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EN
Schemes are presented for calculating tuples of solutions of matrix polynomial equations using continued fractions. Despite the fact that the simplest matrix equations were solved in the second half of the 19th century, and the problem of multiplier decomposition was then deeply analysed, many tasks in this area have not yet been solved. Therefore, the construction of computer schemes for calculating the sequences of solutions is proposed in this work. The second-order matrix equations can be solved by a matrix chain function or iterative method. The results of the numerical experiment using the MatLab package for a given number of iterations are presented. A similar calculation is done for a symmetric square matrix equation of the 2nd order. Also, for the discrete (time) Riccati equation, as its analytical solution cannot be performed yet, we propose constructing its own special scheme of development of the solution in the matrix continued fraction. Next, matrix equations of the n-th order, matrix polynomial equations of the order of non-canonical form, and finally, the conditions for the termination of the iterative process in solving matrix equations by branched continued fractions and the criteria of convergence of matrix branching chain fractions to solutions are discussed.
2
EN
Time-of-use (TOU) electricity pricing has been applied in many countries around the world to encourage manufacturers to reduce their electricity consumption from peak periods to oﬀ-peak periods. This paper investigates a new model of Optimizing Electricity costs during Integrated Scheduling of Jobs and Stochastic Preventive Maintenance under time of-use (TOU) electricity pricing scheme in unrelated parallel machine, in which the electricity price varies throughout a day. The problem lies in assigning a group of jobs, the ﬂexible intervals of preventive maintenance to a set of unrelated parallel machines and then scheduling of jobs and ﬂexible preventive maintenance on each separate machine so as to minimize the total electricity cost. We build an improved continuous-time mixed-integer linear programming (MILP) model for the problem. To the best of our knowledge, no papers considering both production scheduling and Stochastic Preventive Maintenance under time of-use (TOU) electricity pricing scheme with minimization total Electricity costs in unrelated parallel machine. To evaluate the performance of this model, computational experiments are presented, and numerical results are given using the software CPLEX and MATLAB with then discussed.
3
Using fuzzy logic to stabilize the position of a Multi Rotor
EN
The article is a continuation of research into a stabilization system for the Unmanned Aerial Vehicle of vertical takeoff and landing. The stabilization system was designed on the basis of a fuzzy logic Mamdani type controller. In the framework of the research, the authors built a test stand with a Multi Rotor model, which allows "Hardware In The Loop" testing in real time. The control system was written in the Matlab/Simulink software and implemented to the Arduino microcontroller.
PL
Artykuł stanowi kontynuację badań nad układem stabilizacji do modelu Bezzałogowego Statku Powietrznego pionowego startu i lądowania. System stabilizacji zaprojektowany został w oparciu o regulator logiki rozmytej typu Mamdani. W ramach badań wykonane zostało stanowisko testowe z modelem quadrocoptera pozwalające na wykonywanie testów HIL „Hardware In The Loop” w czasie rzeczywistym. System sterowania napisany został w oprogramowaniu Matlab/Simulink i zaimplementowany do mikrokontrolera Arduino.
EN
At present, concentrations of pharmaceuticals in surface and ground waters are low; however, even low concentrations of certain substances may prove very harmful. One of such pharmaceutical drugs is diclofenac, a popular non-steroidal anti-inflammatory drug (NSAID). For this reason, it is important to determine its mobility in groundwater and to estimate parameters of migration. Authors conducted column tests for two porous media: an artificial one, consisting of glass granules, and a natural one, i.e., sandur sand obtained from a site north of the city of Poznań (Poland). During the test, impulse breakthrough curves of chloride ions and diclofenac were recorded. The results were used to identify a specific sorption model and to determine values of migration parameters. Solutions of the inverse problem using optimisation methods and of equations of mathematical migration models were carried out in a MATLAB environment. Based on test results, the mobility of diclofenac is shown to be very high and comparable to that of chloride ions. The tests also revealed a slight and irreversible sorption of diclofenac on grains of both porous media.
