Indiana University-Purdue University Indianapolis (IUPUI) / In order to conform to pollutant-control regulations and minimize NOx emissions, modern household boilers and central heating systems are moving toward premixed combustors. These combustors have been successful with regards to emissions along with efficiency. However, their implementation has been associated with acoustical instability problems that could be solved through precise optimization in design rather than trial and error experimentation. This thesis introduces an experimental apparatus, which is designed to investigate the acoustic instability problem at the flame level. The goal is an experimental determination of the flame transfer function and comparison of the experimental data with a theoretical model of the flame. An experimental procedure is designed to diagnose the origins of the combustion instabilities by measurement of the flame transfer function. This research is carried out in three steps. The first step is to understand the acoustic instability problem through study of the theoretical models of the flame transfer function and selection of a model, which is most functional in industrial applications. A xiii measurement technique for the flame transfer function is developed according to the required accuracy in measurements, repeatability, and configurability for a wide range of operating conditions. Subsequently, an experimental apparatus is designed to accommodate the flame transfer function measurement technique. The components of the acoustic system are carefully sized to achieve precise measurement of the system parameters such as flows, pressures, and acoustic responses, and the apparatus is built. The apparatus is operated to measure the flame transfer function at several operating conditions. The experimentally measured flame transfer function is compared with a theoretical model for further verification. The experimental apparatus provides an improved assessment of the acoustic instability problem for industrial applications.

No description available.

LISA, the Laser Interferometry Space Antenna, is the 3rd large mission (L3) of the ESA program Cosmic Vision with a junior partnership from NASA planned to be launched around 2034. Space-based gravitational wave observatories such as LISA have been developed for observation of sources that produce gravitational wave (GW) signals with frequencies in the mHz regime. The frequency band is achievable by having a longer-baseline interferometer compared to ground-based detectors. In addition, the significant size of the LISA arms-length guarantees the detection of many astrophysical sources. The absence of Newtonian noise in space, which is the dominant source of noise below few hertz for ground-based detectors, allows LISA to be sensitive to lower frequency compared to the former. Thus, going to space allows studying different sources with respect to the ones of interest for ground-based detectors such as supermassive black holes. Although having very long baselines between the satellites generally increases the sensitivity to gravitational waves, it also implies many technical challenges, such that a balance must be found between scientific performance and technical feasibility.In the actual proposal LISA is designed to be a constellation of three identical spacecraft in a triangular formation with six active laser links connecting the three spacecraft, which are separated by 2.5 million km. To fulfil the observatory program every spacecraft has a minimum requirement of two free-falling test masses, two telescopes, and two lasers. The detector’s center-of-mass follows a circular, heliocentric trajectory, trailing 20 degrees behind the Earth and the plane of the detector is tilted by 60 degrees with respect to the ecliptic.The goal of LISA is to detect GWs which manifest themselves as a tiny fluctuation in the frequency of the laser beam measured at the phase-meter. Thus, to detect GW you need to compete with many sources of disturbance that simulate the effect of a GW frequency modulation. Laser noise is an example of those. Therefore, one key element in the LISA data production chain is the post-processing technique called Time Delay Interferometry aimed at suppressing the intense laser frequency noise that would completely cover the astrophysical signal. Data from the six independent inter-satellite links, connecting the three spacecraft, are properly time-shifted and combined to form the final scientific signal. This post-processing technique circumvents the impossibility of physically building in space an equal arm interferometer, which would intrinsically beat the frequency noise by comparing light generated at the same time.The following work is focused on revisiting the Time-Delay-Interferometry (TDI) for LISA and studying the usage of all the possible TDI combinations we can build for the LISA instrument characterisation and science extraction. Many possible TDI combinations that suppress the frequency noise have been identified in the past and this thesis revisits the TDI technique focusing on the physical interpretation of it, that is a virtual interference of photons that have been travelling through the constellation via different paths but performing the same total distance. We illustrate all possible TDI configurations that suppress the laser noise contribution to the level required by the mission to understand how TDI channels can be best used for the diagnostic of the instrument and LISA science. With this philosophy, we develop an algorithm to search for all possible combinations that suppress laser noise at the same level as the classical TDI X, Y, and Z combinations presented in the TDI literature. This algorithm finds new combinations that fulfill the noise suppression requirement as accurately as X, Y, and Z.The LISA mission has been also advertised to probe the early Universe by detecting a stochastic GW background. Once the laser frequency noise has been subtracted, the stochastic signal, both cosmological and astrophysical, is itself going to contribute to the noise curve. Therefore it is necessary to have a good estimate of the noise of the instrument to discriminate between the stochastic background signal and the LISA noise.The strategy that has been suggested in the literature is to use the TDI T, insensitive (up to a certain order) to GW signals to estimate the pure instrumental noise in order to distinguish between the LISA background noise and the GW stochastic signal. Following this idea, as instrument noise is expected to have multiple, independent sources, this thesis explores combinations that could allow discriminating among those sources of noise, and between them and the GW signal, with the purpose of understanding how we can characterise our instrument using TDI. We illustrate special TDI combination signals in LISA, in addition to TDI T, that we call null-channels, which are ideally insensitive to gravitational waves and only carry information about instrumental noise. Studying the noise properties that can be extracted by monitoring these interferometric signals, we state that individual acceleration noise parameters are not well constrained. All null-channels behave as an ideal Sagnac interferometer, sensitive just to a particular linear combination of the six test masses acceleration that resembles a rotational acceleration signal of the entire constellation. Moreover, all null-channels show approximately the same signal to noise ratio remarkably suppressed relative to that of the TDI X. In support and application of our theoretical studies, we also give an introduction on calibrating the LISA instrument by injecting spurious signals in a LISA link and see how these propagates through a TDI channel. Indeed, this will be useful to calibrate the instrument during operations and also to build the basis for the data analysis to discriminate spurious signals from gravitational waves. My contribution to the results we present in this thesis can be summarised as the following. I supported the studies and the realisation of the search TDI algorithm whose results are published in the article. In particular, I took care of cataloging the new TDI combinations and consolidating the results we found. I have updated the TDI combinations reported in the above-mentioned work, the final version of it is reported in this thesis. I worked on the characterisation of these combinations concerning secondary noises such as clock noise, readout noise, residual laser frequency noise, and acceleration noise. In particular, I studied how these noises are transferred through the various TDI and I derive the correspondent analytical models. I then realize a software with Wolfram Mathematica, design to load and combines phase data produced by an external simulator to build the final TDI outputs, besides I also did the noise models’ validation. The basis of this program was then used to implement these TDI combinations in LISANode. Finally, I developed the algorithm to study how disturbances in force, such as glitches, and simple GW signals, such as monochromatic GW binaries, propagate through TDI and null-channels. Moreover, I tested through simulations the validity of these TDI and null-channels to distinguish instrumental artefact from GW signals and to characterise the instrumental noise.

