Open and throughfall precipitation samples were collected at Haliburton Forest for a total of nine events from July – November of 2009. The following species were analyzed quantitatively: NO3-, SO42-, Cl-, HCOO-, C2O42-, NH4+, Na+, K+, Ca2+, and Mg2+. Wet deposition inputs to the system were quantified and the sources of wet-deposited species were probed. The throughfall method was employed to quantify inputs to the forest floor and probe canopy-precipitation interactions. Leaf wash samples at three heights aided in the interpretation of throughfall data and allowed for an examination of vertical profiles of dry deposition to the canopy. Results suggest possible nitrate foliar leaching during the growing season, although this appears to cease during senescence. This finding supports previous evidence that Haliburton Forest has shifted from nitrogen-limitation toward nitrogen-saturation and estimated total atmospheric N inputs to the system are close to the proposed critical load of 10 kg N ha-1 yr-1.

Landfills are considered to be one of the major sources of anthropogenic methane (CH4) emissions in the environment. A landfill biocover system optimizes environmental conditions for biotic CH4 consumption that controls the fugitive and residual emissions from landfills. A compost material has more oxidation potential in comparison to any other material due to its high porosity, organic content, free flux for gases and water holding capacity. Thermal, hydraulic, bio – chemical and mechanical (THMCB) properties are important factors that can significantly affect the performance of biocover material with regards to CH4 oxidation potential as well as structural stability. Technical data on the thermal, hydraulic and mechanical (THM) properties of compost based biocover materials are quite limited. Hence, a detailed experimental program has been carried out at the University of Ottawa to study the THM properties and behaviour of compost biocover material by conducting experimental tests on small compost samples as well as by performing column experiments. The test results indicate that lower water content (dry of optimum for compaction curve) shows more free air space (FAS) in comparison to higher water content. The compost has almost the same shear strength for various initial water contents and dry unit weights; however, it settles and swells more at higher water content than lower water content per mechanical test results. The thermal and hydraulic properties of compost are a function of the compaction degree in addition to various other parameters. It is also found that the THM properties of compost are strongly coupled and the degree of saturation greatly affects the FAS.

Partial saturation of porous rock by two fluids substantially affects compressional wave propagation. In particular, partial saturation causes significant attenuation and dispersion due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. When partial saturation is mesoscopic, i.e. existing on a length scale much greater than pore scale but less than wavelength scale, significant attenuation can arise for frequencies 10-1000 Hz. Models for attenuation and dispersion due to mesoscale heterogeneities mostly assume fluids are distributed in a regular way. Recent experiments indicate mesoscopic heterogeneities have less idealised distributions and distribution affects attenuation/dispersion. Thus, theoretical models are required to simulate effects due to realistic fluid distributions. / The thesis focus is to model attenuation and dispersion due to realistic mesoscopic fluid distributions and fluid contrasts. First X-ray tomographic images of partially saturated rock are analysed statistically to identify spatial measures useful for describing fluid distribution patterns. The correlation function and associated correlation length for a specific fluid type are shown to be of greatest utility. Next a new model, called 3DCRM (CRM stands for continuous random media) is derived, utilizing a correlation function to describe the fluid distribution pattern. It is a random media model, is accurate for small fluid contrast and approximate for large fluid contrast. Using 3DCRM attenuation and dispersion are shown to depend on fluid distribution. / Next a general framework for partial saturation called APS (acoustics of partial saturation) is extended enabling estimation of attenuation and dispersion due to arbitrary 1D/3D fluid distributions. The intent is to construct a versatile model enabling attenuation and dispersion to be estimated for arbitrary fluid distributions, contrasts and saturations. Two crucial parameters within APS called shape and frequency scaling parameters are modified via asymptotic analysis using several random media models (which are accurate for only certain contrasts in fluid bulk moduli and percent saturation). For valid fluid contrasts and saturations, which satisfy certain random media conditions there is good correspondence between modified APS and the random media models, hence showing that APS can be utilized to model attenuation and dispersion due to more realistic fluid distributions. / Finally I devise a numerical method to test the accuracy of the analytical shape parameters for a range of fluid distributions, saturations and contrasts. In particular, the analytical shape parameter for randomly distributed spheres was shown to be accurate for a large range of saturations and fluid contrasts.

