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The Importance of Laplace Transform in Regulation Theory
Kovářová, Karolína ; Dobrovský, Ladislav (referee) ; Dosoudilová, Monika (advisor)
This bachelor's thesis deals with the significant role of Laplace transform in regulation theory. The theoretical part is dedicated to the properties of this integral transform and the description of the control system. The usage of Laplace transform in search of process variable, step and impulse function is demonstrated on specific examples of oscillation theory. The final part offers a view on Laplace transform using MATLAB software.
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OPC client for regulatory control modelling in COMES system
Brzobohatý, Jan ; Šír, Michal (referee) ; Pásek, Jan (advisor)
It was created program of the OPC client which simulates behavior of a continuous dynamical system. The simulated continuous dynamical system is described by the differential equation. The numerical solution of the differential equation simulates response of the dynamical system. The OPC client is connected to the control system with the regulatory program via the OPC server. The response calculated by OPC client and the action of the control system program transferred via OPC communication allow modeling and tuning the continuous control program implemented in the control system.
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Periodic problem for the Duffing equation
Asante, Michael Onwona ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
Při matematickém modelování fyzikálních systémů se používají obyčejné diferenciální rovnice různých tvarů. Diferenciální rovnice popisující tyto systémy jsou často složité nelineární rovnice, avšak pomocí vhodných aproximací nelinearity lze odvodit jednoduché rovnice zvané Duffingovy rovnice, které lze analyticky studovat. V matematickém modelování mechaniky problém hledání periodických řešení těchto Duffingových rovnic úzce souvisí s existencí periodických vibrací jeho odpovídajícího nelineárního oscilátoru. V této práci je provedena analýza řešení a existence řešení v autonomních a neautonomních případech uvažované Duffingovy rovnice s podporou simulací v MATLAB.
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Automatic Computation Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of numerical calculations. The reader is acquainted with the numerical solution of differential equations and the parallel, serial, and series-parallel numerical integrator. The practical aim of this work is to design control circuits for the three mentioned variants of integrators. The design includes the development of a software simulator of the control circuit for the series-parallel integrator in a fixed point.
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Frequency Responses
Urbánek, Radim ; Kraus, Michal (referee) ; Kunovský, Jiří (advisor)
The aim of this MSc Thesis is to create a system for automatic generation of frequency characteristics of electrical circuits. These circuits are described by differential equations. A special simulator of RLC circuit has been created and frequence response, vector diagram can be generated. This system has been mainly suggested for application in education. The process of solving differential equations is based on the Taylor method. Systems in general is the theoretical part of this project. Different definitions of systems their divission ,basic phenomenons and mathematical devices are described there. Next chapter deals with the mathematical devices for solving differential equations which makes the basis for description of phenomenons in these systems. There are also systems TKSL and TKSL/C. In the next chapter I was investigaty the analyze of vector diagrams for simple and more difficult circuits. I have found a solution for actual circuit by this technique. The last chapter is devoted to the frequency characteristics and descriptions of simulation program for generation the frequency characteristics.
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Pursuit problems: basic models and their analysis
Neugebauer, Tomáš ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This thesis is focused on creation of mathematical models and analysis of basic pursuit problems. In particular, the Perrault's problem, the Bouguer's problem, the Hathaway’s problem, the snail–racehorse problem and the Bailey's problem are involved. Each of the problems is solved analytically or numerically, including qualitative analysis.
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Simulation of electrophysiological experiments
Kubáček, Svatopluk ; Provazník, Ivo (referee) ; Rychtárik, Milan (advisor)
Simulation of electrophysiological experiments enables to gain valuable data about bioelectrical processes occurring on isolated cells. This thesis deals with basic principals allowing the creation of bioelectrical phenomenons and measuring techniques that need to be used in order to collect information about these phenomenons. The outcome of the thesis is a programme that serves as an instrument for simulation of measuring techniques applied on Luo-Rudy model. The programme contains basic measuring techniques – current clamp and voltage clamp – providing the possibility to change basic parameters of the model. The results of this work are later compared with the accessible literature.
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Electric Circuits Simulations in a Specialized Parallel System
Janko, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
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