The objective of this research is to verify the three degree of freedom capabilities of a bio-inspired quad flapping-wing micro aerial vehicle in simulation and in hardware. The simulation employs a nonlinear plant model and input-output feedback linearization controller to verify the three degree of freedom capabilities of the vehicle. The hardware is a carbon fiber test bench with four flapping wings and an embedded avionics system which is controlled via a PD linear controller. Verification of the three degree of freedom capabilities of the quad flapping-wing concept is achieved by analyzing the response of both the simulation and test bench to pitch, roll, and yaw attitude commands.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

O objetivo deste trabalho é estudar as principais características de uma família de modelos que busca retratar a dinâmica do equilíbrio geral de uma economia. Por equilíbrio em economia entende-se como sendo uma situação onde nenhum agente econômico tem qualquer incentivo para modificar a sua estratégia escolhida. Neste trabalhamos não haverá uma preocupação em demonstrar a existência, unicidade e estabilidade do equilíbrio, mas sim entender como alterações exógenas afetam o equilíbrio. Brevemente, podemos entender a definição de equilíbrio geral como sendo a perspectiva de análise de equilíbrio simultâneo entre todos os mercados de uma economia. No conceito de equilíbrio geral todos os mercados devem estar em equilíbrio, de modo que nenhuma mudança em um mercado específico não venha a recompensar um determinado agente. O equilíbrio geral é constratado com a perspectiva de equilíbrio parcial, no qual parte da economia é considerada, tomando-se como dado o que está acontecendo nos demais mercados. Os modelos de equilíbrio geral que envolvem dinâmica e choques estocástico são conhecidos pelo acrônimo DSGE, ou seja, Dynamic Stochastic General Equilibrium. Na realidade trata-se de uma família de modelos, pois compreendem uma gama variada de modelos com diferentes níveis de sofisticação. Neste exercício pelo caráter generalista da modelagem decidimos por estudar o modelo DSGE proposto por Smets-Wouters (2003). Veremos neste estudo uma descrição deste modelo, seus fundamentos teóricos, e uma simulação deste modelo, de modo a vermos quais as direções de política econômica que tal modelo nos permite compreender. Os resultados obtidos utilizando-se dados da economia americana nos permitiu inferir direções para as variáveis produto e consumo diante de um choque de inovação. Foi possível por meio do modelo adotado estimar uma direção para a trajetória do PIB para os próximos anos. / The purpose of this academic work is to study a family of models called stochastic economic general equilibrium models (DSGE), and implement a solution to a general model developed model by Smets-Wouters (2003). We will note in this essay a description of this model, its theoretical foundations, and a simulation of this model, so as to see what the economic policy directions that such a model allows us to understand. The results obtained using data from the US economy allowed us to infer directions for the variables product and consumption under a innovation shock. Yet we will be able to estimate a direction to the trajectory of PIB for years to next years.

Scaling of CMOS to nanometer dimensions has enabled dramatic improvement in digital power efficiency, with lower VDD supply voltage and decreased power consumption for logic functions. However, most traditionally prevalent ADC architectures are not well suited to the lower VDD environment. The improvement in time resolution enabled by increased digital speeds naturally drives design toward time-domain architectures such as voltage-controlled-oscillator (VCO) based ADCs. The major obstacle in the VCO-based technique is linearizing the VCO voltage-to-frequency characteristic. Achieving signal-to-noise (SNR) performance better than -40dB requires some form of calibration, which can be realized by analog or digital techniques, or some combination. A further challenge is implementing calibration without degrading energy efficiency performance. This thesis project discusses a complete design of a 10 bit three stage ring VCO-based ADC. A lookup-table (LUT) digital correction technique enabled by the "Split ADC" calibration approach is presented suitable for linearization of the ADC. An improvement in the calibration algorithm is introduced to ensure LUT continuity. Measured results for a 10 bit 48.8-kSps ADC show INL improvement of 10X after calibration convergence.

