597 resultados para Cabos elétricos
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In this work are presented the results of research on the variation of vertical plasma drift from the F layer that commonly occurs during the period close to the going down of the sun (between 21UT - 22UT), and consisting of an increase in the F layer in time of day and a drop at night on the cities of Natal / RN (The 33.7º, 5.6º S), Fortaleza / CE (38.45º O, 3.9º S) and Cachoeira Paulista / SP (45.0ºO, 22.7º S ). Thus, data was used (ionograms) virtual height t ( h' ) as a function of the frequency F for the layer of the ionosphere. These data were collected through ionossonda type CADI (Canadian Advanced Digital Ionosonde) to the cities of Natal and Fortaleza, and the Digisonde DPS to the town of Cachoeira Paulista. They considered only the data available 2000 maximum solar year. With the virtual height ( h' ) data reduced in the frequencies of 6MHz and 5MHz, the next step was to calculate. The results showed that the variability of the vertical drift rate F ionospheric layer periods of magnetic storms is related both to the penetration of the electric fields as the disturbance dynamo electric fields.
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Ceramic materials the alumina base are large industrial applications. They are required for these products, specific characteristics obtained by following strict criteria during the manufacturing process. However, after life, not always these products are reused by a suitable waste management process. In ceramist context, advance research aimed at the reuse of waste aimed at obtaining ceramics and composite materials, with marked reduction of conventional raw materials. Aiming to generate scientific, technological and environmental contribution, this work studied to obtain a composite of alumina ceramic (Al2O3) and sodium beta alumina (NaAl11O17 ), and as starting materials the residue of the ceramic insulator of spark plugs, as a source alumina (Al2O3) powder and unusable sodium bicarbonate (NaHCO3) of fire extinguishers, as a source of sodium oxide (Na2O). The final ceramic product was obtained from a conventional mixture of sodium aluminum oxide in appropriate molar proportions. Sample spark plugs were obtained, discarded by lifetime, specific to a manufacturer, which, after passing through mechanical stress (grinding, magnetic purification, washing, drying and grinding the high energy), which resulted in residue powder with ceramic content of 84.34 % alumina (Al2O3), found by FRX chemical analysis, the phases present and identified by DRX. The dry chemical fire extinguisher, baking soda-based (NaHCO3) with expired, was obtained through direct collection of the waste generated during maintenance. Subjected to heat treatment at 120 °C , the NaHCO3 powder was decomposed in sodium oxide ( Na2O), which, subjected to chemical analysis (FRX) and mineralogical (DRX) revealed a content of 86.62 % sodium oxide (Na2O) . In the following steps the experimental procedure, chemical formulations were made on a molar basis of the starting material (1:9, 1:10 and 1:11 de Na2O/ Al2O3) inclusion of additives, milling parameters, sieve analysis, dilatometry, conformation of specimens, sintering in firing steps at 800 °C , 1000 °C and 1.200 °C with varying stays 30 , 60 and 120 minutes in each of the levels. The characterization of the final product was made by the following physical tests: water absorption, porosity, linear shrinkage, mineralogical analysis by DRX and microstructural analysis by MEV. A higher formation of sodium beta alumina (NaAl11O17), in sintered specimens in levels of 1.200 °C and 120 minutes, despite the prevailing coexistence of alpha phase alumina (Al2O3). From the results obtained opens up prospects for the reuse of waste studied in this work, the potter context and in other technological areas.
