A presente tese trata do estudo dos estimadores algébricos aplicados a sistemas de controle. Tais estimadores são filtros variantes no tempo que estimam as derivadas dos sinais de entrada e funcionam como uma alternativa ao uso de observadores. Este trabalho inclui uma contribuição teórica que permite determinar um limite superior do erro do estimador algébrico. Também, mostramos um resultado que garante estabilidade em malha fechada no contexto do princípio da separação para esta classe particular de sistemas. Um exemplo de levitação magnética baseado em linearização exata com estimadores algébricos de derivadas até segunda ordem implementados digitalmente é tratado com detalhe. Simulações em computador são apresentadas mostrando excelentes resultados. / This thesis deals with the algebraic estimators and their application in closed loop control systems. The algebraic estimators can be implemented as time-varying filters that produce an estimation of the derivatives of the input signal, and they can be an interesting alternative for substituting classical observers. This work includes a theoretic contribution that allows to compute a bound of the estimation error of the algebraic estimator. Furthermore it is shown that any derivative estimator that respects this bound will assure closed loop stability in the context of the separation principle, at least for a class of nonlinear systems. An example of magnetic levitation based on exact linearization and in closed loop with an estimator of the first and second derivatives is considered. A digital implementation of the algebraic estimation is also discussed, and simulations are presented, showing excellent results.

A presente tese trata do estudo dos estimadores algébricos aplicados a sistemas de controle. Tais estimadores são filtros variantes no tempo que estimam as derivadas dos sinais de entrada e funcionam como uma alternativa ao uso de observadores. Este trabalho inclui uma contribuição teórica que permite determinar um limite superior do erro do estimador algébrico. Também, mostramos um resultado que garante estabilidade em malha fechada no contexto do princípio da separação para esta classe particular de sistemas. Um exemplo de levitação magnética baseado em linearização exata com estimadores algébricos de derivadas até segunda ordem implementados digitalmente é tratado com detalhe. Simulações em computador são apresentadas mostrando excelentes resultados. / This thesis deals with the algebraic estimators and their application in closed loop control systems. The algebraic estimators can be implemented as time-varying filters that produce an estimation of the derivatives of the input signal, and they can be an interesting alternative for substituting classical observers. This work includes a theoretic contribution that allows to compute a bound of the estimation error of the algebraic estimator. Furthermore it is shown that any derivative estimator that respects this bound will assure closed loop stability in the context of the separation principle, at least for a class of nonlinear systems. An example of magnetic levitation based on exact linearization and in closed loop with an estimator of the first and second derivatives is considered. A digital implementation of the algebraic estimation is also discussed, and simulations are presented, showing excellent results.

Diffusion is a fundamental process which occurs in a wide variety of phases. It plays an important role in chemistry, physics, biology, materials science etc. In recent times, diffusion in confined systems has been widely investigated. Porous aluminosilicates such as zeolites, carbon nano tubes and metal organic frameworks(MOF) provide confined regions within which small molecules can diffuse. Indeed, diffusion within these materials have attracted considerable attention in the past few decades (see for example, “Diffusion in Zeolites and Other Microporous Solids”, J. Ka¨rger and D..M. Ruthven, John Wiley &Sons, NewYork,1992). Diffusion in confined spaces exhibits rich variety. For example, single file diffusion, window effect, levitation effect (LE), super-and sub-diffusive motion have all been observed in confined regions. Levitation effect provides an explanation for the dependence of self-diffusivity on the diameter of the diffusant. Consider a diffusant diffusing within a porous material. The pore network provided by the pore material may be characterized by the void and the neck distribution where the necks are the narrower regions interconnecting larger voids. It has been seen that diffusivity is maximum when the size of the diffusant is large and when it is comparable to the diameter of the bottleneck of the pore network. Recently it has been demonstrated that the levitation effect also exists in dense liquids such as water and dense solids. These developments essentially unify our understanding of diffusion in widely differing condensed matter phases. These results show that there is fundamentally no