|
|
Mathematical modelling of walking robots
Kiša, Daniel ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
Tato diplomová práce se zabývá matematickými modely kráčejících robotů. Dva z těchto modelů jsou vybrány a analyzovány. Pasivní model "rimless wheel" , který slouží jako základ pro další, složitější modely, je podrobně analyzován. "Compass gait" model dvounohého robota je v práci analyzován a numericky simulován v programovacím jazyce Python. Metoda pro nalezení podmínek pro pasivní chůzi robota je rovněž implementována.
|
|
|
Unconventional Signals Oscillators
Hruboš, Zdeněk ; Galajda, Pavol (referee) ; Štork, Milan (referee) ; Petržela, Jiří (advisor)
Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.
|
|
|
Process Control with Dynamic Resource Scheduling
Šinkora, Jan ; Kočí, Radek (referee) ; Janoušek, Vladimír (advisor)
This project pursues issues on the border of information technologies and process optimization. Previously published concepts of~modeling projects and shared resources with object-oriented Petri nets are presented and further expanded. The possibilites of~the use of~genetic algorithms for dynamic realtime optimization of the resource schedules are explored. The resource constrained project sheduling problem is presented and it is shown, how instances of the problem can be implemented. A more complex model that is inspired by real production systems is then created. Next, a control agent, which monitors a running production system and allows for it's dynamic optimization is designed. The whole system is implemented in the Squeak Smalltalk environment with the use of the tool PNtalk, which is an experimental implementation of the object oriented Petri nets paradigm.
|
|
| |
|
|
Modelling of postcritical states of slender structures
Mašek, Jan ; Eliáš, Jan (referee) ; Frantík, Petr (advisor)
The aim of the presented thesis is to create a compact publication which deals with properties, solution and examination of behavior of dynamical systems as models of mechanical structures. The opening portion of the theoretical part leads the reader through the subject of description of dynamical systems, offers solution methods and investigates solution stability. As the introduction proceeds, possible forms of structure loading, damping and response are presented. Following chapters discuss extensively the possible approaches to system behavior observation and identification of nonlinear and chaotic phenomena. The attention is also paid to displaying methods and color spaces as these are essential for the examination of complex and sensitive systems. The theoretical part of the thesis ends with an introduction to fractal geometry. As the theoretical background is laid down, the thesis proceeds with an application of the knowledge and shows the approach to numerical simulation and study of models of real structures. First, the reader is introduced to the single pendulum model, as the simplest model to exhibit chaotic behavior. The following double pendulum model shows the obstacles of observing systems with more state variables. The models of free rod and cantilever serve as examples of real structure models with many degrees of freedom. These models show even more that a definite or at least sufficiently relevant monitoring of behavior of such deterministic systems is a challenging task which requires sophisticated approach.
|
|
| |
|
|
Attractors in the complex dynamics of turbulent convection
Kašný, Jakub ; Nechvátal, Luděk (referee) ; Macek, Michal (advisor)
This Bachelor's thesis deals with an application of the HAVOK (Hankel Alternative View of Koopman) numerical method, which seeks attractors and predicts intermittent phenomena in dynamical systems, to data from Rayleigh-Bénard convection (RBC), which are measured at Brno Institute of Scientific Instruments in the group of Cryogenics and Superconductivity. This thesis discusses the theory on which the HAVOK is built and further deepens it compared to the article [2]. Furthermore, it enlightens some issues as the best selection of the embedding dimension r, which we selected based on the quality of regression that HAVOK creates, or the use of the Koopman operator and Taken's embedding theorem, that weren't explicitly explained in the article [2]. We discovered three different methods to compute HAVOK regressions based on and using the codes attached to the article. In the thesis, we inspect the matrices of ordinary differential equations, their behaviour when the initial values are changed and their stability for the different regression models and embedding dimensions. The solution with different initial conditions is plotted so that the attractivity can be seen. Part of the thesis contains description of RBC, its equations of motion and characteristic dimensionless numbers that describe the convection. Moreover, the thesis describes how the data are obtained and processed normally and how are processed in new ways based on the HAVOK method.
|
|
|
Model of Properties of Dynamic Systems
Sztefek, Jan ; Kolka, Zdeněk (referee) ; Biolková, Viera (advisor)
The thesis deals with modeling algorithm for mathematical description of dynamical system written in status description, which makes it possible to changing coefficients status array A, B. Algorithm is programmed in MATLAB-SIMULINK environment. Dynamical system in this thesis is side movement of plane in space. Created program don’t deal with changing coefficients of status array A, B only, but it deals with automatic change this coefficients when surveyed output function exceed requested limit too. Among others the thesis is focused on dynamical properties of plane, inference of theorems, linearization and derived side movement. Last but not least this thesis deals with analysis and approximation of side movement. This all is made for possibility of derive final status movement of plane. The thesis is supplemented for detail description created program and user guide for work with program, which make it possible to easier usage for ignorant peoples. The end of thesis is supplemented for tested simulations of side movement of plane in space with usage real data. All this simulations are real so it’s possible to claim that program works correctly.
|
|
|
Attractors in the complex dynamics of turbulent convection
Kašný, Jakub ; Nechvátal, Luděk (referee) ; Macek, Michal (advisor)
This Bachelor's thesis deals with an application of the HAVOK (Hankel Alternative View of Koopman) numerical method, which seeks attractors and predicts intermittent phenomena in dynamical systems, to data from Rayleigh-Bénard convection (RBC), which are measured at Brno Institute of Scientific Instruments in the group of Cryogenics and Superconductivity. This thesis discusses the theory on which the HAVOK is built and further deepens it compared to the article [2]. Furthermore, it enlightens some issues as the best selection of the embedding dimension r, which we selected based on the quality of regression that HAVOK creates, or the use of the Koopman operator and Taken's embedding theorem, that weren't explicitly explained in the article [2]. We discovered three different methods to compute HAVOK regressions based on and using the codes attached to the article. In the thesis, we inspect the matrices of ordinary differential equations, their behaviour when the initial values are changed and their stability for the different regression models and embedding dimensions. The solution with different initial conditions is plotted so that the attractivity can be seen. Part of the thesis contains description of RBC, its equations of motion and characteristic dimensionless numbers that describe the convection. Moreover, the thesis describes how the data are obtained and processed normally and how are processed in new ways based on the HAVOK method.
|
|
|
On a model of corruption in a democratic society
Splítek, Martin ; Janovský, Vladimír (advisor) ; Mlčoch, Lubomír (referee)
The aim of this work is to study the behavior of serious social pheno- menon - corruption, and we do this through a mathematical model of corruption in a democratic society, published in [1]. The model is a dynamical system of three differential equations, specified by three variables and ten parameters. The model is studied by means of numerical analysis, namely, the method of nume- rical integration of ordinary differential equations and the method of numerical continuation. We used toolbox Matcont [2], which works in the environment of program MATLAB [3]. The result is commented parametric study of the pheno- menon of corruption. Keywords: ordinary diferential equations, dynamic systems, bifurcation ana- lysis 1
|
guest ::
