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1

Transfer function for a controllable pitch propeller with added water mass

Leshchev Volodimir, Maslov Igor, Palagin Oleksandr, Naydyonov Andrii

Polish Maritime Research

|

2023

|

nr 4

74--80

EN

The relevance of this study lies in the fact that it presents a mathematical model of the dynamics of the propulsion system of a ship that takes into consideration the mass of water added to it. The influence of this phenomenon on the resonant frequencies of the propeller shaft is examined, and a transfer function for a controllable-pitch propeller is obtained for various operating modes. The purpose of the study is to improve the calculation of the dynamic operating modes of a controllable-pitch propeller by examining the features of a visual models. The VisSim software package is used in the study. A visual model is developed that considers the influence of the rotational speed on the value of the rotational inertia attached to the variable-pitch screw of the mass of water, and a special transfer function is proposed. The study shows that a transfer function of this type has a loop enabling negative feedback. An analysis of the operation of the propeller shaft at its resonant frequency is conducted based on the application of frequency characteristics using the transfer functions obtained. We show that in the low-frequency region, a consideration of the added rotational inertia using the proposed transfer function leads to a significant difference compared to the result obtained with the existing calculation method.

2

The influence of friction force and hysteresis on the dynamic responses of passive quarter-car suspension with linear and non-linear damper static characteristics

Klockiewicz Zbyszko, Ślaski Grzegorz

Acta Mechanica et Automatica

|

2023

|

Vol. 17, no. 2

205--218

EN

Vehicle passive suspensions consist of two major elements generating force – spring and passive damper. Both possess non-linear characteristics, which are quite often taken into account in simulations; however, the friction forces inside the hydraulic damper and the damping force’s hysteresis are usually left out. The researchers in this paper present the results of examination of the influence of using complex damper models – with friction and hysteresis; and with linear and non-linear static characteristics – on the chosen dynamic responses of a suspension system for excitations in the typical exploitation frequency range. The results from the simulation tests of the simplified and advanced versions of the damper model – different transfer functions and their relation to the reference model’s transfer functions – are compared. The main conclusion is that friction and hysteresis add extra force to the already existing damping force, acting similar to damping increase for the base static characteristics. But this increase is not linear – it is bigger for smaller frequencies than for higher frequencies. The research shows the importance of including non-linear characteristics and proposed modules in modelling passive dampers.

3

Vibration transmission analysis through mounting elements of wall cladding panels

Idczak Julia, Rubacha Jarosław, Kamisiński Tadeusz

Vibrations in Physical Systems

|

2022

|

Vol. 33, nr 2

art. no. 2022207

EN

Vibrations in building constructions may propagate through mounting elements to wall cladding panels. It is confirmed that they can have an impact on the sound pressure level radiated from panels and might have a significant influence on the total SPL in a room. In this work possibilities for calculating a parameter determining a change of SPL value depending on the number of panels and its mounting method are presented. A computational model based on vibration velocity measurements was used to estimate the total SPL value in a room. The laboratory and in situ measurements are presented. Transfer function for two elastic elements used as additional elements in a junction was calculated. Finally, ΔLp and ΔLv were calculated, as parameters defining the impact of various panel mounting methods on the reduction of sound pressure level and vibration level value, respectively.

4

Mathematical and simulation modeling of dual active bridge

Barlik Roman, Grzejszczak Piotr, Koszel Mikołaj

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2022

|

Vol. 70, nr 5

art. no. e142653

EN

The paper is a structured, in-depth analysis of dual active bridge modeling. In the research new, profound dual active bridge converter (DAB) circuit model is presented. Contrary to already described idealized models, all critical elements including numerous parasitic components were described. The novelty is the consideration of a threshold voltage of diodes and transistors in the converter equations. Furthermore, a lossy model of leakage inductance in an AC circuit is also included. Based on the circuit equations, a small-signal dual active bridge converter model is described. That led to developing control of the input and output transfer function of the dual active bridge converter model. The comparison of the idealized model, circuit simulation (PLECS), and an experimental model was conducted methodically and confirmed the high compatibility of the introduced mathematical model with the experimental one. Proposed transfer functions can be used when designing control of systems containing multiple converters accelerating the design process, and accurately reproducing the existing systems, which was also reported in the paper.