Time-lapse seismic is a modern technology for monitoring production-induced changes in and around a hydrocarbon reservoir. Time-lapse (4D) seismic may help locate undrained areas, monitor pore fluid changes and identify reservoir compartmentalization. Despite several successful 4D projects, there are still many challenges related to time-lapse technology. Perhaps the most important are to perform quantitative time-lapse and to model and interpret time-lapse effects in thin layers. The former requires one to quantify saturation and pressure effects on rock elastic parameters. The latter requires an understanding of the combined response of time-lapse effects in thin layers and overcoming seismic vertical resolution limitation. / This thesis presents an integrated study of saturation and pressure effects on elastic properties. Despite the fact that Gassmann fluid substitution is standard practice to predict time-lapse saturation effects, its validity in the field environment rests upon a number of assumptions. The validity of Gassmann equations, ultimately, can only be tested in real geological environments. In this thesis I developed a workflow to test Gassmann fluid substitution by comparing saturated P-wave moduli computed from dry core measurements with those obtained from sonic and density logs. The workflow has been tested on a turbidite reservoir from the Campos Basin, offshore Brazil. The results show good statistical agreement between the P-wave elastic moduli computed from cores using the Gassmann equations and the corresponding moduli computed from log data. This confirms that all the assumptions of the Gassmann theory are adequate within the measurement error and natural variability of elastic properties. These results provide further justification for using the Gassmann theory to interpret time-lapse effects in this sandstone reservoir and in similar geological formations. / Pressure effects on elastic properties are usually obtained by laboratory measurements, which can be affected by core damage. I investigated the magnitude of this effect on compressional-wave velocities by comparing laboratory experiments and log measurements. I used Gassmann fluid substitution to obtain low-frequency saturated velocities from dry core measurements taken at reservoir pressure, thus mitigating the dispersion effects. The analysis is performed for an unusual densely cored well from which 43 cores were extracted over a 45 m thick turbidite reservoir. These computed velocities show very good agreement with the sonic-log measurements. This is encouraging because it implies that core damages that may occur while bringing the core samples to the surface are small and do not adversely affect the measurement of elastic properties on these core samples. Should core damage have affected our measurements, we would have expected a systematic difference between properties measured in situ and on the recovered. This confirms that, for this particular region, the effect of core damage on ultrasonic measurements is less than the measurement error. Consequently, stress sensitivity of elastic properties as obtained from ultrasonic measurements are adequate for quantitative interpretation of time-lapse seismic data. / In some circumstances, stress sensitivity may not be obtained by ultrasonic measurements. Cores may be affected by damage, bias in the plugging process and scale effects and therefore may not be representative of the in situ properties. Consequently it is desirable to obtain this dependence from an alternative method. This other approach ideally should provide the pressure - velocity dependence from an intact rock. Few methods can sample the in situ rock. Seismic, for instance, provides in situ information, but lacks vertical resolution. Well logs, on the other hand, can provide high vertical resolution information, but usually are not available before and after production changes. I propose a method to assess the in situ pressure - velocity dependence using well data. I apply this method to a reservoir made up of sandstone. I used 23 wells drilled and logged in different stages of development of a hydrocarbon field providing rock and fluid properties at different pressures. For each well logged at a specific time, pore pressure, velocity and porosity, among other properties, are known. Pore pressure is accessed from a Repeat Formation Tester (RFT). As a field depletes and new wells are drilled and logged, similar data sets related to different stages of depletion are available. I present an approach expanding Furre et al. (2009) study incorporating porosity and obtaining a three dimensional relationship with velocity and pressure. The idea is to help to capture rock property variability. / Quantitative time-lapse studies require precise knowledge of the response of rocks sampled by a seismic wave. Small-scale vertical changes in rock properties, such as those resulting from centimetre scale depositional layering, are usually undetectable in both seismic and standard borehole logs (Murphy et al., 1984). I present a methodology to assess rock properties by using X-ray computed tomography (CT) images along with laboratory velocity measurements and borehole logs. This methodology is applied to rocks extracted from around 2.8 km depth from offshore Brazil. This improved understanding of physical property variations may help to correlate stratigraphy between wells and to calibrate pressure effects on velocities, for seismic time-lapse studies. / Small scale intra-reservoir shales have a very different response from sands to fluid injection and depletion, and thus may have a strong effect on the equivalent properties of a heterogeneous sandstone reservoir. Since shales have very low permeability, an increase of pore pressure in the sand will cause an increase of confining pressure in the intra-reservoir shale. I present a methodology to compute the combined seismic response for depletion and injection scenarios as a function of net to gross (NTG or sand – shale fraction). This approach is appropriate for modelling time-lapse effects of thin layers of sandstones and shales in repeated seismic surveys when there is no time for pressure in shale and sand to equilibrate. I apply the developed methodology to analyse the sand - shale combined response to typical shale and sandstone stress sensitivities for an oil field located in Campos Basin, Brazil. For a typical NTG of 0.6, there is a difference of approximately 35% in reflection coefficient during reservoir depletion from the expected value if these shales are neglected. Consequently, not considering the small shales intra-reservoir may mislead quantitative 4D studies. / The results obtained in this research are aimed to quantify pressure and saturation effects on elastic properties. New methodologies and workflows have been proposed and tested using real data from South America (Campos Basin) datasets. The results of this study are expected to guide future time-lapse studies in this region. Further investigations using the proposed methodologies are necessary to verify their applicability in other regions.