Text in Afrikaans / Summaries in Afrikaans and English / In Afrikaans, soos in NederJands en Duits, word saamgestelde woorde aanmekaar geskryf. Nuwe woorde word dus voortdurend geskep deur woorde aanmekaar te haak Dit bemoeilik die proses van woordafkapping tydens teksprosessering, wat deesdae deur rekenaars gedoen word, aangesien die verwysingsbron gedurig verander. Daar bestaan verskeie afkappingsalgoritmes en tegnieke, maar die resultate is onbevredigend. Afrikaanse woorde met korrekte lettergreepverdeling is net die elektroniese weergawe van die handwoordeboek van die Afrikaanse Taal (HAT) onttrek. 'n Neutrale netwerk ( vorentoevoer-terugpropagering) is met sowat. 5 000 van hierdie woorde afgerig. Die neurale netwerk is verfyn deur 'n gcskikte afrigtingsalgoritme en oorfragfunksie vir die probleem asook die optimale aantal verborge lae en aantal neurone in elke laag te bepaal. Die neurale netwerk is met 5 000 nuwe woorde getoets en dit het 97,56% van moontlike posisies korrek as of geldige of ongeldige afkappingsposisies geklassifiseer. Verder is 510 woorde uit tydskrifartikels met die neurale netwerk getoets en 98,75% van moontlike posisies is korrek geklassifiseer. / In Afrikaans, like in Dutch and German, compound words are written as one word. New words are therefore created by simply joining words. Word hyphenation during typesetting by computer is a problem, because the source of reference changes all the time. Several algorithms and techniques for hyphenation exist, but results are not satisfactory. Afrikaans words with correct syllabification were extracted from the electronic version of the Handwoordeboek van die Afrikaans Taal (HAT). A neural network (feedforward backpropagation) was trained with about 5 000 of these words. The neural network was refined by heuristically finding a suitable training algorithm and transfer function for the problem as well as determining the optimal number of layers and number of neurons in each layer. The neural network was tested with 5 000 words not the training data. It classified 97,56% of possible points in these words correctly as either valid or invalid hyphenation points. Furthermore, 510 words from articles in a magazine were tested with the neural network and 98,75% of possible positions were classified correctly. / Computing / M.Sc. (Operasionele Navorsing)