EN
The aim of this study is to optimize the volume of a furniture frame to make it lighter, while still meeting the same load requirements. The finite element method (FEM) and MATLAB nonlinear programming were utilized for the optimization. A beech stool frame was taken as an example. First, the finite element model was set up and analyzed to obtain the internal forces of the stool frame, and the internal forces were investigated to obtain the maximum critical forces in each type of member. Then constraints were obtained to determine the limitations for minimizing the volume of the stool frame, which was defined as the objective function subject to constraints. Finally, the objective function and constraints were programmed and solved using MATLAB software, and as a result the minimum volume and dimensions of members were determined. An experimental test was conducted to determine whether the optimized stool was strong enough to carry the same loads. The results showed the optimized stool to be 58% lighter than the non-optimized version, while also satisfying the requirements of GB 10357-3. In conclusion, the method is suitable for the optimization of a furniture frame, making it lighter and reducing the manufacturer’s material costs.
6
Neural network model of vehicle suspension
EN
Vehicle suspension is a complex mechanical system – many interconnected parts, influencing each other. There are some components which mathematical description is complicated. For example, damper itself, has nonlinear characteristic. Therefore, creating of accurate mathematical model of suspension system is a bit difficult work. In this paper we present two ways how to do it – classical and non-classical approach with using artificial intelligence tool (artificial neural network).
PL
Zawieszenie pojazdu to złożony system mechaniczny -wiele wzajemnie połączonych części wpływa na siebie nawzajem. Istnieją pewne elementy, których opis matematyczny jest skomplikowany. Na przykład sam tłumik ma charakter nieliniowy. Dlatego stworzenie dokładnego matematycznego modelu układu zawieszenia jest skomplikowane. W niniejszym artykule przedstawiono dwa sposoby budowy modelu matematycznego - klasyczne i nieklasyczne podejście z wykorzystaniem narzędzia sztucznej inteligencji (sztucznej sieci neuronowej).
PL
Artykuł przedstawia analizę wydajności samonadążnego systemu fotowoltaicznego własnego projektu. Za pomocą opracowanych skryptów wyznaczono charakterystyki zmiany napięcia i prądu w czasie. W badaniach zastosowano luksomierz do zmierzenia natężenia różnych źródeł światła (żarówki, świetlówki, światła słonecznego w słoneczny oraz pochmurny dzień). Na podstawie zmierzonego napięcia na wyjściu z modułu fotowoltaicznego i prądu ładowania akumulatora, wyznaczono charakterystyki dla zastosowanego układu w środowisku MATLAB i przeanalizowano wyniki pomiarów. Sprawdzono również wydajność modułu fotowoltaicznego podczas symulacji zabrudzeń jego powierzchni. Opisano skrypt sterujący napisany w środowisku Keil, który odpowiadał za pomiary wydajności nadążnego systemu fotowoltaicznego.
EN
The article presents the analysis of the efficiency of your own self-directed solar system. Using the developed scripts, the characteristics of voltage and current change over time were determined. The studies used a luxmeter to measure the intensity of various light sources (light bulbs, fluorescent lamps, sunlight on sunny and cloudy day). Based on the measured voltage at the output from the photovoltaic module and the battery charging current, the characteristics for the applied system in the MATLAB environment were determined and the measurement results were analyzed. The efficiency of the photovoltaic module during simulation of soil contamination was also checked. A control script written in the Keil environment was described, which was responsible for the performance measurements of the follow-up photovoltaic system.
8
Symulator robota mobilnego uwzględniający uszkodzenia
PL
Przedmiotem pracy badawczej jest symulator robota mobilnego Explorer 6WD, który uwzględnia stan pełnej zdatności oraz stany z uszkodzeniami. Omówiono elementy składowe symulatora robota oraz przedstawiono modele jego otoczenia, które zrealizowane są w środowisku V-REP. W ramach prac badawczych zaprojektowano i utworzono sieć ROS, która umożliwia integrację symulatora z modułami zewnętrznymi zrealizowanymi z wykorzystaniem środowiska MATLAB®/Simulink®. W tej części pracy objaśniono sposób komunikacji pomiędzy programami oraz omówiono strukturę i zawartość poszczególnych wiadomości. Scharakteryzowano modele uszkodzeń oraz przedstawiono interfejs użytkownika. W artykule zawarto również opis wybranych wyników badań weryfikacyjnych, które potwierdzają dużą przydatność opracowanego rozwiązania.