5

The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters

Winnicki Ireneusz, Jasinski Janusz, Pietrek Sławomir, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

|

2022

|

Vol. 71, no. 2

art. no. e23, 2022

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.

6

Diagnostics of turbine blades, based on estimation of frequency response function

Kotkowski Jerzy, Rokicki Edward, Lindstedt Paweł, Spychała Jarosław, Perczyński Jerzy, Karbowiak Hieronim

Journal of KONBiN

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2021

|

Vol. 51, iss. 2

63--78

EN

The aim of the study is to propose a diagnostics method based on blade’s vibration model in frequency domain. Amplitude spectrum A(ω) and phase spectrum φ(ω) have been experimentally identified which define transfer function G(jω) = P(ω) + jQ(ω) and their real P(ω) and imaginary Q(ω) parts. Transfer function G(jω) and resulting frequency, amplitude, phase characteristics and real P(ω) and imaginary Q(ω) parts are parts of blade’s diagnostics model. Changes in those characteristics are directly related to changes in the technical condition of the blades. It has been noticed that small changes in the technical condition cause large changes in frequency characteristics, which proves their usefulness in the diagnosis process.

PL

Celem badania jest zaproponowanie metody diagnostycznej opartej na modelu drgań łopatek w dziedzinie częstotliwości. Zidentyfikowano eksperymentalnie widma ampli-tudowe A(ω) i fazowe φ(ω), które definiują transmitancję operatorową G(jω) = P(ω) + jQ(ω) oraz jej rzeczywiste P(ω) oraz urojone Q(ω) części. Transmitancja operatorowa G(jω) i wynikająca z niej częstotliwość, amplituda, charakterystyka fazowa oraz rzeczywiste P(ω) i urojone Q(ω) części są częściami modelu diagnostycznego łopatki. Zmiany w tych charakterystykach są bezpośrednio związane ze zmianami w stanie technicznym łopatek. Zauważono, że małe zmiany w stanie technicznym powodują duże zmiany w charakterystykach częstotliwościowych, co świadczy o ich przydatności w procesie diagnostycznym.

7

Extremal values of differential equations with application to control systems

Górecki Henryk, Zaczyk Mieczysław

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2021

|

Vol. 69, nr 1

art. no. e136041

EN

In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1=s2=...=sn.

8

Modelling of Dry-Low Emission Gas Turbine Fuel System using First Principle Data-Driven Method

Omar Mediah Binti, Ibrahim Rosdiazli, Abdullah Mohd Faris, Tarik Mohammad Haizad Mohd

Journal of Power Technologies

|

2020

|

Vol. 100, nr 1

1--13

EN

Achieving reliable power generation from Dry Low Emission gas turbines together with low CO2 and NOx discharge is a great challenge, as the rigorous control strategy is susceptible to frequent trips. Therefore, it is crucial to establish a dynamic model of the turbine (such as the one commonly attributed to Rowen) to ascertain the stability of the system. However, the major distinctive fuel system design in the DLE gas turbine is not constructed in the well-established model. With this issue in mind, this paper proposes a modelling approach to the DLE gas turbine fuel system which consists of integrating the main and pilot gas fuel valve into Rowen’s model, using the First Principle Data-Driven (FPDD) method. First, the structure of the fuel system is determined and generated in system identiﬁcation. Subsequently, the validated valve models are integrated into Rowen’s model as the actual setup of the DLE gas turbine system. Ultimately, the core of this modelling approach is fuel system integration based on the FPDD method to accurately represent the actual signals of the pilot and main gas fuel valves, gas fuel ﬂow and average turbine temperature. Then, the actual signals are used to validate the whole structure of the model using MAE and RMSE analysis. The results demonstrate the high accuracy of the DLE gas turbine model representation for future utilization in fault identiﬁcation and prediction study.