difference between porous substances and dense media at least with regard to dependence of self-diffusivity on the diameter of the diffusant. Chapter 1 provides a brief introduction to the subject of hydrocarbons confined within zeolites and ionic conductivity in polar solvents. We have given a description of the different applications of zeolites in the area of catalysis, separation etc. Window effect, single file diffusion, levitation effect and enhancement of viscosity of confined fluids are described. A brief review of various computational studies of hydrocarbons confined within zeolites is given. This is followed by a discussion of different experimental techniques and their use in the study of diffusion and adsorption within zeolites by many different groups in the last few decades. In the last section of the chapter we have discussed the anomalous size dependence of ionic conductivity in polar solvents which presumably has its origin in the Levitation Effect(LE). We have explained different theories proposed previously to understand the non-monotonic behavior of ionic conductivity as a function of ionic radius. A molecular dynamics(MD) investigation and quasi-elastic neutron scattering (QENS) study of pentane isomers in zeolite NaY is pre-sented in Chapter 2. QENS provides the first direct experimental evidence for LE. In an earlier study, a maximum in diffusivity as a function of the diameter of the diffusant for monatomic sorbates confined within zeolite NaY was observed by MD simulation. Since LE has been invoked to explain the diffusion in a wide variety of condensed matter phases, an experimental evidence of the levitation effect would be of great value. QENS measurements were carried out by Dr. Herve Jobic. Surprisingly we found that neopentane shows higher diffusivity than n-pentane and isopentane although its cross-sectional diameter perpendicular to the long molecular axis is larger compared to isopentane and n-pentane in agreement with predictions of LE. There is an excellent agreement between QENS results and MD simulation. LE predicts that the isomer with high diffusivity has low activation energy. The activation energies have been calculated from the Arrhenius plots using QENS as well as MD data. These follow the order Ea(n−pentane)>Ea(isopentane)>Ea(neopentane). Various other properties such as potential energy barrier at the bottleneck, velocity auto correlation function, intermediate scattering function, k dependence of the width of the dynamic structure factor have been computed. These provide additional insights into the nature of the motion of these isomers. They suggest that the barrier at the 12-ring window depends on the molecular diameter and levitation parameter of isomer. In Chapter 3, we report molecular dynamics simulation study of n-hexane and 2,2-dimethylbutane(DMB) mixture confined within the pores of zeolite NaY. We have taken an equimolar composition of the mixture consisting of n-hexane and DMB. The total number of hydrocarbon molecules in the system is 128. The simulations were carried out at various temperatures of 170, 200, 250 and 300 K. We have computed the self-diffusivities from the slope of the mean square displacement. It is found that the diffusivity of DMB is 0.82 ×10−9 m2/sec and that of n-hexaneis0.38 ×10−9 m2/sec. All previous studies of linear hydrocarbon and its branched analogue in different zeolites in the literature suggest that it is the linear member which has higher self-diffusivity. The cross-sectional diameter of DMB perpendicular to the long molecular axis is higher than that of n-hexane. Thus, DMB should have lower diffusivity. In order to understand this behavior of diffusivity we have computed the activation energies from the Arrhenius plots. The activation energy of DMB is found to be lower than that of n-hexane. This is inconformity with the levitation effect which states that the molecule with larger diameter comparable to that of the bottleneck diameter has low activation energy. We have also computed the potential energyprofileatthe12-ring window. The potential energy profile shows a barrier for n-hexane and a minimum for DMB at the window. This is in agreement with the previous results on monatomic species. We have computed other properties such as velocity auto correlation function, intermediate scattering function as well as wave number dependence of full width at half maximum of dynamic structure factor. These properties explain in detail the motion of n-hexane and DMB within NaY zeolite. In Chapter 4 molecular dynamics investigation into diffusion of n-decane and 3-methylpentane mixture within zeolite NaY. We have studied an equimolar mixture of n-decane and 3-methylpentane (36 of each) in the supercages of NaY zeolite in such a way that the con-centration is one molecule for every three cages. Simulations were performed at four different temperatures : 300, 350, 400 and 450 K. The distribution and orientation of the molecules inside the cage and at