Doctor of Philosphy (PhD) / This thesis describes the work carried out during four treks, each over 10-11 days, from 1400m to 5000m in the Nepal Himalaya and further work performed during several two-night sojourns at the Barcroft Laboratory at 3800m on White Mountain in California, USA. Nineteen volunteers were studied during the treks in Nepal and seven volunteers were studied at White Mountain. All subjects were normal, healthy individuals who had not travelled to altitudes higher than 1000m in the previous twelve months. The aims of this research were to examine the effects on sleep, and the ventilatory patterns during sleep, of incremental increases in altitude by employing portable polysomnography to measure and record physiological signals. A further aim of this research was to examine the relationship between the ventilatory responses to hypoxia and hypercapnia, measured at sea level, and the development of periodic breathing during sleep at high altitude. In the final part of this thesis the possibility of preventing and treating Acute Mountain Sickness with non-invasive positive pressure ventilation while sleeping at high altitude was tested. Chapter 1 describes the background information on sleep, and breathing during sleep, at high altitudes. Most of these studies were performed in hypobaric chambers to simulate various high altitudes. One study measured sleep at high altitude after trekking, but there are no studies which systematically measure sleep and breathing throughout the whole trek. Breathing during sleep at high altitude and the physiological elements of the control of breathing (under normal/sea level conditions and under the hypobaric, hypoxic conditions present at high altitude) are described in this Chapter. The occurrence of Acute Mountain Sickness (AMS) in subjects who travel form near sea level to altitudes above 3000m is common but its pathophysiology not well understood. The background research into AMS and its treatment and prevention are also covered in Chapter 1. Chapter 2 describes the equipment and methods used in this research, including the polysomnographic equipment used to record sleep and breathing at sea level and the high altitude locations, the portable blood gas analyser used in Nepal and the equipment and methodology used to measure each individual’s ventilatory response to hypoxia and hypercapnia at sea level before ascent to the high altitude locations. Chapter 3 reports the findings on the changes to sleep at high altitude, with particular focus on changes in the amounts of total sleep, the duration of each sleep stage and its percentage of total sleep, and the number and causes of arousals from sleep that occurred during sleep at increasing altitudes. The lightest stage of sleep, Stage 1 non-rapid eye movement (NREM) sleep, was increased, as expected with increases in altitude, while the deeper stages of sleep (Stages 3 and 4 NREM sleep, also called slow wave sleep), were decreased. The increase in Stage 1 NREM in this research is in agreement with all previous findings. However, slow wave sleep, although decreased, was present in most of our subjects at all altitudes in Nepal; this finding is in contrast to most previous work, which has found a very marked reduction, even absence, of slow wave sleep at high altitude. Surprisingly, unlike experimental animal studies of chronic hypoxia, REM sleep was well maintained at all altitudes. Stage 2 NREM and REM sleep, total sleep time, sleep efficiency and spontaneous arousals were maintained at near sea level values. The total arousal index was increased with increasing altitude and this was due to the increasing severity of periodic breathing as altitude increased. An interesting finding of this research was that fewer than half the periodic breathing apneas and hypopneas resulted in arousal from sleep. There was a minor degree of upper airway obstruction in some subjects at sea level but this was almost resolved by 3500m. Chapter 4 reports the findings on the effects on breathing during sleep of the progressive increase of altitude, in particular the occurrence of periodic breathing. This Chapter also reports the results of changes to arterial blood gases as subjects ascended to higher altitudes. As expected, arterial blood gases were markedly altered at even the lowest altitude in Nepal (1400m) and this change became more pronounced at each new, higher altitude. Most subjects developed periodic breathing at high altitude but there was a wide variability between subjects as well as variability in the degree of periodic breathing that individual subjects developed at different altitudes. Some subjects developed periodic breathing at even the lowest altitude and this increased with increasing altitude; other subjects developed periodic breathing at one or two altitudes, while four subjects did not develop periodic breathing at any altitude. Ventilatory responses to