Orientador: John Fredy Franco Baquero / Resumo: O planejamento bem-sucedido de redes de distribuição requer uma metodologia que inclua um modelo de rede preciso que considere não apenas os custos econômicos, mas também os custos associados à confiabilidade do sistema. Considerando estas duas características essenciais, esta tese propõe modelos matemáticos que permitam incluir a avaliação da confiabilidade dentro do problema do planejamento de expansão de sistemas de distribuição com múltiplos estágios, visando expandir os ativos de rede (ramos e subestações) e minimizar os custos de confiabilidade do sistema. Em relação às características da rede, o modelo de planejamento proposto utiliza um fluxo de potência AC não-linear e não convexo, que é convertido em um problema convexo usando reformulação cônica, técnicas de linearização por partes, com o intuito de obter tratabilidade computacional usando técnicas clássicas de otimização. Além disso, a avaliação de confiabilidade convencional baseada em simulação é implementada de forma equivalente por meio de expressões algébricas dentro do modelo matemático. Vários casos de estudo são usados ​​para demostrar a eficácia da metodologia de planejamento proposta. / Abstract: Successful planning of distribution networks requires a methodology that includes an accurate network model that considers not only the economic costs but also the costs associated with system reliability. Considering these two essential characteristics, this thesis proposes mathematical models that include reliability assessment within multi-stage expansion planning problem of distribution systems, aiming at expanding network assets (branches and substations) and minimizing reliability costs of the system. In relation to the network characteristics, the proposed planning model uses a non-convex nonlinear AC power flow, which is converted into a convex problem using conic reformulation and piece-wise linearization, to obtain the computational treatability using classical optimization techniques. In addition, conventional simulation-based reliability assessment is implemented equivalently through algebraic expressions. Several benchmarks are used to demonstrate the effectiveness of the proposed planning methodology. / Doutor

As válvulas de controle são elementos finais muito importantes na indústria de processos, pois são as responsáveis por controlar a pressão em dutos ou vazão dos fluidos de processo, impactando diretamente na qualidade do produto final. Por serem elementos mecânicos móveis estão sujeitas ao atrito, uma não linearidade que quando excessiva, pode causar oscilações e erros na abertura da válvula. A presença de oscilações nas malhas de controle aumenta a variabilidade das variáveis de processo, o desgaste dos componentes e o consumo de energia, além de provocar o desperdício de materiais. O desenvolvimento de novas técnicas de compensação de atrito é fundamental para melhorar o desempenho das malhas de controle, sendo, portanto, de grande interesse para a indústria de processos industriais. Este trabalho apresenta o estudo de cinco compensadores não lineares: controlador rastreador de trajetória, controlador por modos deslizantes, controlador por modos deslizantes integrador, controlador por modelo interno não linear e controlador PI não linear, os quais são desenvolvidos desde a teoria à implementação prática em uma válvula de controle real. Os resultados obtidos, mostram que os controladores projetados apresentaram desempenho bastante satisfatórios, sendo que o controlador por modos deslizantes e por modos deslizante integrador apresentaram os melhores desempenho. / Control valves are very important final elements in process industry, due they are the responsible to control the pressure in pipelines and the flow of the process fluids, directly impacting in the quality of the final product. Due to the mechanical mobile elements, they are subjected to friction, a nonlinearity that can generate oscillations and errors in the valve aperture. Oscillations in the control loops increase the process variability, wear in the actuators and the power consumption, besides generating raw material waste. The development of new friction compensation techniques is very important to increase the control loops performance, therefore, it is of great interest for the process industry. This work presents the study of five nonlinear compensators: Trajectory tracking controller, sliding mode controller, sliding mode controller integrator, nonlinear internal model controller and nonlinear PI controller, which ones are developed from theory to practical implementation in a real control valve. The results show that the controllers presented satisfactory performance, where the sliding mode controller and sliding mode control integrator presented the best performance.