the window plane have been studied. Inside the cage, 3-methylpentane stays more close to the inner surface of the zeolite whereas n-decane prefers to stay close to the center of the cage. Both the species prefer to stay with their long molecular axis parallel to the surface of the zeolite. During passage through the window, 3-methylpentane is closer to the window center than n-decane. The distribution of the angle subtended by the end-to-end vector of the molecule with the normal to the window plane, while the molecular center is in the window plane, shows that 3-methylpentane samples a larger range of orientation than n-decane. This may lead to an entropic barrierfor n-decane. We have computed the diffusivity of both the molecules. Diffusivity of 3-methylpentane is found to be higher than n-decane. This behavior is consistent with the observations made in the last two chapters. The activation energy of 3-methylpentane is found to be 3.17 kJ/mol and forn-decaneitis6.0kJ/mol. This agrees with the prediction of levitation effect. The energy profile a the window shows shallow minimum for both n-decane and 3-methylpentane. Therefore, the energy profile does not describe the nature of motion of the molecules. We have computed the the dihedral angle distribution when the molecule is at the adsorption site and when it is at the window plane. The distributions essentially remain same for 3-methylpentane whereas a considerable change in the distributions is seen for n-decane. The gauche population of n-decane increases at the cost of trans population when it goes from the adsorption site to the window. The lower diffusivity of n-decane can be partly attributed to the change in the dihedral angle. Also, the orientational entropic barrier may be another cause of the slow motion of n-decane. Thus, in the present study the slow motion of n-decane is partly explained by levitation effect and partly by the change in the dihedral angle as well as the entropic barrier. Overall, the results in the last three chapters leads to the main conclusion that the branched isomer will diffuse faster than a linear hydrocarbon in zeolites with 12-ring window such as zeolite NaY. In Chapter 5, diffusion of pentane isomers in zeolites NaX and NaY has been investigated using pulsed field gradient nuclear magnetic resonance(PFG-NMR) and molecular dynamics(MD) techniques respectively. Temperature as well as concentration dependence of diffusivity have been studied. The diffusivities obtained from NMR are roughly an order of magnitude smaller than those obtained from MD. The dependence of diffusivity on loading at high temperatures exhibits a type I behavior according to the classification of K¨arge rand Pfeifer. NMR diffusivities of the isomers exhibit the order D(n−pentane)>D(isopentane)>D(neopentane). The results from MD are in agreement with the QENS results where the diffusivities of the isomers follow the order D(n-pentane)<D(isopentane)<D(neopentane). The activation energies from NMR show Ea(n-pentane)<Ea(isopentane) <Ea(neopentane) whereas those from MD suggest the order Ea(n-pentane) >Ea(isopentane) >Ea(neopentane). The latter follows the predictions of levitation effect whereas those of NMR appears to be due to the presence of defects in the zeolite crystals. The differences between NMR and MD are attributed to the long time and length scales over which NMR samples are probed compared to MD or QENS. Th eresults from these studies suggests that although branched isomer intrinsically have higher diffusivities than linear hydrocarbons in zeolites such as NaY, the presence of defects can effectively annul this higher diffusivity of the branched isomer. Correlation of self-diffusivity and entropy of monatomic sorbates con-fined within zeolite NaY has been investigated in Chapter 6. We have carried out molecular dynamics simulation on monatomic sor-bates within zeolite NaY at 150, 110 and 90 K. As suggested by the Levitation Effect, the self-diffusivity shows a non-monotonic behavior as a function of the diameter of the sorbates. We have computed the entropy of the sorbates of various sizes ranging from 3.07˚ A to 7.0˚ A using the method proposed by Goddard and his co-workers as well as from the radial distribution function. The variation of entropy with the diffusant diameter exhibits a behavior similar to that of the self-diffusivity on diffusant diameter, thereby showing a strong correlation between the entropy and diffusivity. The loss of entropy on adsorption is a minimum for the diffusant with maximum diffu-sivity. This is in agreement with the experimental measurements of Kemball. Thus, entropy follows the prediction of the levitation effect. With decrease in temperature both self-diffusivity as well as entropy show more pronounced maximum as a function of the diameter of the sorbate. The dimensionless diffusivity from three different isotherms follow a Rosenfeld type of excess entropy scaling rule, D∗= Aexp(αSe) where A and α are the scaling coefficients. In