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Ceramic materials the alumina base are large industrial applications. They are required for these products, specific characteristics obtained by following strict criteria during the manufacturing process. However, after life, not always these products are reused by a suitable waste management process. In ceramist context, advance research aimed at the reuse of waste aimed at obtaining ceramics and composite materials, with marked reduction of conventional raw materials. Aiming to generate scientific, technological and environmental contribution, this work studied to obtain a composite of alumina ceramic (Al2O3) and sodium beta alumina (NaAl11O17 ), and as starting materials the residue of the ceramic insulator of spark plugs, as a source alumina (Al2O3) powder and unusable sodium bicarbonate (NaHCO3) of fire extinguishers, as a source of sodium oxide (Na2O). The final ceramic product was obtained from a conventional mixture of sodium aluminum oxide in appropriate molar proportions. Sample spark plugs were obtained, discarded by lifetime, specific to a manufacturer, which, after passing through mechanical stress (grinding, magnetic purification, washing, drying and grinding the high energy), which resulted in residue powder with ceramic content of 84.34 % alumina (Al2O3), found by FRX chemical analysis, the phases present and identified by DRX. The dry chemical fire extinguisher, baking soda-based (NaHCO3) with expired, was obtained through direct collection of the waste generated during maintenance. Subjected to heat treatment at 120 °C , the NaHCO3 powder was decomposed in sodium oxide ( Na2O), which, subjected to chemical analysis (FRX) and mineralogical (DRX) revealed a content of 86.62 % sodium oxide (Na2O) . In the following steps the experimental procedure, chemical formulations were made on a molar basis of the starting material (1:9, 1:10 and 1:11 de Na2O/ Al2O3) inclusion of additives, milling parameters, sieve analysis, dilatometry, conformation of specimens, sintering in firing steps at 800 °C , 1000 °C and 1.200 °C with varying stays 30 , 60 and 120 minutes in each of the levels. The characterization of the final product was made by the following physical tests: water absorption, porosity, linear shrinkage, mineralogical analysis by DRX and microstructural analysis by MEV. A higher formation of sodium beta alumina (NaAl11O17), in sintered specimens in levels of 1.200 °C and 120 minutes, despite the prevailing coexistence of alpha phase alumina (Al2O3). From the results obtained opens up prospects for the reuse of waste studied in this work, the potter context and in other technological areas.
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Dissertação (Mestrado)
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Variable reluctance motors have been increasingly used as an alternative for variable speed and high speed drives in many industrial applications, due to many advantages like the simplicity of construction, robustness, and low cost. The most common applications in recent years are related to aeronautics, electric and hybrid vehicles and wind power generation. This paper explores the theory, operation, design procedures and analysis of a variable reluctance machine. An iterative design methodology is introduced and used to design a 1.25 kW prototype. For the analysis of the machine two methods are used, an analytical method and the finite element simulation. The results obtained by both methods are compared. The results of finite element simulation are used to determine the inductance profiles and torque of the prototype. The magnetic saturation is examined visually and numerically in four critical points of the machine. The data collected in the simulation allow the verification of design and operating limits for the prototype. Moreover, the behavior of the output quantities is analyzed (inductance, torque and magnetic saturation) by variation of physical dimensions of the motor. Finally, a multiobjective optimization using Differential Evolution algorithms and Genetic Algorithms for switched reluctance machine design is proposed. The optimized variables are rotor and stator polar arcs, and the goals are to maximize the average torque, the average torque per copper losses and the average torque per core volume. Finally, the initial design and optimized design are compared.
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The search for mitigation solutions, with respect to the effects of overvoltages linked to the energization and reclosing maneuvers of transmission lines include a challenging subject with strong impact on the insulation coordination of electrical systems. Although the recognition of classical and commercial proposals to mitigate these phenomena, other possibilities are certainly still worthwhile highlighting and investigations. In this context, the present work is grounded in the exposure of the physical and mathematical foundations of a strategy based on controlled switchings, whose moments to the line reclosing are pre-programmed. The computational evaluation of the effectiveness of the methodology is made using the ATP simulator, which are studies in a typical electrical system subjected to the action of short-circuits fallowed by shutdowns and subsequent reclosing, under the action of technology here focused and lack thereof.
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This work intent to study the motive power provided by the plane linear induction motor, in a lock condition. It uses a method of imposition of the electric current to the stator via a frequency convertor PWM driven by a refed platform. The reading of the motive power was performed by a load cell using an electronic circuit for reading and conditioning of the signal. Aiming a complete analysis of the linear motor, it was performed a computational modeling that employs all relevant parameters to the study of the locked machine. At the end it was held a theoric-experimental confrontation that evaluated the effectiveness of the proposed method.
