This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

Neste trabalho foram desenvolvidos sistemas microfluídicos para aplicações na produção de micro e nanopartículas. Os dispositivos microfluídicos foram microfabricados em vidros do tipo borosilicato e em cerâmica verde LTCC (Low Temperature Co-fired Ceramic). Para os dispositivos em vidro foram utilizadas técnicas de fotolitografia, corrosão úmida e soldagem por cola UV. Com estas técnicas foram produzidos sistemas planares com diversas geometrias, sistemas com dispositivos em paralelo com duas e três camadas de vidros. Além disso, dois polímeros o Benzociclobuteno (BCB) e o Parylene-C foram apresentados como ferramenta para a modificação da superfície do vidro de hidrofílica para hidrofóbica. A cerâmica LTCC foi utilizada para a produção de um sistema microfluídico para focalização hidrodinâmica em 3 dimensões. Os dispositivos microfabricados foram utilizados para estudos sobre a produção de emulsões simples e duplas, observando a influência de parâmetros como taxa de fluxo, razão entre fluxos e diferentes tipos de emulsificantes no tamanho das gotas e no tipo de corte obtido em cada situação. Observou-se que o tamanho máximo das gotas obtidas fica restringido ao tamanho do canal microfabricado, cerca de 50m e o tamanho mínimo obtido foi de 15m. Além da produção de emulsões, foi estudada a produção de nanosuspensões pela técnica de nanoprecipitação anti-solvente. Para este estudo, além das geometrias planares, foram testadas as geometrias 3D e também sistemas para o aumento de escala de produção, onde o sistema integrado possuía 4 dispositivos para nanoprecipitação. Os resultados obtidos indicaram que os sistemas microfluídicos permitem a produção de nanopartículas amorfas, na faixa de 100 a 1000 nm, com baixa polidispersão, sendo ainda reprodutíveis em sistema de maior escala. O desenvolvimento deste trabalho mostrou que a microfluídica oferece ferramentas importantes na obtenção de micro e nanopartículas. / In this work microfluidic systems were developed for applications in micro and nanoparticles production. Microfluidic devices were microfabricated in borosilicate glasses substrates and LTCC ceramic (Low Temperature Co-fired Ceramic). For glass devices were used techniques such as photolithography, wet etching and UV glue for sealing glass wafers. With these techniques were manufactured planar systems with various geometries, systems with devices in parallel with two and three glass layers. In addition, two polymers, BCB and Parylene-C, were presented as a tool for glass surface modification, from hydrophilic to hydrophobic. The ceramic LTCC was used for the production of a microfluidic system for hydrodynamic focusing in three dimensions. The devices were used for studies on the single and double emulsions production, observing the influence of parameters such as flow rate, ratio between flows and different types of surfactants at the droplet size and droplet cut type obtained in each situation. It was observed that the maximum size of the droplets obtained is restricted by the channel size, the maximum was about 50m and the minimum size of 15m. Besides, the devices were used to produce nanoparticles using anti-solvent nanoprecipitation technique. For these studies, besides the planar geometries, 3D geometries were tested and also systems for increasing scale production, where 4 devices were integrated in one system for nanoprecipitation. The results indicated that the microfluidic systems allow the production of amorphous nanoparticles in the range of 100 to 1000 nm with low polydispersity, being also reproducible in a larger scale system. The development of this work has shown that microfluidics offers valuable tools in obtaining micro-and nanoparticles.

Neste trabalho foram desenvolvidos sistemas microfluídicos para aplicações na produção de micro e nanopartículas. Os dispositivos microfluídicos foram microfabricados em vidros do tipo borosilicato e em cerâmica verde LTCC (Low Temperature Co-fired Ceramic). Para os dispositivos em vidro foram utilizadas técnicas de fotolitografia, corrosão úmida e soldagem por cola UV. Com estas técnicas foram produzidos sistemas planares com diversas geometrias, sistemas com dispositivos em paralelo com duas e três camadas de vidros. Além disso, dois polímeros o Benzociclobuteno (BCB) e o Parylene-C foram apresentados como ferramenta para a modificação da superfície do vidro de hidrofílica para hidrofóbica. A cerâmica LTCC foi utilizada para a produção de um sistema microfluídico para focalização hidrodinâmica em 3 dimensões. Os dispositivos microfabricados foram utilizados para estudos sobre a produção de emulsões simples e duplas, observando a influência de parâmetros como taxa de fluxo, razão entre fluxos e diferentes tipos de emulsificantes no tamanho das gotas e no tipo de corte obtido em cada situação. Observou-se que o tamanho máximo das gotas obtidas fica restringido ao tamanho do canal microfabricado, cerca de 50m e o tamanho mínimo obtido foi de 15m. Além da produção de emulsões, foi estudada a produção de nanosuspensões pela técnica de nanoprecipitação anti-solvente. Para este estudo, além das geometrias planares, foram testadas as geometrias 3D e também sistemas para o aumento de escala de produção, onde o sistema integrado possuía 4 dispositivos para nanoprecipitação. Os resultados obtidos indicaram que os sistemas microfluídicos permitem a produção de nanopartículas amorfas, na faixa de 100 a 1000 nm, com baixa polidispersão, sendo ainda reprodutíveis em sistema de maior escala. O desenvolvimento deste trabalho mostrou que a microfluídica oferece ferramentas importantes na obtenção de micro e nanopartículas. / In this work microfluidic systems were developed for applications in micro and nanoparticles production. Microfluidic devices were microfabricated in borosilicate glasses substrates and LTCC ceramic (Low Temperature Co-fired Ceramic). For glass devices were used techniques such as photolithography, wet etching and UV glue for sealing glass wafers. With these techniques were manufactured planar systems with various geometries, systems with devices in parallel with two and three glass layers. In addition, two polymers, BCB and Parylene-C, were presented as a tool for glass surface modification, from hydrophilic to hydrophobic. The ceramic LTCC was used for the production of a microfluidic system for hydrodynamic focusing in three dimensions. The devices were used for studies on the single and double emulsions production, observing the influence of parameters such as flow rate, ratio between flows and different types of surfactants at the droplet size and droplet cut type obtained in each situation. It was observed that the maximum size of the droplets obtained is restricted by the channel size, the maximum was about 50m and the minimum size of 15m. Besides, the devices were used to produce nanoparticles using anti-solvent nanoprecipitation technique. For these studies, besides the planar geometries, 3D geometries were tested and also systems for increasing scale production, where 4 devices were integrated in one system for nanoprecipitation. The results indicated that the microfluidic systems allow the production of amorphous nanoparticles in the range of 100 to 1000 nm with low polydispersity, being also reproducible in a larger scale system. The development of this work has shown that microfluidics offers valuable tools in obtaining micro-and nanoparticles.