9

Extremal properties of linear dynamic systems controlled by Dirac’s impulse

Białas Stanisław, Górecki Henryk, Zaczyk Mieczysław

International Journal of Applied Mathematics and Computer Science

|

2020

|

Vol. 30, no. 1

75--81

EN

The paper concerns the properties of linear dynamical systems described by linear differential equations, excited by the Dirac delta function. A differential equation of the form a_n x⁽ⁿ⁾ (t) + ∙∙∙ a₁ x’(t) + a₀ x(t) = b_m u (t) + ∙∙∙ + b₁ u’(t) + b₀ u(t) is considered with a_i, b_j >0. In the paper we assume that the polynomials M_n(s) = a_nsⁿ + ∙∙∙ + a₁s + a₀ and L_m(s) = b_ms^m + ∙∙∙ + b₁s + b₀ partly interlace. The solution of the above equation is denoted by x(t, L_m, M_n). It is proved that the function x(t, L_m, M_n) is nonnegative for t ∊ (0, ∞) , and does not have more than one local extremum in the interval (0, ∞) (Theorems 1, 3 and 4). Besides, certain relationships are proved which occur between local extrema of the function x(t, L_m, M_n), depending on the degree of the polynomial M_n(s) or L_m(s) (Theorems 5 and 6).

10

Approximate state-space and transfer function models for 2x2 linear hyperbolic systems with collocated boundary inputs

Bartecki Krzysztof

International Journal of Applied Mathematics and Computer Science

|

2020

|

Vol. 30, no. 3

475--491

EN

Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.

11

Próba znalezienia transmitancji węzła ciernego

Szews Maciej

Developments in Mechanical Engineering

|

2020

|

nr 16(8)

73--80

PL

W pracy przedstawiono model matematyczny procesu hamowania w postaci transmitancji obiektu statycznego pierwszego rzędu, wyznaczony na podstawie danych uzyskanych podczas badań eksploatacyjnych. Do optymalizacji procesu wykorzystano dodatek Solver w arkuszu kalkulacyjnym Excel. We wprowadzeniu przedstawiono analizę teoretyczną modelu hamowania i wykazano, że prowadzi ona do równań różniczkowych nieliniowych.

EN

The paper presents the mathematical model of the braking process in the form of the first order static element transfer function determined on the basis of data obtained during operational tests. The Solver add-on in the Excel spreadsheet was used to optimize the process. In the introduction the theoretical analysis of braking process was presented and it was shown that it leads to nonlinear differential equations.

12

Positive extremal values and solutions of the exponential equations with application to automatics

Górecki H., Zaczyk M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2020

|

Vol. 68, nr 3

585--591

EN

In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. There are obtained the analytical solutions of the equations and also the maximal positive values of these solutions. The obtained sufficient conditions of the positivity of these solutions are defined by the Theorems. There are also formulated the necessary conditions of the positivity of these solutions. The analytical formulae enable the design of the system with prescribed properties.

13

Wykrywanie zwarć zwojowych w transformatorze energetycznym przy użyciu metody SFRA

Lewandowski K., Morańda H.

Przegląd Elektrotechniczny

|

2018

|

R. 94, nr 10

118--121

PL

W artykule przedstawiono wyniki badań odpowiedzi częstotliwościowej transformatora bez zwarcia oraz ze zwartymi wybranymi cewkami uzwojenia górnego napięcia. Do pomiarów zwierano od jednej do pięciu pierwszych cewek uzwojenia fazy L3. Pomiary wykonywano jednym z czterech sposobów: pomiar odpowiedzi danego uzwojenia przy rozwartych i zwartych zaciskach pozostałych uzwojeń oraz pomiar międzyuzwojeniowy indukcyjny i pojemnościowy. Z przeprowadzonych badań wynika, że najskuteczniejszym układem pomiarowym do wykrywania zwarcia zwojowego w transformatorach jest pomiar odpowiedzi częstotliwościowej przy pozostawieniu pozostałych zacisków na potencjale swobodnym.

EN

The article presents the results of the transformer frequency response investigations without and with shorting the selected upper voltage winding coils. For measurements first coils, from one to five, of the L3 phase winding, were shorted. The measurements were carried out in one of four ways: measurement of the frequency response of a selected winding with open and closed terminals of the remaining windings, measurement in an induction inter-winding system and measurement in a capacitive inter-winding system. The conducted tests show that the most effective measurement method for detecting of a winding short-circuit in transformers is to measure the frequency response with the remaining terminals on the floating potential.

14

Analiza właściwości dynamicznych wybranych podstawowych członów automatyki niecałkowitych rzędów

Luft M., Nowocień A., Pietruszczak D.