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This work's objective is the development of a methodology to represent an unknown soil through a stratified horizontal multilayer soil model, from which the engineer may carry out eletrical grounding projects with high precision. The methodology uses the experimental electrical apparent resistivity curve, obtained through measurements on the ground, using a 4-wire earth ground resistance tester kit, along with calculations involving the measured resistance. This curve is then compared with the theoretical electrical apparent resistivity curve, obtained through calculations over a horizontally strati ed soil, whose parameters are conjectured. This soil model parameters, such as the number of layers, in addition to the resistivity and the thickness of each layer, are optimized by Differential Evolution method, with enhanced performance through parallel computing, in order to both apparent resistivity curves get close enough, and it is possible to represent the unknown soil through the multilayer horizontal soil model fitted with optimized parameters. In order to assist the Differential Evolution method, in case of a stagnation during an arbitrary amount of generations, an optimization process unstuck methodology is proposed, to expand the search space and test new combinations, allowing the algorithm to nd a better solution and/or leave the local minima. It is further proposed an error improvement methodology, in order to smooth the error peaks between the apparent resistivity curves, by giving opportunities for other more uniform solutions to excel, in order to improve the whole algorithm precision, minimizing the maximum error. Methodologies to verify the polynomial approximation of the soil characteristic function and the theoretical apparent resistivity calculations are also proposed by including middle points among the approximated ones in the verification. Finally, a statistical evaluation prodecure is presented, in order to enable the classication of soil samples. The soil stratification methodology is used in a control group, formed by horizontally stratified soils. By using statistical inference, one may calculate the amount of soils that, within an error margin, does not follow the horizontal multilayer model.
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As preocupações com o elevado consumo de combustíveis fósseis e a crescente poluição atmosférica conduziram ao desenvolvimento dos veículos elétricos e dos veículos elétricos híbridos. O crescimento do parque automóvel elétrico levou à necessidade de considerar a sua integração na rede eléctrica, ao nível dos impactos estimados, mas também na sua potencial contribuição para uma gestão inteligente do sistema, funcionando como um buffer da energia produzida, permitindo desacoplar a produção do consumo, e assim melhor a eficiência global. Neste trabalho foi efetuado um estudo relacionado com a ligação bidirecional entre os veículos eléctricos e a rede eléctrica que permitirá o uso das baterias instaladas nos veículos participar nesse apoio à rede, debruçando-se primeiramente sobre o desenvolvimento das baterias que permanecem como elos mais fracos. Utilizando diferentes ferramentas de simulação e de análise de resultados foi depois efetuado um estudo sobre dois sistemas alternativos capazes de implementar o conceito V2G respeitando as restrições do ponto de vista normativo. Os resultados obtidos a partir de uma simulação coordenada entre os programas Simulink/Matlab e PSIM permitiram demostram o bom funcionamento dos 2 sistemas propostos, permitindo ficar com a convicção que o conversor multinível será capaz de proporcionar os resultados desejados com um menor tempo de resposta.
Monitorização da carga de treino em Futsal: estudo piloto com jogadores amadores juniores e seniores
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Este foi um estudo piloto que pretendeu monitorizar a carga de treino em Futsal, com jogadores amadores juniores e seniores. A amostra do presente estudo foi composta por 8 jogadores de Futsal do sexo masculino, 4 juniores com idade média de 16.5±0.5 anos (estatura de 1.67±0.04 m e 59.2±2.21 Kg de massa corporal) e 4 seniores com idade média de 27.2±2.7 anos (estatura de 1.71±0.05 m e 69.7±7.5 Kg de massa corporal). Os jogadores competiam nos campeonatos distritais amadores de Futsal, na sua categoria, organizados pela Associação de Futebol de Leiria. Para a realização deste estudo recorreu-se a 4 unidades do ZephyrTM BioHarnessTM System (Zephyr Technology, Auckland, New Zealand). Trata-se de um sistema de monitorização wireless de dados fisiológicos e que tem a capacidade de medir a frequência cardíaca (FC), frequência respiratória (FR) e acelerometria (ACC). Os resultados obtidos mostram que o sistema utilizado registou as variáveis que se pretendiam estudar, sem limitações para o atleta, isto é, sem cabos ou artefactos, que limitassem os movimentos durante a unidade de treino. Verificou-se também que, no somatório de 8 unidades de treino, a frequência cardíaca média no grupo de juniores foi mais elevada do que a dos jogadores seniores (p = 0.029). A monitorização permitiu avaliar a intensidade das unidade de treino, permitindo identificar as respostas fisiológicas por jogador e por treino. Utilizando esta tecnologia é possível fazer um acompanhamento monitorizado de cada atleta por forma a analisar a sua adaptação e evolução fisiológica e fazer uma prescrição/planificação da sessão de treino mais adaptada a cada atleta.
