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Classical and fractional modelling of oscillatory motion
Hošek, Jaromír ; Tomášek, Petr (referee) ; Kisela, Tomáš (advisor)
In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position.
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Integral transforms and their applications
Béreš, Lukáš ; Štarha, Pavel (referee) ; Franců, Jan (advisor)
This bachelor's thesis deals with integral transforms and their applications. Its aim is to get together basic properties of Laplace and Fourier transforms and then illustrate their application in solving partial dierential equations, by calculating specic tasks with numerical experiments in MATLAB software.
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Foundations of Fractional Calculus on Time Scales
Dolník, Matej ; Nechvátal, Luděk (referee) ; Kisela, Tomáš (advisor)
Bakalářská práce pojednává o zlomkovém kalkule na časových škálach, přesněji - zavádí zlomkový kalkulus na časových škálach a taktéž vyšetřuje jednoznačnost axiomatické definice zavádějící mocninné funkce. Po zavedení základních pojmů je předmětem diskuze hlavně zobecněná Laplaceova transformace a důkaz jednoznačnosti zobecněné Laplaceovy transformace, která je použita jako nástroj pro dokázání jednoznačnosti zlomkových mocniných funkcií na časových škálach.
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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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Fractional order LTI SISO systems modelling using generalized Laguerre functions
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.
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Transient effect at the output of a continuous-time LTI second order system controlled pulse-width modulation
Petera, Martin ; Richter, Miloslav (referee) ; Jura, Pavel (advisor)
The aim of this thesis is to determine the size of overshoot produced at the output of a linear continuous second order system controlled by pulse width modulation depending on the period and duty cycle of the modulation and system parameters. This thesis contains analytic calculation of the size of overshoot produced at the output of the second order system with damping ratio > 0, except the damping ratio equals to 1 (i.e. both underdamped and damped system) depending on period and duty cycle of the modulation. This thesis also includes a comparison of partial analytic results to numerical simulation in Matlab program and also with measurement at second order system model.
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Transient effect at the output of a linear dynamic system controlled pulse-width modulation
Petera, Martin ; Richter, Miloslav (referee) ; Jura, Pavel (advisor)
The goal of this work is to determine the size of overshoot produced at the output of a linear continuous second order system controlled by pulse width modulation. This work contains the calculation of the output signal response of the system in the time domain using the Laplace transform. The calculations of the amplitude of the output signal based on the pulse width modulation and system parameters are performed in this work. Finally the possibilities was given to determine the suitable period of pulse width modulation for required ripple. All the important calculations were compared with the simulations in the MATLAB-SIMULINK program and with the measurement at the real inertia second order cell.
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Electronic circuits with fractal dynamics
Vojtová, Klára ; Guzan,, Milan (referee) ; Petržela, Jiří (advisor)
In the first section of this work is further analyzed the theories of differential equations and their computation and applications. The second part I addict to more detailed description of the Laplace transform, a sentence that is relevant to this area and also using the Laplace transform to solve electronic circuits. The third part of this project involves the theory of electronic circuits, especially the analysis and synthesis. The final and most important part is attended to circuits with fractal dynamics, design fractal approximation of the dynamics of capacitors in the frequency domain, has finally created its own electronic circuit measurement and evaluation results.
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