

Autex Research Journal

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2021

|

Vol. 21, no. 4

491--500

EN

This article presents the kinematic modeling and analysis of cam profiles of two different types of modulator: a cam-link and a cam-slider modulators. Kinematic and dynamic models of the two different modulators were established based on the motion curves of the main shaft of the rotary dobby. Simulations were carried out in Simulink to analyze the vibration responses under different rotary speeds, and vibration responses of the two mechanisms were compared. The results show that the cam-link modulator vibrates smoothly at speeds of <700 rpm, and theoretically, the speed should not exceed 1,400 rpm. The cam-slider modulator vibrates smoothly at speeds of <500 rpm, and theoretically, the speed should not exceed 1,000 rpm. The cam-slider modulator is more suitable for use at low speeds, whereas the cam-link modulator is more appropriate for high speeds. When both the cam-slider and cam-link modulators operate at high speeds, vibration distortion occurs, leading to bifurcation and chaotic vibration. Further knowledge of the complex behaviors associated with detachment of the follower from the cam can support the design of more sophisticated controllers aimed at avoiding follower detachment.

17

Identyfikacja modeli dynamicznych jako element procesu konstruowania

Dąbrowski Zbigniew

Przegląd Mechaniczny

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2020

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nr 1

30--33

PL

W artykule zamieszczono podstawowe definicje i równania identyfikacji parametrycznej i strukturalnej. Przedstawiono praktyczne aspekty formułowania problemu identyfikacji. Pokazano na prostym przykładzie, że pominięcie procedury identyfikacji prowadzi do poważnych błędów, nawet w przypadku nieskomplikowanych modeli.

EN

The paper reminds of basic definitions and formalisms of parametric and structural identification. Practical aspects of formulation of identification problem were presented. Furthermore, the simple example shows that the omission of identification procedure leads to serious errors, even for not complicated models

18

A Model of time Variability of Characteristic Parameters of the Water Distribution System as a Base of Information and the Basis of Mathematical Modelling

Trębicka Agnieszka

Journal of Ecological Engineering

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2020

|

Vol. 21, nr 1

46--51

EN

The subject of the paper is the Bialystok water supply network. The studies on the Bialystok water supply network are aimed at identifying new, more rational ways of operation (decreasing the pressure value) and defining the conditions for expansion and modernization of the water supply network, with the particular system analysis as a part of identifying the most dangerous places on the network. The increase of requirements concerning the quality and the time of realisation in the scope of the design studies requires the introduction of computer technology in calculations. The work presents the processes based on mapping and refinement of specific conservative states of the water distribution system (SDW), using mathematical modelling taking into account the latest available computer techniques.

19

Laboratory bench to analyze of automatic control system with a fuzzy controller

Tryputen Mykola, Kuznetsov Vitaliy, Kuznetsov Valeriy, Kuznetsova Yevheniia, Tryputen Maksym, Kuznetsova Alisa

Diagnostyka

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2020

|

Vol. 21, No. 2

61--68

EN

The paper represents laboratory bench to analyse a system of automated control with a fuzzy controller. The laboratory bench consists of a thermal object, and software and hardware complex involving logic controller VIPA System 200 V as well as HMI / SCADA system Zenon Supervisor 7.0. The thermal object is described with the help of the second-order differential equation using “current value within the power converter of electric heater-air temperature inside a thermal object” control channel. Coefficients of the differential equation depend upon location of a dampener and upon rotation frequency of a centrifugal fan. Control error (ie deviation between the specified temperature value within the thermal object and its current value), and derivative of the error, represented in the form of linguistic variables involving five triangular terms and two trapezoidal (extreme) ones have been used as the input values of the fuzzy controller. Output value of the fuzzy controller is the electric power supplied to the electric heater and assuming seven specified values. Selection of the specific value of electric power depends upon knowledge base being a finite set of rules of fuzzy sets falling into line with the applied linguistic variables. To implement such a system of automated control with a fuzzy controller, original software has been developed making it possible to analyze a process of thermal object heating with the use of human-computer interface. Interaction algorithm of certain program elements has been described. Experimental results, concerning the thermal object transfer from different initial conditions to terminal ones, have been demonstrated. A dependence of mean-square error of the controlled value upon the control period has been demonstrated.

20

Dynamiczny model planu produkcji folii polimerowej

Csikósová Adriana, Malindžák Dušan, Janošková Mária, Čulková KatarÍna

Przemysł Chemiczny

|

2019

|

T. 98, nr 2

214--219

PL

Obecnie firmy muszą mierzyć się z wielką presją konkurencji oraz przewagą podaży nad popytem, co oznacza konieczność opracowania biznesowej strategii produkcyjnej. Aby zarządzać zapotrzebowaniem, należy wykorzystywać bardziej nowoczesne i bardziej złożone metody także w planowaniu sprzedaży. Zaproponowano dynamiczny model planu produkcji w przemyśle chemicznym, którego zadaniem jest zmiana sposobu obecnego planowania w odniesieniu do realizacji kontraktowo zagwarantowanych i nowych zamówień.

EN

Rules and recommendations for dynamic planning the com. production of polypropylene films were given. An algorithm for development of an extended prodn. plan was elaborated.