Chapter 7 we have investigated the self-diffusivity as well as cor-rected diffusivity of pure methane in faujasite NaY combining quasi elastic neutron scattering experiment and molecular dynamics simu-lation. The QENS experiment carried out at 200 K led to an unex-pected dependence of self-diffusivity on loading for pure methane with the presence of a maximum at 32 CH4/unit cell. This is at variance with previous reports. Typically, diffusivity of a polar species such as methane in a zeolite such as NaY exhibits a monotonic decrease with loading. Molecular dynamics simulation was performed to reproduce this experimentally observed behavior. We could reproduce the diffusivity behavior qualitatively with a maximum at 16 CH4/unit cell. The corrected diffusivities obtained from both experiment as well simulation show similar behavior as the self-diffusivity with maximum at an intermediate loading. The experimental behavior was reproduced only when the interaction of methane with the sodium cation is in-creased suggesting that this interaction may be important. In Chapter8 we have investigated the role of attractive interaction on size dependent diffusivity maximum of ions in water. We have per-formed molecular dynamics simulation of mode lions in water. Earlier study of systems interacting only through van der Waals interaction shows that the size dependent diffusivity maximum or the levitation effect disappears when the attractive term(r−6 term) of the Lennard-Jones potential is put equal to zero. It is not clear whether the absence of the dispersion interaction in a system where there is electrostatic attraction will lead to a size dependent diffusivity maximum. There-fore, two sets of simulations with and without dispersion interaction between the ion and water have been carried out at700Kinorderto understand the influence of the attractive interaction. It is found that the self-diffusivity of the ions indeed exhibits an anomalous maximum as a function of the vanderWaals diameter for both the sets, viz., with dispersion and without dispersion interaction. In fact, the diffusivity maximum is seen to be more pronounced when there is no dispersion interaction. This existence of the maximum in self diffusivity when there is no dispersion interaction between the ion and the water is attributed to the attractive term from electrostatic interactions. De-tailed analysis shows that the solvent shell is more well defined in the presence of dispersion interactions. The velocity auto correlation function shows undulation at short times for the smaller ions indicating rattling motion inside the cage formed by the surrounding water molecules. Smaller ion exhibits a bi-exponential decay while a single exponential decay is seen for the ion with maximum diffusivity in the intermediate scattering function. The solvent structure appears to determine much of the dynamics of the ion. Interesting trends are seen in the activation energies and these can be understood in terms of the Levitation Effect.

Orientador: Átila Madureira Bueno / Resumo: O som é uma onda mecânica e como tal transporta energia que age sobre partículas devido às forças de radiação acústica. O princípio para suspender corpos é aplicar uma força de tal forma a equilibrar seu peso. Na técnica de levitação acústica (AcLev) uma pequena esfera pode ser suspensa pela força de radiação acústica gerada por uma onda estacionária, sendo que o ponto de levitação está localizado na região em que o potencial acústico é mínimo, que é condição necessária para levitar uma esfera com raio muito menor que o comprimento de onda. Levitação acústica (AcLev) é uma ferramenta importante para manusear objetos sem contêineres. Nos anos recentes muitos dispositivos foram desenvolvidos com sucesso devido ao comportamento estável dos dispositivos AcLev. Como resultado, a maioria dos trabalhos sobre Aclev se concentram sobre simulações numéricas ou testes experimentais para estudar a geometria e arranjos dos emissores acústicos, ou a influência de vários tipos de perturbações, e a maioria desses modelos matemáticos considera somente o potencial acústico. Neste trabalho, a equação não linear de movimento para uma partícula levitada imersa em campo acústico de eixo único foi desenvolvida, considerando também forças dissipativas. O espaço parâmetro foi examinado buscando a existência de bifurcações, e faixas de projeto para os ganhos do dispositivo AcLev foram determinadas a partir da condição de existência de pontos de equilíbrio. Em adição, o comportamento dinâmico do dispos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Sound is a mechanical wave and aims to carry energy that acts on particles due to acoustic radiation forces, while the principle to suspend bodies is to apply a force in such a way as to balance their weight. In the acoustic levitation technique (Aclev) a small sphere can be suspended by the acoustic radiation force generated by a stationary wave and the levitation point is located