hypoxia and hypercapnia, measured at sea level before departure to high altitude, was not significantly related to the development of periodic breathing when the group was analysed as a whole. However, when the subjects were grouped according to the steepness of their ventilatory response slopes, there was a pattern of higher amounts of periodic breathing in subjects with steeper ventilatory responses. Chapter 5 reports the findings of an experimental study carried out in the University of California, San Diego, Barcroft Laboratory on White Mountain in California. Seven subjects drove from sea level to 3800m in one day and stayed at this altitude for two nights. On one of the nights the subjects slept using a non-invasive positive pressure device via a face mask and this was found to significantly improve the sleeping oxyhemoglobin saturation. The use of the device was also found to eliminate the symptoms of Acute Mountain Sickness, as measured by the Lake Louise scoring system. This finding appears to confirm the hypothesis that lower oxygen saturation, particularly during sleep, is strongly correlated to the development of Acute Mountain Sickness and may represent a new treatment and prevention strategy for this very common high altitude disorder.

Th. doct.-ing.--Toulouse 3, 1977. N°: 583.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-03-15T16:57:36Z No. of bitstreams: 1 KAMILA FREITAS PORTO - DISSERTAÇÃO PPGEQ 2017..pdf: 2416618 bytes, checksum: 9e62c85bd253dcc11c3e6cb2c6a8e8ac (MD5) / Made available in DSpace on 2018-03-15T16:57:36Z (GMT). No. of bitstreams: 1 KAMILA FREITAS PORTO - DISSERTAÇÃO PPGEQ 2017..pdf: 2416618 bytes, checksum: 9e62c85bd253dcc11c3e6cb2c6a8e8ac (MD5) Previous issue date: 2017-03-30 / Visando a problemática da disponibilidade e da qualidade hídrica, a dessalinização de águas através de processos com membranas é uma das alternativas para amenizar o problema da baixa qualidade e da escassez, produzindo água de boa qualidade. Porém, neste método ainda existem alguns obstáculos a serem vencidos, um deles é a incrustação nas membranas. Para resolver este problema em sistemas de osmose inversa, geralmente utilizam-se antiincrustantes comerciais, os quais são específicos para determinados sais. Dentre os íons comumente presentes em águas estão o bicarbonato (HCO3-) e o carbonato (CO32-), este último facilmente encontrado na forma de carbonato de cálcio (CaCO3), que em determinadas condições precipita, baixando a eficiência da membrana e, consequentemente, a quantidade de água produzida. Através do Índice de Saturação de Langelier (ISL) é possível detectar o risco de formação de precipitados deste sal nas águas salobras. Esse trabalho descreve os resultados da pesquisa realizada no estudo do pré-tratamento de águas para a diminuição do ISL, comparando o desempenho do ácido clorídrico versus antiincrustante comercial, Flocon 260. Para este fim, neste estudo inicialmente utilizou de águas sintéticas e posteriormente águas de poços, realizando testes em pequena e grande escalas. O HCl se mostrou um bom antiincrustante, uma vez que foi possível obter valores do ISL abaixo de zero para os dois tipos de experimentos, em escala de bancada e de piloto. Para os dois tipos de água foi possível se observar bons resultados e, quando comparado com o antiincrustante comercial observou-se uma melhor relação custo-benefício / Aiming at the issue of availability and water quality, the desalination of water through membrane processes is one of the alternatives to alleviate the problem of low quality and scarcity, producing good quality water. However, in this method there are still some obstacles to be overcome, one of them is the incrustation in the membranes. To solve this problem in reverse osmosis systems, commercial antifoulants are generally used, which are specific for particular salts. Among the ions commonly present in water are bicarbonate (HCO3-) and carbonate (CO32-), the latter easily found in the form of calcium carbonate (CaCO3), which under certain conditions precipitates, lowering the efficiency of the membrane and, consequently , The amount of water produced. Through the Langelier Saturation Index (ISL) it is possible to detect the risk of precipitation of this salt in brackish waters. This work describes the results of the research carried out in the study of water pretreatment for the reduction of ISL, comparing the performance of hydrochloric acid versus commercial antifoulant, Flocon 260. For this purpose, in this study initially used synthetic waters and later waters of Wells, performing tests on small and large scales. HCl proved to be a good antifouling since it was possible to obtain ISL values below zero for the two types of experiments, bench scale and pilot scale. For both types of water it was possible to observe good results and, when compared with the commercial antifoulant, a better cost-benefit ratio was observed.