EN
The focus of the paper is on the simulator of the Explorer 6WD mobile robot taking into account faultless and faulty conditions. There are discussed the components of the mobile robot simulator and environment models which are implemented in the V-REP software. As a part of the research work, a ROS network has been designed and created, which enables integration of the simulator with external modules realized using the MATLAB®/ Simulink® environment. This part of the paper explains how to communicate between ROS nodes and discusses the structure and content of ROS messages. In the paper, fault models are characterized and a user interface is presented as well. This study also contains a description of selected results of verification tests that confirm the effectiveness of the developed approach.
9
Structural optimization coupled with materials selection for stiffness improvement
EN
An application of a Finite Element Model updating is presented in this paper. Two Finite Element models were considered: a reinforced plate and a thin-walled beam. The two parts were numerically calculated in ANSYS Mechanical APDL and MATLAB programs. ANSYS performs Finite Element calculations, and a MATLAB programming code was used to control the optimization procedure. Geometric variables were chosen, to evaluate the value of the defined objective function. The material was picked using available selection charts, to find the most adequate one for the study. It has been concluded that the transveral displacement of the models modified by the optimization process decreased sharply in relation to the original state.
EN
In this paper an extensive comparative performance study is carried out between No-load and load condition of an open loop model of a Brushless Direct Current (BLDC) Motor drive fed from a two-level voltage source inverter (VSI) under 120-degree conduction mode, using simulations in a MATLAB based software environment. BLDC motors are currently growing in popularity and replacing the brush motor in many applications, as they can be used in both low and high-speed vehicle systems and also in servo drives. The high reliability, torque to inertia ratio, high efficiency, high power density, ease of control and mainly the brushless operation make BLDC motors superior to others. It has a permanent magnet as a rotor with a balanced 3-phase armature in its stator. The armature winding is driven by a power electronics inverter which is switched in synchronism with the rotor position, sensed by an optical encoder or a Hall Effect sensor. It is found that torque ripple can be minimized by tuning the value of rotor position, no load condition and trapezoidal armature phase current. The different performance parameters for no-load and load condition of the BLDC motor such as phase voltages, phase currents, speed, electromagnetic torque, d and q axis current and rotor position etc. are determined in MATLAB environment.
EN
The article discusses the automatic control system of the Diamond DA42 aircraft anti-icing system. In the analysis of the issue of icing, four parameters were taken into account: air temperature, cloud humidity, temperature of the aircraft and precipitation. On the basis of the initial parameters, the authors determined the icing intensity, which is likely to occur on the aircraft skin. By automating the activities related to the activation of the de-icing system, it is possible to significantly relieve the pilot and increase the safety of air operations, particularly in conditions, which are conducive to the formation of icing. The authors performed a thirty-minute electronic simulation of the flight in real atmospheric conditions. The article discusses the obtained results of the simulation. Designed system uses fuzzy logic. The system inputs and output were determined and fuzzy expert inference system was developed in MATLAB software and Fuzzy Logic Toolbox. The proper system work was verified with use of MATLAB/Simulink software. Use of that kind of systems can significantly relieve the pilot and increase the safety of air operations, particularly in conditions, which are conducive to the formation of icing.