<p>Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.</p> <p> </p> <p>To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.</p> <p> </p> <p>In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.</p> <p> </p> <p>The main objectives of this thesis are:</p> <p>1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver</p> <p>2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).</p> <p>3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.</p> <p> </p> <p>The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.</p> <p> </p><br>

L’identification et la caractérisation des sources acoustiques restent encore aujourd’hui deux sujets d’importance pour les industriels qui ont besoin de techniques permettant d’identifier des sources acoustiques ou vibratoires sur des surfaces complexes dans un environnement acoustique non contrôlé. La thèse que nous présentons ici s'inscrit dans ce cadre. Nous y étudions les qualités d'une méthode inverse, appelée iPTF (pour inverse Patch Transfer Functions, pour la résolution de ce problème particulier. Nous consacrerons le premier chapitre de notre étude à la synthèse bibliographique des méthodes les plus pertinentes permettant de résoudre des problèmes similaires. Nous soulignerons également les difficultés de ces méthodes pouvant être liées à leurs applications pratiques ou à leurs fondements théoriques. Dans un second chapitre, nous présenterons la méthode iPTF à partir de sa formulation directe, c'est-à-dire de la source vers le bruit rayonné. Celle-ci est une approche par sous-structuration de domaines permettant l’étude des problèmes vibro-acoustiques en basses et moyennes fréquences. Nous montrerons particulièrement la façon dont l'association des deux formulations directe et indirecte permet de définir une méthode pouvant conduire jusqu'à l'identification des trois champs de vitesses, de pressions et d'intensités sur la surface de l'objet source. Notre troisième chapitre sera consacré à la présentation des premiers résultats d'identification dans un cas d'application numérique simple. Nous effectuerons, dans les chapitres quatre et cinq, une étude des principaux paramètres conditionnant les résultats donnés par la méthode. Le premier de ces deux chapitres présentera la mise en place d'un code de calcul permettant de résoudre rapidement le problème de rayonnement d'une structure simple. La méthode ainsi définie sera utilisée dans le chapitre cinq afin de générer de nombreux champs rayonnés présentant des caractéristiques différentes de façon à étudier la stabilité de la méthode iPTF face à la variation de différents paramètres. Un sixième chapitre présentera une étude approfondie faite sur les ondes évanescentes qui prennent une part non négligeable dans le champ rayonné par les structures. Ces ondes évanescentes, par définition, ne peuvent pas être mesurées au delà du champ proche, ce qui peut être la cause d'une part des défauts d'identification rencontrés lors de l'application de notre méthode. L'étude faite ici aura pour but de déterminer l'importance de ces ondes évanescentes dans le champ rayonné. Nous présenterons enfin, dans un dernier chapitre, les résultats de mesures expérimentales réalisées. / Nowadays, both identification and characterization of acoustical sources remain two important topics in industry as such method are often required to localize acoustical or vibrational sources on complex surfaces in an acoustical environment that may not be well-known. The PhD Thesis we present hereby is set in this purpose. We will study the ability of an inverse method, named iPTF (standing for inverse Patch Transfert Functions) used to solve this particular problem. In our first chapter we will present a bibliographical study of the different methods dealing with the resolution of similar problems. We will particularly underline the difficulties encountered with these methods, either regarding their practical application or their theoretical bases. The presentation of the iPTF method will be made in the second chapter. This presentation will be organized starting from the direct formulation, that is from the source to the radiated sound. This direct method is a sub-domai decomposition based approach, allowing the study of vibro-acoustical problems in low and mid frequencies. We will especially explain how the association of both direct and reverse formulation enables to identify the pressure, velocity and intensity fields on the source. The third chapter will concerne the presentation of the first identification results in a simple numerical application. In the fourth and fifth chapters, the main parameters conditioning the results given by our method will be studied. The first of these two chapters will introduce a calculation routine used to compute quickly the radiation field of a simple structure. This routine will then be used in our fifth chapter in order to build numerous fields having different characteristics. Using all these fields will let us know the stability of our method regarding different parameters. A sixth chapter will present a precise study of evanescent waves that constitute a non-neglectful part of the radiated field. According to their definition, those evanescent waves cannot be taken into account beyond the near-field, and this may be the reason of some difficulties while applying our method. The objective of the study herein presented is to determine the importance of those evanescent waves in the radiated field. We eventually present, in a last chapter, the results of experimental measures conducted during the preparation of this PhD Thesis.