Este trabalho apresenta estratégias de controle para a sincronização de dois sistemas não-lineares do tipo Lur'e sob controle saturante. O objetivo no uso de controlador e para que os estados de um sistema escravo sigam a referência dos estados do sistema mestre. Resultados teóricos para a síntese de controladores são propostos considerando diferentes hipóteses sobre a não-linearidade do sistema Lur'e. Primeiramente esta e tratada como uma função genérica que satisfaz globalmente uma condição de setor, enquanto que posteriormente assume-se que a função não-linear e uma função linear por partes e um modelo equivalente baseado em funções saturação e empregado para descrever os efeitos da mesma no comportamento dinâmico do sistema. São considerados, ainda, duas estrat egias de controle: realimentação estática dos estados dos sistemas e realimentação dinâmica da saída dos sistemas, incluindo neste ultimo caso elementos referentes as não-linearidades inerentes do sistema Lur'e e um elemento anti-windup. O projeto dos parâmetros de cada controlador e feito através de problemas de otimização convexa com restrições na forma de desigualdades matriciais lineares (LMI s) tendo como objetivo maximizar o conjunto de estados inicias nos quais a sincronização e assegurada. A formulação dos problemas de otimização e obtida através de inequações matriciais lineares, utilizando-se a teoria de estabilidade de Lyapunov juntamente com métodos baseados em condições de setor para assegurar a convergência assintótica do erro de sincronização para zero, i.e. garantir que os estados do sistema mestre são seguidos pelos do escravo. Os métodos propostos são ilustrados por meio de exemplos numéricos tendo como objetivo a sincronização de dois circuitos de Chua. / This work presents control strategies for the synchronization of two nonlinear Lur'e systems subject to control saturation. The objective of the use of controllers is so that the states of a slave system follow the reference of the states of the master system. Theoretical results for the synthesis of controllers are proposed considering di erent hypothesis about the nonlinearity of the Lur'e system. Initially it is considered as being a generic function that satis es globally a sector condition, while afterwards it is assumed that the non-linear function is a piecewise-linear function and an equivalent saturation function model is employed in order to describe its effect on the system's dynamic behaviour. Two controller strategies are considered: a static feedback of the system's states and a dynamic feedback of the system's output, coupled, in the last case, with elements based on the system's non-linearities and an anti-windup element is considered. The design of the parameters of each controller is generated by convex optimization problems with restrictions in the form of linear matriz inequalities (LMI) having as objective maximizing the set of initial conditions for which synchronization is guaranteed. The optimization problems are formulated by the means of linear matrix inequalities based on Lyapunov's stability theory and a sector-based approach to ensure null synchronization error, i.e. to ensure the local asymptotic convergence of the slave state to the master one. The proposed methods are illustrated by numerical examples with the objective of the synchronization of two Chua's circuits.