EN
The numerical modelling of combustion phenomena is an important task due to safety issues and development and optimization of engines. Laminar burning velocity (LBV) is one of the most important physical properties of a flammable mixture. Knowing its exact value if crucial for assessment of flame stabilization, turbulent flame structure. It influences strongly safety, probability of knocking combustion and it is one of parameters used for assessment and development of detailed chemical kinetic mechanisms. Hence, the goal of this work is to develop models by means of Machine Learning algorithms for predicting laminar burning velocities of single-fuel C1-C7 normal hydrocarbon and air mixtures. Development of the models is based on a large experimental data set collected from literature. In total more than 1000, LBVs were accumulated for hydrocarbons from methane up to n-heptane. The models are developed in MATLAB 2018a with use of Machine Learning toolbox. Algorithms taken into account are multivariate regression, support vector machine, and artificial neural network. Performance of the models is compared with most widely used detailed chemical kinetics mechanisms’ predictions obtained with use of LOFEsoft. These kind of models might be efficiently used in CFD combustion models based on flamelet approach. The main advantage in comparison to chemical kinetics calculation is much shorter computational time needed for computations of a single value and comparable performance in terms of R2 (coefficient of determination), RMSE (root-mean-square error) and MAE (mean absolute error).
EN
This paper presents different models and results of simulations of MEMS vibrating gyroscope in Matlab/SIMULINK environment. Each model is created with different approach, using different blocks and different physics. Therefore author presents his proposal of mathematical, electrical equivalent and physical models. Results obtained from these models can give some hints regarding design and dimensions of some crucial parts of MEMS gyroscope. Here, decoupled vibrating sensor is considered, which minimize drive and sense motion mutual influence.
PL
W publikacji przedstawiono zagadnienie modelowania matematycznego dynamiki ruchu kończyny górnej. Do opracowania modelu wykorzystano równanie różniczkowe Lagrange’a drugiego stopnia, które wymaga znajomości trajektorii ruchu bez konieczności poznawania sił reakcji w stawach. Można dzięki temu przybliżać momenty działające w stawach bez konieczności stosowania specjalistycznej aparatury medycznej przystosowanej do badania momentów, a wykorzystując jedynie systemy „Motion Capture”, które wyznaczają położenie znaczników na podstawie danych pomiarowych. Modelowanie dynamiki ruchu przy użyciu jedynie współrzędnych znaczników może być wykorzystywane w medycynie, szczególnie w fizjoterapii oraz rehabilitacji. Na podstawie założonych ruchów w stawach obliczono momenty, które wywołują dane ruchy i następnie rozwiązano proste zagadnienie dynamiki. Założenia modelowe opracowano na podstawie danych antropologicznych. Do sprawdzenia poprawności działania modelu wykorzystano dane literaturowe oraz własne przemyślenia na temat mechaniki ruchu po okręgu.
EN
The issue of mathematical modelling of upper limb motion is presented in the article. The Lagrange differential equation of secondary order was used for development of the presented model. The solution of the equation requires data describing of movement trajectory without necessity of assessment of reaction forces in joints. Referring to above it is possible to estimate the moments of force activated in joints which are determined by position of markers presented ony in the Motion Capture System. The calculation of moments of force was performed with predetermined motions in joints. Model assumptions were developed on the base of literature and own experiences, particularly on anthropological data and fundamentals of mechanics of circular motion.
EN
This paper presents a digraph-building method designed to find the determination of realization of two-dimensional dynamic system. The main differences between the method proposed and other state-of-the-art solutions used include finding a set of realizations (belonging to a defined class) instead of only one realization, and the fact that obtained realizations have minimal size of state matrices. In the article, the proposed method is described, compared to state-of-the-art methods and illustrated with numerical examples. To the best of authors’ knowledge, the method shown in the paper is superior to all other state-of-the-art solutions both in terms of number of solutions and their matrix size. Additionally, MATLAB function for determination of realization based on the set of state matrices is included.