Autobusy : technika, eksploatacja, systemy transportowe

|

2018

|

R. 19, nr 12

514--525

PL

W artykule przedstawiono zastosowanie rachunku różniczkowego niecałkowitych rzędów (ang. fractional calculus) do opisu dynamiki zjawisk wybranych podstawowych członów automatyki. Dla analizowanych modelów, wyznaczono transmitancję operatorową całkowitego i niecałkowitego rzędu. Wyznaczono zależności opisujące charakterystyki czasowe i częstotliwościowe; na drodze symulacji komputerowej uzyskano charakterystyki analizowanych układów. Do badań symulacyjnych wykorzystano oprogramowanie MATLAB.

EN

The paper presents the application of the fractional calculus to describe the dynamics of selected basic elements of automation. For the analyzed models, the integer and noninteger order transmittance was determined. Relationships describing time characteristics were determined and frequency; on the path of computer simulation, the characteristics of the analyzed systems were obtained. MATLAB software was used for simulation research.

15

Propagation of rectangular pulses in the cascade of four-terminal networks

Włodarczyk M., Szczepaniak J.

Prace Naukowe Politechniki Śląskiej. Elektryka

|

2017

|

z. 3-4

31--36

EN

The paper presents a method of determining the transmittance of circuits with distributed parameters, in this case a transmission line consisting of a cascade of identical four-terminal networks. To construct the transmittance, signal flow graph theory was used. The result is provided in the form of a rational function which has two single poles and four multiple poles ((N-2)-tuple poles), if network consists of N four-terminal networks loaded with resistance. On the basis of the transmittance we calculated load voltage with unit step function or rectangular pulse at the input. Conclusions on transmission possibilities for digital signals have been formulated on the basis of obtained results.

PL

W pracy przedstawiono metodę wyznaczania transmitancji operatorowej obwodów o parametrach rozłożonych – linii długiej w oparciu o kaskadę jednakowych czwórników. Do konstrukcji tej transmitancji wykorzystano teorię grafów przepływu sygnałów. W wyniku otrzymano wyrażenie w postaci funkcji wymiernej, która posiada dwa bieguny jednokrotne i cztery bieguny N-2 krotne przy N czwórnikach obciążonych rezystancją. Na podstawie transmitancji obliczono przebieg napięcia na obciążeniu przy wymuszeniu funkcją jednostkową i impulsem prostokątnym. Uzyskane wyniki pozwoliły na sformułowanie wniosków dotyczących możliwości transmisyjnych dla sygnałów cyfrowych.

16

Analisis of field dynamics using numerically obtained normalized ordinary moments

Dudziak K., Brykalski A., Stawicki K.

Prace Naukowe Politechniki Śląskiej. Elektryka

|

2017

|

z. 1-2

49--60

EN

The article presents possibilities of describing the dynamics of the electromagnetic field making use of ordinary normalized moments. Numerical calculations has been carried out with the help of computer software COMSOL. Calculated moments have been used for determination of transfer function parameters.

PL

W artykule przedstawiono możliwości opisu dynamiki pola elektromagnetycznego z wykorzystaniem momentów zwykłych znormalizowanych. W pracy wykorzystano dane otrzymane w wyniku przeprowadzenia eksperymentu numerycznego, symulacji komputerowej w programie COMSOL. Obliczone momenty posłużyły do wyznaczenia modeli transmitancyjnych badanego układu.

17

Dynamic characteristics of magnetic coupling in horizontal axis wave energy device

Zhang J., Liu Y., Liu J., He T., Xie Y.

Polish Maritime Research

|

2017

|

S 3

165--170

EN

To solve the dynamic response problems of magnetic coupling in the horizontal axis wave energy device, this has researched the dynamic characteristicsof magnetic coupling. The fitting formula about torque and angle of the magnetic coupling is obtained through experiments. The mathematical models of the magnetic coupling torque transmission are established. The steady state error of the magnetic coupling and the transfer function of the output angle are obtained. The analytical solution of the step response of the output angle in time domain is derived. The influence of the torsional rigidity, the damping coefficient and the driven rotor’s rotational inertia on dynamic characteristics of the magnetic coupling isanalyzed. According to the analysis results, the design rules of magnetic coupling are proposed.