O objetivo deste trabalho é estudar as principais características de uma família de modelos que busca retratar a dinâmica do equilíbrio geral de uma economia. Por equilíbrio em economia entende-se como sendo uma situação onde nenhum agente econômico tem qualquer incentivo para modificar a sua estratégia escolhida. Neste trabalhamos não haverá uma preocupação em demonstrar a existência, unicidade e estabilidade do equilíbrio, mas sim entender como alterações exógenas afetam o equilíbrio. Brevemente, podemos entender a definição de equilíbrio geral como sendo a perspectiva de análise de equilíbrio simultâneo entre todos os mercados de uma economia. No conceito de equilíbrio geral todos os mercados devem estar em equilíbrio, de modo que nenhuma mudança em um mercado específico não venha a recompensar um determinado agente. O equilíbrio geral é constratado com a perspectiva de equilíbrio parcial, no qual parte da economia é considerada, tomando-se como dado o que está acontecendo nos demais mercados. Os modelos de equilíbrio geral que envolvem dinâmica e choques estocástico são conhecidos pelo acrônimo DSGE, ou seja, Dynamic Stochastic General Equilibrium. Na realidade trata-se de uma família de modelos, pois compreendem uma gama variada de modelos com diferentes níveis de sofisticação. Neste exercício pelo caráter generalista da modelagem decidimos por estudar o modelo DSGE proposto por Smets-Wouters (2003). Veremos neste estudo uma descrição deste modelo, seus fundamentos teóricos, e uma simulação deste modelo, de modo a vermos quais as direções de política econômica que tal modelo nos permite compreender. Os resultados obtidos utilizando-se dados da economia americana nos permitiu inferir direções para as variáveis produto e consumo diante de um choque de inovação. Foi possível por meio do modelo adotado estimar uma direção para a trajetória do PIB para os próximos anos. / The purpose of this academic work is to study a family of models called stochastic economic general equilibrium models (DSGE), and implement a solution to a general model developed model by Smets-Wouters (2003). We will note in this essay a description of this model, its theoretical foundations, and a simulation of this model, so as to see what the economic policy directions that such a model allows us to understand. The results obtained using data from the US economy allowed us to infer directions for the variables product and consumption under a innovation shock. Yet we will be able to estimate a direction to the trajectory of PIB for years to next years.

Denna avhandling är fokuserad på modellering av elkraftsystemkomponenter och deras representation vid simuleringar av elkraftsystem. Avhandlingen jämför olika linjäriseringstekniker. Dessa tekniker är såväl numeriska som analytiska och används vid linjärisering av ett dynamiskt system. Efter en linjärisering är det möjligt att beräkna egenvärdena av det linjäriserade systemet samt använda andra verktyg ämnade för studier av linjära system. I avhandlingen visas hur olika linjäriseringtekniker influerar egenvärdesberäkningen av det linjära systemet. I avhandlingen tas fram bandviddsreducerade linjära modeller av en kraftsystemkomponent med hjälp av två tekniker. Senare görs simuleringar med de linjära modellerna tillsammans med ett introducerat gränssnitt. Den studerade kraftsystemkomponenten är en tyristorstyrd seriekondensator (TCSC). En fördel med att använda en linjär representation av en kraftsystemkomponent är att det förenklar simuleringarna. Storleken på komplexiteten av en simulering vid lösandet av ekvationerna minskar och den konsumerade fysiska tiden att simulera minskar. En nackdel med en linjär modell är att dess giltighet kan vara begränsad. Behovet av att bygga linjära modeller av kraftsystemkomponenter torde även finnas i framtiden. Med dagens horisont (år 2006) finns behov av att bygga linjära modeller utgående från detaljerade modeller av bl a högspända likströmslänkar (HVDC-länkar), reaktiva effektkompensatorer (SVC) samt tyristorstyrda seriekondensatorer (TCSC). Hur skall dessa representeras när vi vill studera dynamiken av ett helt kraftsystem och det då är nödvändigt att reducera deras komplexitet? Denna frågeställning uppkommer när vi vill genomföra tidsdomänsimuleringar på en inte alltför detaljerad nivå av de individuella kraftsystemkomponenterna eller när vi vill linjärisera kraftsystemet för att studera dess stabilitet med hjälp av småsignalanalys. / This thesis is focused in modelling of power system components and their representation in simulations of power systems. The thesis compares different linearization techniques. These techniques are both numerical as well as analytical and are utilized when linearization of a dynamic system is desired. After a linearization it is possible to calculate the eigenvalues of the linearized system as well as to perform other applicable activities on a linear system. In the thesis it is shown how the linearization techniques influence the calculation of eigenvalues of the linear system. In the thesis bandwidth-reduced linear models of a power system component are developed using two techniques. The simulations with the linear models are done with an introduced interface system. The studied power system component is a Thyristor-Controlled Series Capacitor (TCSC). One advantage with using a linear representation of a power system component is that it simplifies the simulations. The size of the complexity of a simulation when solving the equations decreases and the consumed physical time to simulate becomes shorter. A disadvantage of a linear model is that its validity might be limited. The need of building linear models of power systems will continue to attract interest in the future. With the horizon of today (year 2006) there is a need of among other models to build linear models of detailed models of High Voltage Direct Current-links (HVDC-links), Static Var Compensators (SVCs), as well as Thyristor-Controlled Series Capacitors (TCSCs). How should these be represented when we want to study the dynamics of a whole power system and it is necessary to reduce their complexity? This question rises when we want to perform time-domain simulations with a not too detailed level of complexity of each individual power system component or if we want to linearize the power system and study it within small-signal stability analysis. / QC 20100915