PL
Celem pracy było wykonanie badań symulacyjnych oraz opracowanie procedury numerycznej do automatycznego generowania danych z programu EPANET poprzez nadrzędne oprogramowanie MATLAB. W badaniach wykorzystano dokładny model matematyczny sieci, który uzupełniono o zawory. Zakres pracy obejmował wykonanie badań symulacyjnych modelowej sieci wodociągowej z uwzględnieniem dwóch różnych modeli sieci (uproszczonego i dokładnego) oraz różnych stanów operacyjnych (poborów wody). Następnie dokonano wyboru odpowiedniego zestawienia procedur numerycznych i środowisk programistycznych w celu automatycznego generowania danych poprzez połączenie programu do modelowania EPANET ze środowiskiem MATLAB. Dzięki prawidłowo wykonanemu i skalibrowanemu modelowi sieci udało się przeprowadzić założone badania symulacyjne. Opracowana procedura programistyczna do generowania danych numerycznych z modelu w programie EPANET umożliwiła pełną automatyzację obliczania i przetwarzania generowanych z symulacji danych w środowisku MATLAB.
EN
The purpose of the work was to perform simulation tests and develop a numerical procedure for the automatic generation of data from the EPANET program through MATLAB's superior software. The research used the exact mathematical model of the network, which was supplemented by valves. The scope of work included performing simulation tests of the model water supply network, taking into account 2 different network models (simplified and precise) and various operational states (water abstraction). The selection of an appropriate set of numerical procedures and programming environments was then made to generate data automatically by combining the EPANET modeling program with the MATLAB environment. Thanks to a properly made and calibrated network model, simulation tests were successfully carried out. The developed programming procedure for generating numerical data from the EPANET model enabled full automation of the calculation and processing of data generated from simulation in the MATLAB environment.
EN
This paper presents an algorithm for programming an industrial robot’s end effector path based on 2D images. The first section gives a brief overview of modern solutions for industrial robot implementation. The next section describes the test set-up and the software used in tests. The work also presents the key elements of the controller algorithm and their operation: 2D image processing with MATLAB software, generating the code for robot control in AS language, and implementation of the produced codes to the Kawasaki RS003N robot.
EN
Solution of a dynamic system is commonly demanding when analytical approaches are used. In order to solve numerically, describing the motion dynamics using differential equations is becoming indispensable. In this article, Newton’s second law of motion is used to derive the equation of motion the governing equation of the dynamic system. A quarter model of the suspension system of a car is used as a case and sinusoidal road profile input was considered for modeling. The state space representation was used to reduce the second order differential equation of the dynamic system of suspension model to the first order differential equation. Among the available numerical methods to solve differential equations, Euler method has been employed and the differential equation is coded MATLAB. The numerical result of the second degree of freedom, quarter suspension system demonstrated that the approach of using numerical solution to a differential equation of dynamic system is suitable to easily simulate and visualize the system performance.
PL
W pracy przedstawiamy przykładowe wykorzystanie GeoGebry do wizualizacji pojęć matematycznych za pomocą apletów do ćwiczeń, oraz animacji do umieszczenia w e-kursach. Opisujemy też scenariusz wykorzystania GeoGebry i MATLABA na zajęciach stacjonarnych z algebry liniowej.
EN
In the first part of the paper we present some applets created in GeoGebra. These examples can be used in the process of teaching mathematics both in classroom and as online materials in e-courses. Visualizing difficult mathematical terms and notions we help young people to understand mathematics and even touch and feel it. The second part of our article is devoted to possible scenarios of utilizing MATLAB and GeoGebra in classroom teaching during linear algebra lessons. MATLAB is commonly used software by students of technology universities for performing numerical calculations.
EN
The article proves the possibility of implementing a software package for digital overcurrent protection testing in the Matlab-Simulink environment. A comparison of simulation results obtained with the use of the proposed software package with the results obtained with the use of the other software, as well as with the calculations of transient processes has been performed. The parameters calculation methods of the proposed software package are presented.
PL
Artkuł udowadnia możliwość implementacji pakietu oprogramowania przeznaczonego do badania cyfrowego zabezpieczenia nadprądowego w środowisku Matlab-Simulink. Przeprowadzono porównanie wyników uzyskanych za pomocą proponowanego pakietu oprogramowania i innego oprogramowania, jak również obliczeń stanów przejściowych. Zaprezentowano metody wyznaczania parametrów proponowanego pakietu oprogramowania.
Strona / 13
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