Este trabalho tem como objetivo o desenvolvimento de um conjunto de procedimentos de avaliação da qualidade de equipamentos mamográficos a partir do processamento de imagens digitais obtidas com a exposição radiográfica de objetos de testes (phantoms) padronizados. O sistema desenvolvido permite a avaliação de diversos parâmetros físicos de qualidade da imagem radiográfica com simplicidade e rapidez, sem abrir mão da precisão, com o mínimo tempo e uso dos equipamentos. Os principais parâmetros avaliados relacionados à qualidade de um sistema de imagem são: a resolução espacial - pela medida da função de transferência de modulação (MTF) - o contraste - medido pela curva sensitométrica e o ruído - pela medida da densidade espectral de ruído (NPS). Dessa forma, o sistema desenvolvido atende às recomendações do ICRU (International Commission on Radiation Units and Measurements), que trata das diretrizes para controle de qualidade de imagens radiográficas em todo o mundo. A partir da medida desses três parâmetros de qualidade é possível também aferir a eficiência de detecção quântica (DQE) do sistema de imagem mamográfica, que permite uma avaliação completa da qualidade da imagem em função da dose recebida pelo paciente. Os resultados obtidos comprovam a possibilidade da aplicação prática do sistema desenvolvido, o qual proporciona uma avaliação completa da qualidade da imagem formada pelo equipamento. Todos os resultados apresentaram baixa estimativa de erro, fundamentados pela análise da incerteza nos processos de medida. Além disso, a avaliação por meio do DQE permitiu realizar uma comparação entre os sistemas mamográficos envolvidos nessa pesquisa. Assim, com base nesses resultados é possível afirmar que o sistema computacional desenvolvido pode desempenhar um papel fundamental na avaliação da qualidade em sistemas de imagens mamográficas. / The aim of this work is to develop a set of procedures for quality assurance of mammographic equipment by the digital image processing of radiographic images of standard test objects (phantoms) acquired by the radiographic equipment. It allows the evaluation of several physical parameters of the radiographic image quality by a simple and quick procedure, with good accuracy, using the equipment the shortest time as possible. The main evaluated parameters related to the quality of an imaging system are: spatial resolution - by measuring the modulation transfer function (MTF) - image contrast - by the measurement of the H&D curve and noise - evaluated by the noise power spectrum (NPS). Thus, it attends the recommendations of the ICRU (International Commission on Radiation Units and Measurements), which deals as the guidelines for quality assurance of radiographic images all over the world. Through these quality parameters is possible to measure the detective quantum efficiency (DQE) of any mammographic system, which allows a full evaluation of the image quality related to the dose absorbed by the patient. The results confirm the possibility of the practical application of the developed system, which provides a full evaluation of the image quality, acquired by the mammographic equipment. All results showed low error estimation, substantiated by the analysis of the uncertainty in measurements procedures. Moreover, the evaluation through the DQE allowed to perform a comparison of mammography systems involved in this research. Thus, based on these results, it is possible to confirm that its system can perform a fundamental part of the quality assurance in mammographic images system.