18

Diatom assemblages as indicators of salinity gradients : a case study from a coastal lake

Rzodkiewicz M., Gąbka M., Szpikowska G., Woszczyk M.

Oceanological and Hydrobiological Studies

|

2017

|

Vol. 46, No. 3

325--339

EN

In order to understand the variability of diatoms in coastal lakes and its relationship to salinity, the authors have conducted a two-year study at Lake Resko Przymorskie (the Southern Baltic coast), which has a salinity between 1.9-4.8 PSU. Redundancy analysis (RDA) was used to describe the relationship between the species composition and selected variables. Four of the 10 measured variables of surface water chemistry (Cl- and PO43- concentrations, temperature, and pH) significantly explained 23% of the variation in the diatom species composition. We found 82 taxa of diatoms (mostly tychoplanktonic) and determined the optimum and tolerance levels of salinity for predominant taxa (49 species with minimum 2% abundance). The optimum chloride concentration for the predominant diatoms ranged from 1471 to 2961 mg Cl- l-1. The most abundant brackish water species was Pseudostaurosiropsis geocollegarum. Brackish-freshwater diatoms were represented by Cyclotella atomus, Cyclotella meneghiniana, Diatoma tenuis and Staurosira subsalina. The most abundant fresh-brackish water diatoms were Amphora pediculus, Fragilaria sopotensis, Hippodonta hungarica, Pseudostaurosira brevistriata and Staurosira construens. Freshwater taxa accounted for as little as 1% of the population. This study provides new data on the ecology of coastal lakes and the possibility of using diatom-based transfer functions in the reconstruction of past environmental changes.

19

On scaling of ship seakeeping

Artyszuk J.

Prace Naukowe Politechniki Warszawskiej. Transport

|

2016

|

z. 112

9--24

EN

The widely accepted linear model of ship motions in waves is considered in frequencydomain, where the steady-state harmonic motions as response to harmonic waves are of interest. The solution of motion transfer functions is presented in dimensionless form with special concern about the dimensionless wave frequency as independent variable. Though some facts are known within ship model testing methodology, this detailed and careful derivation is aimed to enhance in-depth understanding of the seakeeping characteristics of a ship. It is also expected that a transfer functions data exchange between one full-scale ship and another of close geometry yet of different size will be more encouraged.

PL

Na bazie liniowego modelu dynamiki wyprowadzono funkcje przenoszenia sprzężonych kołysań statku na fali harmonicznej. Szczególny nacisk położono na pełne ujęcie bezwymiarowe, z istotną rolą bezwymiarowej częstości fali. Mimo że ta ostatnia jest szeroko stosowana w okrętowych badaniach modelowych, to jest stosunkowo rzadko wykorzystywana w przeliczaniu funkcji przenoszenia między statkami rzeczywistymi o różnych wielkościach, gdy takie charakterystyki są znane. Ma to znaczenie np. w szybkim modelowaniu większej klasy statków i oceny ryzyka eksploatacji, m.in. w systemach nadzoru ruchu. Zarówno sam sposób niniejszego wywodu, jak i dyskusja poszczególnych założeń i kroków ma stanowić przyczynek do lepszego rozumienia analizy bezwymiarowej ('bezwymiarowania') w odniesieniu do kołysań statku, i tym samym służyć zwiększeniu świadomości użytkowników narzędzi analitycznych i decydentów.

20

Transfer function–based impulse response analysis for a class of hyperbolic systems of balance laws

Bartecki K.

Control and Cybernetics

|

2015

|

Vol. 44, no. 3

327--355

EN

Results of the impulse response analysis for a class of dynamical systems, described by two weakly coupled linear partial diﬀerential equations of hyperbolic type, deﬁned on a one-dimensional spatial domain are presented. For the case of two boundary inputs of the Dirichlet type, the analytical expressions for the impulse response functions are derived based on the inverse Laplace trans form of the 2×2 transfer function matrix of the system. The inﬂuence of the boundary inputs conﬁguration on the impulse response functions is demonstrated. The considerations are illustrated with a practical example of a thin-walled double-pipe heat exchanger operating in parallel- and countercurrent-ﬂow modes, which correspond to the analyzed boundary conditions.