The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers. The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics. Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions. The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions. The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good. Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments. / QC 20100628

A boundedness structure (bornology) on a topological space is an ideal of subsets containing all singletons, that is, closed under taking subsets and unions of finitely many elements. In this paper we deal with the structure of the whole family of bounded subsets rather than the specific properties of them by means of certain functions that we define on a metrizable topological group. Our motivation is twofold: on the one hand, we obtain useful information about the structural features of certain remarkable classes of bounded systems, cofinality, local properties, etc. For example, we estimate the cofinality of these boundedness notions. In the second part of the paper, we apply duality methods in order to obtain estimations of the size of a local base for an important class of groups. This translation, which has been widely exhibited in the Pontryagin-van Kampen duality theory of locally compact abelian groups, is often very relevant and has been extended by many authors to more general classes of topological groups. In this work we follow basically the pattern and terminology given by Vilenkin in 1998.

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Made available in DSpace on 2016-06-02T20:28:30Z (GMT). No. of bitstreams: 1 6065.pdf: 865751 bytes, checksum: 22466d8659637f2282b6be8b0adb5a33 (MD5) Previous issue date: 2014-03-13 / Financiadora de Estudos e Projetos / This work is divided into two parts. In the first part, our goal is to present the theory of Hardy Spaces Hp(Rn), which coincides with the Lebesgue space Lp(Rn) for p > 1, is strictly contained in Lp(Rn) if p = 1, and is a space of distributions when 0 < p < 1. When 0 < p ^ 1, the Hardy spaces offers a better treatment involving harmonic analysis than the Lp spaces. Among other results, we prove the maximal characterization theorem of Hp, which gives equivalent definitions of Hp, based on different maximal functions. We will proof the atomic decom¬position theorem for Hp, which allow decompose any distribution in Hp to be written as a sum of Hp-atoms (measurable functions that satisfy certain properties). In this step, we use the strongly the of Whitney decomposition and generalized Calderon-Zygmund decomposition. In the second part, as a application, we will prove that nonlinear quantities (such as the Jacobian, divergent and rotational defined in Rn) identied by the compensated compactness theory belong, under natural conditions, the Hardy spaces. To this end, in addition to the results seen in the first part, will use the results as Sobolev immersions theorems ans the inequality Sobolev-Poincare. Furthermore, we will use the tings and results related to the context of differential forms. / Esse trabalho está dividido em duas partes.Na primeira, nosso objetivo e apresentar os espaços de Hardy Hp(Rn), o qual coincide com os espaços Lp(Rn), quando p > 1, esta estritamente contido em Lp(Rn) se p = 1, e e um espaço de distribuições quando 0 < p < 1. Quando 0 < p < 1, os espaços de Hardy oferecem um melhor tratamento envolvendo analise harmônica do que os espaços Lp(Rn). Entre outros resultados, provamos o teorema da caracterização maximal de Hp, o qual fornece varias, porem equivalentes, formas de caracterizar Hp, com base em diferentes funcões maximais. Demonstramos o teorema da decomposição atômica para Hp, 0 < p < 1, que permite decompor qualquer distribuição em Hp como soma de Hp-atomos (funções mensuráveis que satisfazem certas propriedades). Nessa etapa, usamos fortemente a de- composição de Whitney e a decomposto de Calderon-Zygmund generalizada. Na segunda parte, como uma aplicação, provamos que quantidades não-lineares (como o jacobiano, divergente e o rotacional definidos em Rn), identificadas pela teoria compacidade compensada pertencem, em condições naturais, aos espaços de Hardy. Para tanto, além dos resultados visto na primeira parte, usamos outros como os Teoremas de Imersões de Sobolev, a desigualdade de Sobolev-Poincaré. Usamos ainda, definições e resultados referentes ao contexto de formas diferenciais.

Analysis of the dead-time effect and other nonlinearities of the voltage source inverter was carried out in the introduction of the doctoral thesis. Three compensation strategies for vector controlled PMSM were proposed based on the analysis. The voltage disturbance observer with cost function of current errors is based on the model of PMSM, known machine parameters and easily measurable quantities. The second observer which estimates the dq- axes currents and the value of the voltage error with one parameter only is designed based on the harmonic analysis and Kalman filter algorithm. The third method combines an adaptive approach with feedback and voltage disturbance observer that is based on the PMSM model. Furthermore, the two compensation methods for vector controlled induction motor were proposed. In the first case, the standard compensation strategy is extended by a harmonic compensator that suppresses the residual 6th harmonic component in dq- axes currents. The last strategy detects the polarity of the estimated phase currents that are obtained by the Kalman filter. All compensation strategies have been verified by MATLAB/Simulink simulations and by experiments on real drives.

This diploma thesis deals with the analysis and design optimization of a speaker cabinet (enclosure) produced by the additive technology of 3D sand printing. The introductory part is devoted to the theory, both in the field of noise, vibration and the method of their calculations, as well as the theory of speakers and their systems. Numerical and experimental modal analysis is performed, which were compared to determine the mechanical properties of the new material, including material damping. This is followed by experimental and numerical harmonic analysis, with output in the form of a numerical model describing the behaviour of the structure during its excitation. The data are compared with a modal analysis of the internal acoustic space and the critical shapes and their frequencies are determined. At the end of the work, construction modifications are proposed to increase the rigidity of enclosures, the influence of which is evaluated on the created numerical models.

This master’s thesis deals with the dynamic behaviour of vertical Francis turbine, which is atypical its shaft length. In the first part of thesis, there is theoretic research of water turbine, which is followed by derivation of equations for the Stodola rotor. The second part deals with the creation of the turbine shaft in 1D and 3D. A modal analysis was performed in the ANSYS Workbench software, based on which the Campbell diagram is created and it was determined the critical speed. And the harmonic analysis from which was determined the forces response in radial bearings, amplitude of deviation in radial direction in the turbine impeller and the generator and the axial displacement located in turbine impeller and axial bearing. 1D and 3D solutions were compared between themselves.

This master’s thesis deals with the computational simulation of low-frequency noise inside the cabin of small commercial airplane VUT 100 Cobra. For this low-frequncy range deterministic methods: Final Element Method (FEM) and Boundary Element Method (BEM) are used for simulation of the dynamic behaviour of the object. FEM has been used to compute eigenmodes and eigenfrequences of the structure of the aeroplane cabin and of the acoustic space inside cabin. Then response to harmonic excitation of engine represented by unit forces in place of contact has been computed. Obtained velocities on the surface of the cabin are then used as the basis for the noise calculation inside the cabin using BEM. After that effect of some construction modifications on sound level inside cabin are evaluated by computational modelling.

The aim of this Master’s thesis Vibration Propagation Analysis of Coupled Structure Acoustic Space is to analyze vibration propagation in combustion engine, from combustion space through solid structure to fluid surroundings. Then analyze the noise increase as pressure changing in fluid space around the solid structure. There was made a analyze of single piston engine in different frequency and piston location. A simulation of distribution of a pressure waves was made in an ANSYS application.

Diploma thesis deals with static and dynamic analysis of a wooden arch footbridge. The computational model of the structure was created in ANSYS 15. Dynamic forces from wind and horses were applied to the model based on the modal analysis. The effects of these forces at resonance were evaluated by harmonic analysis.