Off-road and racing motorcycles require a particular setup of the suspension to improve the comfort and the safety of the rider. Further, due to ground unevenness, off-road motorcycle suspensions usually experience extreme and erratic excursions in performing their function. In this regard, the adoption of nonlinear devices, such as progressive springs and hydro pneumatic shock absorbers, can help limiting both the acceleration experienced by the sprung mass and the excursions of the suspensions. For dynamic analysis purposes, this option involves the solution of the nonlinear differential equations that govern the motion of the motorcycle, which is excited by the stochastic road ground profile. In this study a 4 degrees-of-freedom (4-DOF) nonlinear motorcycle model is considered. The model involves suspension elements with asymmetric behaviour. Further, it is assumed that the motorcycle is exposed to loading of a stochastic nature as it moves with a specified speed over a road profile defined by a particular power spectrum. It is shown that a meaningful analysis of the motorcycle response can be conducted by using the technique of statistical linearization. The validity of the proposed approach is established by comparison with results from pertinent Monte Carlo studies. In this context the applicability of auto-regressive (AR) filters for efficient implementation of the Monte Carlo simulation is pointed out. The advantages of these methods for the synthesis of excitation signals from a given power spectrum, are shown by comparison with other methods. It is shown that the statistical linearization method allows the analysis of multi-degree-of-freedom (M-DOF) systems that present strong nonlinearities, exceeding other nonlinear analysis methods in both accuracy and applicability. It is expected that the proposed approaches, can be used for a variety of parameter/ride quality studies and as preliminary design tool by the motorcycle industry.

This master's thesis deals with the control design method called Non-linear Dynamic Inversion (NDI) and how it can be applied to Unmanned Aerial Vehicles (UAVs). In this thesis, simulations are conducted using a model for the unmanned aerial vehicle SHARC (Swedish Highly Advanced Research Configuration), which Saab AB is developing. The idea with NDI is to cancel the non-linear dynamics and then the system can be controlled as a linear system. This design method needs much information about the system, or the output will not be as desired. Since it is impossible to know the exact mathematical model of a system, some kind of robust control theory is needed. In this thesis integral action is used. A problem with NDI is that the mathematical model of a system is often very complex, which means that the controller also will be complex. Therefore, a controller that uses pure NDI is only discussed, and the simulations are instead based on approximations that use a cascaded NDI. Two such methods are investigated. One that uses much information from aerodata tables, and one that uses the derivatives of some measured outputs. Both methods generate satisfying results. The outputs from the second method are more oscillatory but the method is found to be more robust. If the signals are noisy, indications are that method one will be better.