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Design and realization of a new laboratory exercise with PLC B&R Automation
Cejpek, Zdeněk ; Němec, Zdeněk (referee) ; Lang, Stanislav (advisor)
This bachelor thesis is concerned with designing of a laboratory task primary dedicated for the course „Advanced control methods“, which for the education uses the instruments of company B&R Automation. From possible aproaches chooses modeling of dynamic systems using analog electrical circuits. Those circuits are realized in modular manner, in order to allow building models of various systems. The thesis also includes a desing of proper casing, which simplifies the manipulation by building of the systems. Using designed prototype modules, a model of a separately excited DC motor was built. This model is used for realization of the laboratory task, for which is provided a short manual including some basic program for Automation Studio. The thesis also briefly introduces the company B&R, it´s products and a PLC configuration used in courses „Advanced control methods“.
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Chaotic system modeling using MATLAB
Lejdar, Lukáš ; Raidl, Aleš (advisor) ; Šindelářová, Kateřina (referee)
In the presented bachelor's thesis we study behavior of dynamical systems. Some interesting attributes of dynamical systems are presented using programs written by the author. For computational part of the programs MATLAB was used and for presentation of output data MATLAB in combination with GNUPLOT were used. Basic terms in chaos theory are explained with examples. In one-dimensional case we focus on the logistic map and we demonstrate a transition to chaos on it. In two-dimensional space we study the Hénon map and in three-dimensional space we take a closer look at some interesting attributes of the famous Lorenz system.
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A traffic flow with a bottelneck
Kovařík, Adam ; Janovský, Vladimír (advisor) ; Vejchodský, Tomáš (referee)
Title: A traffic flow with a bottelneck Author: Adam Kovařík Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vladimír Janovský, DrSc. Supervisor's e-mail address: janovsky@karlin.mff.cuni.cz Abstract: In this paper we study a microscopic follow-the-leader traffic model on a circu- lar road with a bottleneck. We assume that all drivers are identical and overtaking is not permitted. We sketch a small part of the rich dynamics of the model including Hopf and Neimark-Sacker bifurcations. We introduce so called POM and quasi-POM solutions and an algorithm how to search them. The main goal of this work is to investigate how the optimal velocity model with a bottleneck deals with so called aggressive behavior of dri- vers. The effect of variable reaction time and a combination of both named factors is also tested. Using numerical simulations we'll find out that aggressiveness and faster reactions have positive effect on traffic flow. In the end we discuss models with two bottlenecks and with one extraordinary driver. Keywords: dynamical systems, ODEs, traffic flow, bottleneck, aggressiveness. 1
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Analýza atraktorů zobecněných Newtonovských tekutin v 3d oblastech
Žabenský, Josef ; Pražák, Dalibor (advisor) ; Bulíček, Miroslav (referee)
We investigate a system of nonlinear partial differential equations, specifically the so-called Ladyzhenskaya model, in three spatial dimensions. It will be shown that after inclusion of a perturbation of a higher order, the model exhibits a considerably better behavior, in particular it will become quite straightforward to prove differentiability of solutions with respect to the initial condition. Due to this fact we may consequently employ the method of Lyapunov exponents to estimate the fractal dimension of the exponential attractor. First, however, it will be necessary to show existence and uniqueness of solutions, improved regularity and existence of a compact invariant set for the entire system.
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Visual Educational System of Fractals
Friedrich, Tomáš ; Škarvada, Jaroslav (referee) ; Gajda, Zbyšek (advisor)
The target of this work is to explain basics of fractals generation and theory. The introdaction to the fractal geometry is mentioned first. Certain types od fractals are explained and demostrated by examples next.For easier understanding of all mentioned types of fractals a grafical aplication was designed where it is possible to experience fractals characteristics and behaviour. The aplication is available on the internet.
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Equivalent circuit realizations of the simple chaotic oscillators
Kobza, Jaromír ; Dostál, Tomáš (referee) ; Petržela, Jiří (advisor)
The aim of this paper is to introduce with basic theory the problems encountered when considering the circuit implementation of autonomous RC chaotic oscillator with nonlinearity. All oscillator prototypes are based on one type of universal oscillator circuit. This circuit is able to generate a lot of attractors on condition of different entrance parameters. The design is based on a mathematical simulation, which includes the generation of electronic circuit values. The work is focused the transformation of these values to operational circuit configuration and simulation in a circuit simulator. The final task is to acquire chaotic attractors. Oscilloscope and spectrum analyser photos will verify the operation.
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Universal and fully analog oscillator with transconductance amplifiers
Kus, Václav ; Zaplatílek, Karel (referee) ; Hruboš, Zdeněk (advisor)
The aim of this thesis is to design a universal analog oscillator using transconductance amplifiers. For studying behaviour of chaotic dynamical systems can be used systems Class C. Suitable way for the purpose modeling dynamic phenomena arising in these systems is an electronic circuit that exhibits the same behavior as modeled system. After familiarization with the basic principles of synthesis of integrators systems, and studying the involvement of frequently used functional blocks were designed the concept of universal chaotic oscillator using transconductance amplifiers. The functionality of this circuit has been verified by PSpice simulation program. A typical feature of chaotic oscillator is extremely sensitivity to initial conditions. Each small change on the initial parameters can lead to major change in the shape of the attractor. The result of this thesis is a functional sample of a universal chaotic oscillator, which was verified by the dynamic behavior of the given differential equations.
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