in the region where the acoustic potential is minimal, which is a necessary condition for levitating a sphere with radius much smaller than the wavelength. AcLev is an important tool for handling objects without the use of containers. In recent years many devices have been successfully developed due to the stable behavior of AcLev. As a result, most works on Aclev focuses on numerical simulations and experimental tests to study the geometry and arrangement of acoustic emitters, or the influence of various kinds of perturbations, and most mathematical models consider only acoustic potential. In this work, the nonlinear equation of motion for a levitated particle immersed in an acoustic field with single axis was developed considering also dissipative forces. The parameter space was searched for the existence of bifurcations and the design range for AcLev device gains were determined from the condition of equilibrium points. In addition, the dynamic behavior of the AcLev device regarding gains has been studied, also considering the microgravity situation. Numerical simulations corroborated the analyt... (Complete abstract click electronic access below) / Mestre

With the unique advantage of great isolation from the thermal environment, levitated optomechanics has emerged as a powerful platform for various fields of physics including microscopic thermodynamics, precision measurements, and quantum mechanics. Experiments with optically levitated micro- and nanoparticles have already obtained remarkable feats of zeptonewton force sensing and ground-state cooling. The novel system has also been proposed to assess various theories including the objective collapse models and macroscopic quantum mechanics. <br><div><br></div><div>This thesis reports experimental results on a levitated Cavendish torsion balance, a GHz nanomechanical rotor, and a torque sensor with unprecedented sensitivity realized with optically levitated nanoparticles in a vacuum environment. The system at room temperature achieves a sensitivity of (4.2±1.2)×10−27Nm/ √ Hz surpassing the sensitivity of most advanced nanofabricated torque sensors at cryogenic environments. Calculations suggest potential detection of Casimir torque and vacuum friction under realistic conditions. Moreover, the nanoparticles are driven into ultrafast rotations exceeding 5 GHz, which achieves the fastest humanmade nanomechanical rotor. Such fast rotations allow studies on the ultimate tensile strength of the nanoparticles as well. <br></div><div><br></div><div>Subsequently, the electron spin control of nitrogen vacancies (NV) in optically trapped diamond naoparticles is demonstrated in low vacuum. The configuration is analogous to trapped atoms and ions which serve as a quantum system with internal states. The effect of the air pressure, surrounding gas, and laser power on the electron spin resonance (ESR) are studied, and the temperature of the diamond is also measured with the ESR. The levitated nanodiamonds will provide the means to implement a hybrid spin-optomechanical system.<br></div>

Cette thèse traite de la compensation magnétique de pesanteur. Tout d’abord, des expériences de lévitation magnétique de fluides sont interprétées à l’aide d’un potentiel magnéto-gravitationnel SL. Puis, l’utilisation d’une méthode générale d’analyse de la force magnétique grâce aux harmoniques du champ magnétique est développée. Elle souligne l’importance et le rôle de chacun des trois premiers harmoniques du champ magnétique sur les configurations de forces résultantes inhérentes à la compensation magnétique de pesanteur. En géométrie cylindrique (invariante par translation) diverses combinaisons de forces d’origines magnétique, gravitationnelle et centrifuge offrent des perspectives nouvelles pour la lévitation magnétique. Une combinaison judicieuse des forces magnétiques et centrifuges permet de compenser exactement la pesanteur sur des matériaux diamagnétiques. En géométrie axisymétrique (invariante par rotation), le dimensionnement de stations de lévitation d’oxygène, techniquement réalisables (NbTi@4,2K), est présenté. Ces stations permettent de léviter des volumes d’oxygène supérieurs à 1 litre avec des inhomogénéités inférieures à 1%. La constitution de ces stations rend possible les variations spatiales et temporelles des configurations d’accélérations résultantes. Enfin, la compensation magnétique dynamique de gravité, à l’aide d’une station de lévitation réelle, est étudiée afin de simuler des phases d’accélération ou de décélération d’engins spatiaux / The thesis deals with magnetic gravity compensation. First of all magnetic levitation experiments are explained with the help of a magneto-gravitational potential SL. Next, a general analysis method of the magnetic force is developed which employs magnetic field harmonics. The method underlines both the significance and role of the first three magnetic field harmonics on the resulting forces inherent in magnetic gravity compensation. In cylindrical