Este trabalho tem como objetivo o desenvolvimento de um conjunto de procedimentos de avaliação da qualidade de equipamentos mamográficos a partir do processamento de imagens digitais obtidas com a exposição radiográfica de objetos de testes (phantoms) padronizados. O sistema desenvolvido permite a avaliação de diversos parâmetros físicos de qualidade da imagem radiográfica com simplicidade e rapidez, sem abrir mão da precisão, com o mínimo tempo e uso dos equipamentos. Os principais parâmetros avaliados relacionados à qualidade de um sistema de imagem são: a resolução espacial - pela medida da função de transferência de modulação (MTF) - o contraste - medido pela curva sensitométrica e o ruído - pela medida da densidade espectral de ruído (NPS). Dessa forma, o sistema desenvolvido atende às recomendações do ICRU (International Commission on Radiation Units and Measurements), que trata das diretrizes para controle de qualidade de imagens radiográficas em todo o mundo. A partir da medida desses três parâmetros de qualidade é possível também aferir a eficiência de detecção quântica (DQE) do sistema de imagem mamográfica, que permite uma avaliação completa da qualidade da imagem em função da dose recebida pelo paciente. Os resultados obtidos comprovam a possibilidade da aplicação prática do sistema desenvolvido, o qual proporciona uma avaliação completa da qualidade da imagem formada pelo equipamento. Todos os resultados apresentaram baixa estimativa de erro, fundamentados pela análise da incerteza nos processos de medida. Além disso, a avaliação por meio do DQE permitiu realizar uma comparação entre os sistemas mamográficos envolvidos nessa pesquisa. Assim, com base nesses resultados é possível afirmar que o sistema computacional desenvolvido pode desempenhar um papel fundamental na avaliação da qualidade em sistemas de imagens mamográficas. / The aim of this work is to develop a set of procedures for quality assurance of mammographic equipment by the digital image processing of radiographic images of standard test objects (phantoms) acquired by the radiographic equipment. It allows the evaluation of several physical parameters of the radiographic image quality by a simple and quick procedure, with good accuracy, using the equipment the shortest time as possible. The main evaluated parameters related to the quality of an imaging system are: spatial resolution - by measuring the modulation transfer function (MTF) - image contrast - by the measurement of the H&D curve and noise - evaluated by the noise power spectrum (NPS). Thus, it attends the recommendations of the ICRU (International Commission on Radiation Units and Measurements), which deals as the guidelines for quality assurance of radiographic images all over the world. Through these quality parameters is possible to measure the detective quantum efficiency (DQE) of any mammographic system, which allows a full evaluation of the image quality related to the dose absorbed by the patient. The results confirm the possibility of the practical application of the developed system, which provides a full evaluation of the image quality, acquired by the mammographic equipment. All results showed low error estimation, substantiated by the analysis of the uncertainty in measurements procedures. Moreover, the evaluation through the DQE allowed to perform a comparison of mammography systems involved in this research. Thus, based on these results, it is possible to confirm that its system can perform a fundamental part of the quality assurance in mammographic images system.

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

The interaction of an HVDC converter with the connected power system is of complex nature. An accurate model of the converter is required to study these interactions. The use of analytical small-signal converter models provides useful insight and understanding of the interaction of the HVDC system and the connected system components. In this thesis analytical models of the HVDC converters are developed in the frequency-domain by calculating different transfer functions for small superimposed oscillations of voltage, current, and control signals. The objective is to study the dynamic proprieties of the combined AC-DC interaction and the interaction between different HVDC converters with small signal analysis. It is well known that the classical Bode/Nyquist/Nichols control theory provides a good tool for this purpose if transfer functions that thoroughly describe the 'plant' or the 'process' are available. Thus, there is a need for such a frequency-domain model. Experience and theoretical calculation have shown that voltage/power stability is a very important issue for an HVDC transmission link based on conventional line-commutated thyristor-controlled converters connected to an AC system with low short circuit capacity. The lower the short circuit capacity of the connected AC system as compared with the power rating of the HVDC converter, the more problems related to voltage/power stability are expected. Low-order harmonic resonance is another issue of concern when line-commutated HVDC converters are connected to a weak AC system. This resonance appears due to the presence of filters and shunt capacitors together with the AC network impedance. With a weak AC system connected to the HVDC converter, the system impedances interact through the converter and create resonances on both the AC- and DC-sides of the converter. In general, these resonance conditions may impose limitations on the design of the HVDC controllers. In order to improve the performance of the HVDC transmission system when it is connected to a weak AC system network, a reactive compensator with a voltage source converter has been closely connected to the inverter bus. In this thesis it is shown that the voltage source converter, with an appropriate control strategy, will behave like a rotating synchronous condenser and can be used in a similar way for the dynamic compensation of power transmission systems, providing voltage support and increasing the transient stability of the converter. / QC 20100708