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The human brain stores, integrates, and transmits information recurring to millions of neurons, interconnected by countless synapses. Though neurons communicate through chemical signaling, information is coded and conducted in the form of electrical signals. Neuroelectrophysiology focus on the study of this type of signaling. Both intra and extracellular approaches are used in research, but none holds as much potential in high-throughput screening and drug discovery, as extracellular recordings using multielectrode arrays (MEAs). MEAs measure neuronal activity, both in vitro and in vivo. Their key advantage is the capability to record electrical activity at multiple sites simultaneously. Alzheimer’s disease (AD) is the most common neurodegenerative disease and one of the leading causes of death worldwide. It is characterized by neurofibrillar tangles and aggregates of amyloid-β (Aβ) peptides, which lead to the loss of synapses and ultimately neuronal death. Currently, there is no cure and the drugs available can only delay its progression. In vitro MEA assays enable rapid screening of neuroprotective and neuroharming compounds. Therefore, MEA recordings are of great use in both AD basic and clinical research. The main aim of this thesis was to optimize the formation of SH-SY5Y neuronal networks on MEAs. These can be extremely useful for facilities that do not have access to primary neuronal cultures, but can also save resources and facilitate obtaining faster high-throughput results to those that do. Adhesion-mediating compounds proved to impact cell morphology, viability and exhibition of spontaneous electrical activity. Moreover, SH-SY5Y cells were successfully differentiated and demonstrated acute effects on neuronal function after Aβ addition. This effect on electrical signaling was dependent on Aβ oligomers concentration. The results here presented allow us to conclude that the SH-SY5Y cell line can be successfully differentiated in properly coated MEAs and be used for assessing acute Aβ effects on neuronal signaling.
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Alkali tantalates and niobates, including K(Ta / Nb)O3, Li(Ta / Nb)O3 and Na(Ta / Nb)O3, are a very promising ferroic family of lead-free compounds with perovskite-like structures. Their versatile properties make them potentially interesting for current and future application in microelectronics, photocatalysis, energy and biomedics. Among them potassium tantalate, KTaO3 (KTO), has been raising interest as an alternative for the well-known strontium titanate, SrTiO3 (STO). KTO is a perovskite oxide with a quantum paraelectric behaviour when electrically stimulated and a highly polarizable lattice, giving opportunity to tailor its properties via external or internal stimuli. However problems related with the fabrication of either bulk or 2D nanostructures makes KTO not yet a viable alternative to STO. Within this context and to contribute scientifically to the leverage tantalate based compounds applications, the main goals of this thesis are: i) to produce and characterise thin films of alkali tantalates by chemical solution deposition on rigid Si based substrates, at reduced temperatures to be compatible with Si technology, ii) to fulfil scientific knowledge gaps in these relevant functional materials related to their energetics and ii) to exploit alternative applications for alkali tantalates, as photocatalysis. In what concerns the synthesis attention was given to the understanding of the phase formation in potassium tantalate synthesized via distinct routes, to control the crystallization of desired perovskite structure and to avoid low temperature pyrochlore or K-deficient phases. The phase formation process in alkali tantalates is far from being deeply analysed, as in the case of Pb-containing perovskites, therefore the work was initially focused on the process-phase relationship to identify the driving forces responsible to regulate the synthesis. Comparison of phase formation paths in conventional solid-state reaction and sol-gel method was conducted. The structural analyses revealed that intermediate pyrochlore K2Ta2O6 structure is not formed at any stage of the reaction using conventional solid-state reaction. On the other hand in the solution based processes, as alkoxide-based route, the crystallization of the perovskite occurs through the intermediate pyrochlore phase; at low temperatures pyrochlore is dominant and it is transformed to perovskite at >800 °C. The kinetic analysis carried out by using Johnson-MehlAvrami-Kolmogorow model and quantitative X-ray diffraction (XRD) demonstrated that in sol-gel derived powders the crystallization occurs in two stages: i) at early stage of the reaction dominated by primary nucleation, the mechanism is phase-boundary controlled, and ii) at the second stage the low value of Avrami exponent, n ~ 0.3, does not follow any reported category, thus not permitting an easy identification of the mechanism. Then, in collaboration with Prof. Alexandra Navrotsky group from the University of California at Davis (USA), thermodynamic studies were conducted, using high temperature oxide melt solution calorimetry. The enthalpies of formation of three structures: pyrochlore, perovskite and tetragonal tungsten bronze K6Ta10.8O30 (TTB) were calculated. The enthalpies of formation from corresponding