Esta dissertação aborda a síntese de leis de controle baseadas em compensação dinâmica de saída para sistemas lineares contínuos invariantes no tempo, sujeitos a restrições no atuador. Baseados em condições suficientes expressas em LMIs, obtidas a partir de uma nova condição de setor para a função zona-morta, dois métodos são propostos. O primeiro método propõe a síntese de compensadores dinâmicos de anti-windup de ordem plena e reduzida para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, ganho L2 limitado da perturbação à saída controlada do sistema, e um conjunto de inicialização dos estados do sistema tolerante à perturbação de norma L2 máxima, conhecida. Na ausência de perturbação a origem é garantida assintoticamente estável. Para o compensador de ordem plena, condições em LMIs garantem a estabilidade local e global da origem. Para o caso de ordem reduzida, inicialmente obtém-se estas condições expressas em termos de BMIs, sobre as quais aplica-se o Lema de Finsler, e pela escolha apropriada de seus multiplicadores, condições expressas em LMIs são obtidas. Dois métodos baseados em BMIs são propostos para estender os resultados obtidos das otimizações, em esquemas de relaxação. O segundométodo proposto aborda a síntese de controladores dinâmicos, para um atuador restrito em amplitude e taxa de variação, sujeito a perturbações limitadas em norma L2. Propõe-se um controlador dinâmico não-linear, composto por um compensador dinâmico linear, um integrador saturante e laços anti-windup. Esta metodologia possibilita a síntese simultânea de um controlador, e da malha de compensação anti-windup. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, ganho L2 limitado da perturbação à saída controlada do sistema, e um conjunto de inicialização do sistema tolerante à perturbação de norma L2 máxima, conhecida. Na ausência de perturbação a origem é garantida assintoticamente estável. As condições para estabilidade local e global são formuladas em LMIs a partir da aplicação do lema de Finsler e da escolha apropriada de multiplicadores. Dois métodos também baseados em BMIs podem estender os resultados obtidos das otimizações em esquemas de relaxação. Casos especiais são propostos a partir do método geral obtido; nestes casos condições diretamente em LMI podem ser obtidas. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída controlada. Exemplos numéricos são apresentados para ilustrar o efeito de cada método na solução do problema de máxima tolerância à perturbação. / This thesis addresses control law synthesis based upon dynamic output compensation of continuous time invariant linear systems. By sufficient conditions expressed in LMIs, obtained from a new sector condition to the dead-zone function, two methods are proposed. The first one, comprises the synthesis of full and reduced order dynamic antiwindup compensators for a system with a linear controller a priori given, regardless the actuators limits. The compensator synthesis considers an amplitude limited actuator and a system subjected to L2-norm limited perturbation. The verification of the announced conditions assures the closed-loop origin stability, limited L2 gain for the perturbation at the system controlled output, and a system states initialization set tolerating the known L2-norm disturbance. In the absence of disturbance the origin is asymptotically stable guaranteed. For the full-order compensator, LMI conditions assure the local and global origin closed-loop stability. For the reduced order case, at first, BMI conditions are obtained, which, by the Finsler Lemma and proper choosing of itsmultipliers, become LMIs. Two methods are presented based on BMIs in order to improve the obtained results, by relaxation schemes. The second method addresses the synthesis of dynamic controllers considering a linear plant with the actuator restricted both in amplitude and rate, the system is meant to be subjected to L2 norm disturbances. The proposed methodology issues a non-linear dynamic controller, composed by a dynamic linear compensator, a saturating integrator and anti-windup loops. This approach allows the simultaneous synthesis of both the controller and the anti-windup loops. The validity of its announced conditions guarantees the closedloop origin stability, an upper-bound to the disturbances L2 gain on the plant’s controlled output, and an initialization set for the system that stands the specified disturbance. In the absence of disturbances the system’s origin is asymptotically stable guaranteed. Both local and global stability conditions are given in terms of LMIs. Two BMI-based methods arise in order to improve the results obtained on the referred optimizations problems by relaxation schemes. Special cases are derived from the general method; in these cases directly LMI conditions may be obtained. Optimization problems arise in both methods in order to maximize disturbance tolerance and rejection, by means of respectively its L2-norm, and L2-gain at the controlled output. Numerical Examples are presented in order to illustrate the effect of each method in the solution of the disturbance toleration problem.