geometry – with translational invariance – various combination of magnetic, gravitational and centrifugal forces open new possibilities for the magnetic levitation. A suitable combination of both magnetic and centrifugal forces allows exactly compensating gravity on diamagnetic materials. In axisymmetric geometry – with rotational invariance – designs of feasible oxygen magnetic levitation stations are introduced (NbTi@4,2K). Levitation of oxygen volumes more than one litre with inhomogeneities less than 1% can be accomplished within these magnetic levitation facilities. The constitution of the stations makes possible both spatial and temporal variations of the resulting acceleration configurations. At last the dynamic magnetic compensation of gravity with a real coil system is studied so as to simulate both acceleration and deceleration of spaceships

Nous présentons une série d’expériences sur des particules micrométriques de polystyrène de formes ellipsoïdales. Les rapports d’aspects (k) des particules sont variables, de 0.2 à 8 environ. Ces ellipsoïdes sont manipulés dans l’eau par faisceau laser modérément focalisé. On observe la lévitation et l’équilibre dynamique de chaque particule, dans le volume et au contact d’une interface, solide-liquide ou liquide-liquide. Dans une première partie, nous montrons que des particules de k modéré sont piégées radialement. Par contre, les ellipsoïdes allongés (k>3) ou aplatis (k<0.3) ne peuvent pas être immobilisés. Ces particules « dansent » autour du faisceau, dans un mouvement permanent associant translation et rotation. Les mouvements sont périodiques, ou irréguliers (chaotiques) selon les caractéristiques de la particule et du faisceau. Un modèle en 2d est proposé qui permet de comprendre l’origine des oscillations. La seconde partie est une application de la lévitation optique pour une étude de la transition mouillage total-mouillage partiel des particules à l’interface eau-air. Nous montrons que la dynamique de la transition ne dépend pratiquement pas de la forme de particule, et qu’elle est déterminée par le mécanisme d’accrochage-décrochage de la ligne de contact. / We report experiments on ellipsoidal micrometre-sized polystyrene particles. The particle aspect ratio (k) varies between about 0.2 and 8. These particles are manipulated in water by means of a moderately focused laser beam. We observe the levitation and the dynamical state of each particle in the laser beam, in bulk water or in contact to an interface (water-glass, water-air, water-oil). In the first part, we show that moderate-k particles are radially trapped with their long axis lying parallel to the beam. Conversely, elongated (k>3) or flattened (k<0.3) ellipsoids never come to rest, and permanently “dance” around the beam, through coupled translation-rotation motions. The dynamics are periodic or irregular (akin to chaos) depending on the particle type and beam characteristics. We propose a 2d model that indeed predicts the bifurcation between static and oscillating states. In the second part, we apply optical levitation to study the transition from total to partial wetting of the particles at the water-air interface. We show that the dynamics of the transition is about independent of particle shape, and mainly governed by the pinning-depinning mechanism of the contact line.

The subject of this thesis is the real-time implementation of algebraic derivative estimators as observers in nonlinear control of magnetic levitation systems. These estimators are based on operational calculus and implemented as FIR filters, resulting on a feasible real-time implementation. The algebraic method provide a fast, non-asymptotic state estimation. For the magnetic levitation systems, the algebraic estimators may replace the standard asymptotic observers assuring very good performance and robustness. To validate the estimators as observers in closed-loop control, several nonlinear controllers are proposed and implemented in a experimental magnetic levitation prototype. The results show an excellent performance of the proposed control laws together with the algebraic estimators. / O tema dessa dissertação é a implementação em tempo real dos estimadores algébricos de derivadas como observadores no controle não-linear de levitação magnética. Esses estimadores são baseados no cálculo operacional e implementados como filtros FIR, resultando em uma implementação viável em tempo real. O método algébrico permite estimar os estados do sistema de maneira rápida e não-assintótica. Para os sistemas de levitação magnética, os estimadores algébricos podem substituir os observadores assintóticos assegurando boas propriedades de robustez e performance. A fim de validar os estimadores como observadores no controle em malha fechada, vários controladores não-lineares são propostos e implementados em um protótipo experimental. Os resultados mostram uma excelente performance dos controladores propostos juntamente com os estimadores algébricos.