oxides, ∆Hfox, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -203.63 ± 2.84 kJ/mol, - 358.02 ± 3.74 kJ/mol, and -1252.34 ± 10.10 kJ/mol, respectively, whereas from elements, ∆Hfel, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -1408.96 ± 3.73 kJ/mol, -2790.82 ± 6.06 kJ/mol, and -13393.04 ± 31.15 kJ/mol, respectively. The possible decomposition reactions of K-deficient KTa2.2O6 pyrochlore to KTaO3 perovskite and Ta2O5 (reaction 1) or to TTB K6Ta10.8O30 and Ta2O5 (reaction 2) were proposed, and the enthalpies were calculated to be 308.79 ± 4.41 kJ/mol and 895.79 ± 8.64 kJ/mol for reaction 1 and reaction 2, respectively. The reactions are strongly endothermic, indicating that these decompositions are energetically unfavourable, since it is unlikely that any entropy term could override such a large positive enthalpy. The energetic studies prove that pyrochlore is energetically more stable phase than perovskite at low temperature. Thus, the local order of the amorphous precipitates drives the crystallization into the most favourable structure that is the pyrochlore one with similar local organization; the distance between nearest neighbours in the amorphous or short-range ordered phase is very close to that in pyrochlore. Taking into account the stoichiometric deviation in KTO system, the selection of the most appropriate fabrication / deposition technique in thin films technology is a key issue, especially concerning complex ferroelectric oxides. Chemical solution deposition has been widely reported as a processing method to growth KTO thin films, but classical alkoxide route allows to crystallize perovskite phase at temperatures >800 °C, while the temperature endurance of platinized Si wafers is ~700 °C. Therefore, alternative diol-based routes, with distinct potassium carboxylate precursors, was developed aiming to stabilize the precursor solution, to avoid using toxic solvents and to decrease the crystallization temperature of the perovskite phase. Studies on powders revealed that in the case of KTOac (solution based on potassium acetate), a mixture of perovskite and pyrochlore phases is detected at temperature as low as 450 °C, and gradual transformation into monophasic perovskite structure occurs as temperature increases up to 750 °C, however the desired monophasic KTaO3 perovskite phase is not achieved. In the case of KTOacac (solution with potassium acetylacetonate), a broad peak is detected at temperatures <650 °C, characteristic of amorphous structures, while at higher temperatures diffraction lines from pyrochlore and perovskite phases are visible and a monophasic perovskite KTaO3 is formed at >700 °C. Infrared analysis indicated that the differences are due to a strong deformation of the carbonate-based structures upon heating. A series of thin films of alkali tantalates were spin-coated onto Si-based substrates using diol-based routes. Interestingly, monophasic perovskite KTaO3 films deposited using KTOacac solution were obtained at temperature as low as 650 °C; films were annealed in rapid thermal furnace in oxygen atmosphere for 5 min with heating rate 30 °C/sec. Other compositions of the tantalum based system as LiTaO3 (LTO) and NaTaO3 (NTO), were successfully derived as well, onto Si substrates at 650 °C as well. The ferroelectric character of LTO at room temperature was proved. Some of dielectric properties of KTO could not be measured in parallel capacitor configuration due to either substrate-film or filmelectrode interfaces. Thus, further studies have to be conducted to overcome this issue. Application-oriented studies have also been conducted; two case studies: i) photocatalytic activity of alkali tantalates and niobates for decomposition of pollutant, and ii) bioactivity of alkali tantalate ferroelectric films as functional coatings for bone regeneration. Much attention has been recently paid to develop new type of photocatalytic materials, and tantalum and niobium oxide based compositions have demonstrated to be active photocatalysts for water splitting due to high potential of the conduction bands. Thus, various powders of alkali tantalates and niobates families were tested as catalysts for methylene blue degradation. Results showed promising activities for some of the tested compounds, and KNbO3 is the most active among them, reaching over 50 % degradation of the dye after 7 h under UVA exposure. However further modifications of powders can improve the performance. In the context of bone regeneration, it is important to have platforms that with appropriate stimuli can support the attachment and direct the growth, proliferation and differentiation of the cells. In lieu of this here we exploited an alternative strategy for bone implants or repairs, based on charged mediating signals for bone regeneration. This strategy includes coating metallic 316L-type stainless steel (316L-SST) substrates with charged, functionalized via electrical charging or UV-light irradiation, ferroelectric LiTaO3 layers. It was demonstrated that the formation of surface calcium phosphates and protein adsorption is considerably enhanced for 316L-SST functionalized ferroelectric coatings. Our approach can be viewed as a set of guidelines for the development of platforms electrically functionalized that can stimulate tissue regeneration promoting direct integration of the implant in the host tissue by bone ingrowth and, hence contributing ultimately to reduce implant failure.