Este trabalho apresenta uma nova metodologia para a síntese simultânea de controlador e laço anti-windup visando o problema de seguimento de referências em sistemas sujeitos à saturação. Além do projeto dos controladores, será apresentada uma estimativa dos domínios de estabilidade e do conjunto de referências admissíveis. O seguimento de referências constantes e a rejeição de perturbações, também constantes, será garantido pelo princípio do modelo interno, ou seja, uma ação integral será adicionada a uma malha de controle com realimentação de saída. Além da adição desta ação integral, uma mudança de coordenadas será aplicada ao sistema, onde será garantido que o único ponto de equilíbrio que garante erro nulo de seguimento está no interior da sua região de linearidade. Os efeitos da saturação no sistema serão considerados através de condições de setor modificadas, as quais introduzem novos graus de liberdade ao projeto. Em um primeiro momento, a metodologia será aplicada para sistemas de tempo contínuo, considerando um esquema de controle conhecido como “integradores inteligentes”. Posteriormente, este esquema será simplificado, no que foi chamado de solução “clássica”. Além de apresentar um esquema de controle mais simples e um número menor de condições, estas condições são obtidas diretamente na forma de LMIs, evitando assim, a utilização de esquemas iterativos. Alguns problemas de otimização serão apresentados, podendo levar a três objetivos de controle distintos: maximização da referência admissível, maximização da condição inicial e maximização da perturbação admissível. Por meio de exemplos, será mostrado que esta solução apresenta resultados menos conservativos do que os apresentados na literatura corrente, além de chamar a atenção para um problema ignorado por outros autores. Este problema se refere à existência de pontos de equilíbrio dentro dos domínios de estabilidade mas fora da região linear, o que impossibilita a garantia de erro de seguimento nulo. Num segundo momento, esta metodologia será estendida para sistemas de tempo discreto. Mais uma vez, condições LMI serão obtidas a fim de projetar os controladores e oferecer estimativas dos domínios de estabilidade. Por não haver uma referência direta para comparação dos resultados, a metodologia será aplicada para exemplos estáveis, instáveis e com integradores, tanto no caso monovariável quanto no caso multivariável. Finalmente, será apresentado um estudo dos pontos de equilíbrio fora da região de linearidade, como mencionado anteriormente, considerando tanto sistemas de tempo contínuo quanto em tempo discreto. Este estudo será realizado para alguns tipos de sistemas, considerando apenas o caso monovariável. Será provado que estes equilíbrios só são possíveis em plantas assintoticamente estáveis, exigindo a consideração de uma condição extra na solução do problema de otimização. / This work addresses the problem of tracking constant references for linear systems subject to control saturation. The main idea is to present LMI conditions in order to design both a stabilizing controller and an anti-windup gain. These conditions ensure that the trajectories of the closed-loop system are bounded by an invariant ellipsoidal set, provided that the initial conditions are taken in this set and the references and the disturbances belong to a certain admissible set. The constant reference tracking and constant disturbance rejection is taken into account by the internal model principle, i. e., considering the introduction of an integral action in a unitary output feedback scheme. We also introduce the error co-ordinate representation, where is proved that there exists only one equilibrium point inside the linearity region and that this equilibrium point ensures perfect reference tracking. In order to consider the saturation effects, we use a modified sector condition, introducing new degrees of freedom to the synthesis problem. In a first step, the proposed framework was applied to the control scheme called “intelligent integrators”, regarding continuous-time systems. However, this control scheme does not allow the simultaneous synthesis so it is simplified to the so called “classical” anti-windup scheme. Based on this simplified control structure, LMI conditions are directly derived, avoiding therefore the necessity of applying iterative schemes. Convex optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed. We show, by means of an example, that the obtained results are less conservative than the ones previously presented in related works. In these examples, we also show that a study about the existence of other equilibria inside the invariant set is worthwhile. Later, the proposed framework is extended to discrete-time systems, where new LMI conditions are presented in order to synthesize the controller and present an estimate of the stability domains. Due to a lack of related works, our framework is applied to stable, unstable and integrator examples. These examples consider both single and multi-variable systems. Finally, we conclude this work with a study about the possibility of existence of other equilibria inside the invariant set. For the single-input case, we show that this is only possible if the open-loop system is asymptotically stable. In this case, in order to avoid convergence to these points, additional constraints on the admissible references to be tracked should be considered. It is worth to emphasize that such kind of analysis has not been performed in previous works.