Sistemas de levitação eletromagnética são de interesse quando se necessita de tecnologia envolvendo redução de atrito, atuação sem contato físico, máquinas rotativas e trens de alta velocidade. Devido à presença de não linearidades em sua dinâmica, pesquisadores têm dado atenção ao desenvolvimento de controladores mais sofisticados, com o objetivo de melhorar o desempenho desses sistemas. Controladores lineares apresentam limitações na faixa de operação da variável controlada e, geralmente apresentam baixa robustez quando aplicados em sistemas não lineares. O objetivo deste trabalho é desenvolver controladores não lineares com diferentes estruturas e analisá-los quando aplicados em um protótipo do sistema físico. Inicialmente, o sistema é modelado matematicamente através da abordagem fenomenológica. Em seguida, os parâmetros do modelo são identificados através de dados obtidos experimentalmente. Conhecendo bem a dinâmica do sistema através do modelo, são projetados três controladores de diferentes estruturas utilizando simulações computacionais. O primeiro é o PID clássico, controle linear amplamente utilizado em processos industriais. O segundo controlador é um PID com topologia não linear, denominado NPID. Este visa reduzir as limitações encontradas no PID linear, através de funções não lineares em seus termos. O último e mais complexo se trata do controle por modos deslizantes (SMC). Também com estrutura não linear, o SMC possui como característica intrínseca a robustez a variações da planta. Ao final, são realizadas simulações e os controladores avaliados são implementados de maneira digital em um hardware de controle e aplicados em uma planta piloto de levitação eletromagnética. Os resultados de desempenho obtidos permitem avaliar qual topologia de controlador melhor se enquadra diante dessa aplicação. / Electromagnetic levitation systems are of interest when it is necessary the use of technology involving reduction of friction, acting without physical contact, rotating machinery and high speed trains. Due to the nonlinear dynamics, researchers have paid attention to the development of more sophisticated controllers, in order to improve the performance of these systems. Linear controllers have limitations in the operating range of the controlled variable and generally have low robustness when applied to linear systems. The objective of this work is to develop nonlinear controllers with different structures and analyze them, when applied to a prototype of the physical system. Initially the system is modeled mathematically through the phenomenological approach. Then the model parameters are identified by experimentally obtained data. Knowing the dynamic of the system through the model, three different controllers are designed using computer simulations. The first is the classic PID, a linear control widely used in industrial processes. The second controller is a PID with nonlinear topology, called NPID. This controller is intended to reduce the limitations found in the linear PID through non linear functions on its terms. The last and most complex is the sliding mode control (SMC). Also a nonlinear structure, the SMC has the intrinsic characteristic of robustness to variations of the plant. In the end, the simulations are performed and the evaluated controllers are implemented in digital form in a hardware control and applied in a pilot plant of an electromagnetic levitation system. With the performance results it is possible to verify which controller topology best fits this application.

The aortic valve maintains unidirectional blood flow between the left ventricle and the systemic circulation. When diseased, the valve is replaced either by a mechanical or a bioprosthetic heart valve, that carry issues such as thrombogenesis, long term structural failure, and calcification, necessitating the development of more structurally and biologically sufficient long-term replacements. Tissue engineering provides a possible avenue for development, combining cells, scaffolds, and biochemical factors to regenerate tissue. The overall goal of this dissertation was to create a foundation for the rational design of a tissue engineered aortic valve. The novel approach taken in this thesis research was to view each of the three leaflets as a laminate structure. The first three aims consider the leaflet as a laminate structure comprising of layers of collagen, elastin, and glycosaminoglycans (GAGs). In the first aim, the effect of GAGs on the tensile properties and stress relaxation in the leaflet was investigated, by removing GAGs through increasing amounts of hyaluronidase. A decrease in GAGs led to significantly higher elastic moduli, maximum stresses, and hysteresis in the leaflet. In the second aim, the 3D elastic fiber network of the leaflet was characterized using immunohistochemistry and scanning electron microscopy. This structure was found to have regionally varying thicknesses and patterns. In the third aim, a novel hydrogel-fiber composite design was proposed to match the anisotropy of the leaflet. This composite composed of aligned electrospun poly(ε-caprolactone) (PCL) within a poly(ethylene glycol) diacrylate (PEGDA) matrix. Surface modification and embedding of the PCL did not significantly alter the anisotropy or strength of the underlying PCL scaffold, providing the basis for an anisotropic, biocompatible scaffold. In the last aim, a novel co-culture model was designed using magnetic levitation as a layered structure of valvular endothelial cells and interstitial cells. This technique was used to create co-culture models within hours, while maintaining cell phenotype and function, and inducing extracellular matrix formation, as shown by immunohistochemical stains and their gene expression profiling. The overall result of this dissertation is a clearer understanding of the layered structure-function relationship of the aortic valve, and its application towards heart valve tissue engineering.