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O presente trabalho descreve um estudo sobre a metodologia matemática para a solução do problema direto e inverso na Tomografia por Impedância Elétrica. Este estudo foi motivado pela necessidade de compreender o problema inverso e sua utilidade na formação de imagens por Tomografia por Impedância Elétrica. O entendimento deste estudo possibilitou constatar, através de equações e programas, a identificação das estruturas internas que constituem um corpo. Para isto, primeiramente, é preciso conhecer os potencias elétricos adquiridos nas fronteiras do corpo. Estes potenciais são adquiridos pela aplicação de uma corrente elétrica e resolvidos matematicamente pelo problema direto através da equação de Laplace. O Método dos Elementos Finitos em conjunção com as equações oriundas do eletromagnetismo é utilizado para resolver o problema direto. O software EIDORS, contudo, através dos conceitos de problema direto e inverso, reconstrói imagens de Tomografia por Impedância Elétrica que possibilitam visualizar e comparar diferentes métodos de resolução do problema inverso para reconstrução de estruturas internas. Os métodos de Tikhonov, Noser, Laplace, Hiperparamétrico e Variação Total foram utilizados para obter uma solução aproximada (regularizada) para o problema de identificação. Na Tomografia por Impedância Elétrica, com as condições de contorno preestabelecidas de corrente elétricas e regiões definidas, o método hiperparamétrico apresentou uma solução aproximada mais adequada para reconstrução da imagem.
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Cette recherche a pour but d analyser l Ecole Augusto Severo, située dans la ville de Natal dont la construction date de 1907,étant le premier établissement d enseignement primaire à l état du Rio Grande do Norte, pendant le processus de restructuration de l enseignement républicain. On cherche à comprendre la représentation de ce milieu scolaire, comme équipement urbain, dans le processus de modernisation de la ville et comme modèle éducationnel pour l état entre 1908 et 1913. En se servant des études historiographes sur le processus de modernisation de quelques villes brésiliennes et des innovations de l enseignement public primaire au pays, à la fin du dix-neuvième siècle et pendant la première décennie du vingtième siècle, comme source pour mieux saisir le contexte général et spécifique. On reconstitue les aspects économiques, sociaux et politiques déterminants des interventions publiques réalisées dans cette ville par les gouvernements républicains ayant comme obectif la construction d une ville embellie,hygiénique et civilisée. Située au quartier Ribeira, principal scénario de la modernité de Natal, l Ecole Augusto Severo est mise em relief comme symbole de civilité du paysage urbain de l époque pour le citoyen du Rio Grande do Norte. Elle disposait de services d énergie et d un tram électrique. Il y avait devant, un grand lac arborisé et une station ferroviaire. A côté, il y avait le théâtre Carlos Gomes (actuellement Alberto Maranhão). Par suíte de son imposante architecture, raffiné style éclectique,on reflète l idéal républicain des elites locales, avec une conception d espace symbolique et éducative de surveillance et contrôle, caractéristiques de l école graduée républicaine
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This work presents the development and modification of techniques to reduce the effects of load variation and mains frequency deviation in repetitive controllers applied to active power filters. To minimize the effects of aperiodic signals resulting from the connection or disconnection of non-linear loads is developed a technique which recognizes linear and nonlinear loads, and operates to reset the controller only when the error due to the transition of considerable value, and the transition is from non-linear to linear load. An algorithm to adapt the gain of the repetitive controller, based on a sigmoid function adaptation, in order to minimize the effects caused by random noise in the measurement system is also used. This work also analyzes the effects of frequency variation and presents the main methods to cope with this situation. Some solutions are the change in the number of samples per period and the variation of the sampling rate. The first has the advantage of using linear design techniques and results in a time invariant system. The second method changes the sampling frequency and leads to a time variant system that demands a difficult analysis of stability. The proposed algorithms were tested using the methods of truncation of the number of samples and the method of changing the sampling rate of the system to compensate possible frequency variations of the grid. Experimental results are presented to validate the proposal.