16 resultados para tilt

em Universidad Politécnica de Madrid


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The use of modular or ‘micro’ maximum power point tracking (MPPT) converters at module level in series association, commercially known as “power optimizers”, allows the individual adaptation of each panel to the load, solving part of the problems related to partial shadows and different tilt and/or orientation angles of the photovoltaic (PV) modules. This is particularly relevant in building integrated PV systems. This paper presents useful behavioural analytical studies of cascade MPPT converters and evaluation test results of a prototype developed under a Spanish national research project. On the one hand, this work focuses on the development of new useful expressions which can be used to identify the behaviour of individual MPPT converters applied to each module and connected in series, in a typical grid-connected PV system. On the other hand, a novel characterization method of MPPT converters is developed, and experimental results of the prototype are obtained: when individual partial shading is applied, and they are connected in a typical grid connected PV array

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In Brazil, a low-latitude country characterized by its high availability and uniformity of solar radiation, the use of PV solar energy integrated in buildings is still incipient. However, at the moment there are several initiatives which give some hints that lead to think that there will be a change shortly. In countries where this technology is already a daily reality, such as Germany, Japan or Spain, the recommendations and basic criteria to avoid losses due to orientation and tilt are widespread. Extrapolating those measures used in high latitudes to all regions, without a previous deeper analysis, is standard practice. They do not always correspond to reality, what frequently leads to false assumptions and may become an obstacle in a country which is taking the first step in this area. In this paper, the solar potential yield for different surfaces in Brazilian cities (located at latitudes between 0° and 30°S) are analyzed with the aim of providing the necessary tools to evaluate the suitability of the buildings’ envelopes for photovoltaic use

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El objetivo principal de esta Tesis es extender la utilización del “Soft- Computing” para el control de vehículos sin piloto utilizando visión. Este trabajo va más allá de los típicos sistemas de control utilizados en entornos altamente controlados, demonstrando la fuerza y versatilidad de la lógica difusa (Fuzzy Logic) para controlar vehículos aéreos y terrestres en un abanico de applicaciones diferentes. Para esta Tesis se ha realizado un gran número de pruebas reales en las cuales los controladores difusos han manejado una plataforma visual “pan-and-tilt”, un helicoptero, un coche comercial y hasta dos tipos de quadrirotores. El uso del método de optimización “Cross-Entropy” ha sido utilizado para mejorar el comportamiento de algunos de los controladores borrosos. Todos los controladores difusos presentados en ésta Tesis han sido implementados utilizando un código desarrollado por el candidato para tal efecto, llamado MOFS (Miguel Olivares’ Fuzzy Software). Diferentes algoritmos visuales han sido utilizados para adquirir la informaci´on visual del entorno, “Cmashift”, descomposición de la homografía y detección de marcas de realidad aumentada, entre otros. Dicha información visual ha sido utilizada como entrada de los controladores difusos para comandar los vehículos en las diferentes applicaciones autonomas. El volante de un vehículo comercial ha sido controlado para realizar pruebas de conducción autónoma en condiciones de tráfico similares a las de una ciudad. El sistema ha llegado a completar con éxito pruebas de más de 6 km sin ninguna interacción humana, mediante el seguimiento de una línea pintada en el suelo. El limitado campo visual del sistema no ha sido impedimento para alcanzar velocidades de hasta 48 km/h y ser guiado autonomamente en curvas de radio reducido. Objetos estáticos y móviles han sido seguidos desde un helicoptero no tripulado, mediante el control de una plataforma visual “pan-and-tilt”. ´Éste mismo helicoptero ha sido controlado completamente para su aterrizaje autonomo, mediante el control del movimiento lateral (roll), horizontal (pitch) y de altitud. El seguimiento de objetos volantes ha sido resulto mediante el control horizontal (pitch) y de orientación (heading) de un quadrirotor. Para tareas de evitación de obstáculos se ha implementado un controlador difuso para el manejo de la orientación (heading) de un quadrirotor. En el campo de la optimización de controladores se ha aportado al estado del arte una extensión del uso del método “Cross-Entropy”. Está Tesis presenta una novedosa implementación de dicho método para la optimización de las ganancias, la posición y medida de los conjuntos de las funciones de pertenecia y el peso de las reglas para mejorar el comportamiento de un controlador difuso. Dichos procesos de optimización se han realizado utilizando “ROS” y “Matlab Simulink” para obtener mejores resultados para la evitación de colisiones con vehículos aéreos no tripulados. Ésta Tesis demuestra que los controladores implementados con lógica difusa son altamente capaces de controlador sistemas sin tener en cuenta el modelo del vehículo a controlador en entornos altamente perturbables con un sensor de bajo coste como es una cámara. El ruido presentes causado por los cambios de iluminación en la adquisición de imágenes y la alta incertidumbre en la detección visual han sido manejados satisfactoriamente por ésta técnica de de “Soft-Computing” para distintas aplicaciones tanto con vehículos aéreos como terrestres.

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The effect of crystal misorientation, geometrical tilt, and contact misalignment on the compression of highly anisotropic single crystal micropillars was assessed by means of crystal plasticity finite element simulations. The investigation was focused in single crystals with the NaCl structure, like MgO or LiF, which present a marked plastic anisotropy as a result of the large difference in the critical resolved shear stress between the “soft” {110}〈110〉 and the “hard” {100}〈110〉 active slip systems. It was found that contact misalignment led to a large reduction in the initial stiffness of the micropillar in crystals oriented in the soft and hard direction. The crystallographic tilt did not modify, however, the initial crystal stiffness. From the viewpoint of the plastic response, none of the effects analyzed led to significant differences in the flow stress when the single crystals were oriented along the “soft” [100] direction. Large differences were found, however, if the single crystal was oriented in the “hard” [111] direction as a result of the activation of the soft slip system. Numerical simulations were in very good agreement with experimental literature data.

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We have analyzed a resonant behavior in the dielectric constant associated to the barrier of YBa2Cu3O7 (YBCO) grain boundary Josephson junctions (GBJJs) fabricated on a wide variety of bicrystalline substrates: 12° [0 0 1] tilt asymmetric, 24° [0 0 1] tilt asymmetric, 24° [0 0 1] tilt symmetric, 24° [1 0 0] tilt asymmetric, 45° [1 0 0] tilt asymmetric and 24° [0 0 1] tilt symmetric +45° [1 0 0] tilt asymmetric bicrystals. The resonance analysis allows us to estimate a more appropriate value of the relative dielectric constant, and so a more adequate value for the length L of the normal N region assuming a SNINS model for the barrier. In this work, the L dependence on the critical current density Jc has been investigated. This analysis makes possible a single representation for all the substrate geometries independently on around which axes the rotation is produced to generate the grain boundary. On the other hand, no clear evidences exist on the origin of the resonance. The resonance frequency is in the order of 1011 Hz, pointing to a phonon dynamic influence on the resonance mechanism. Besides, its position is affected by the oxygen content of the barrier: a shift at low frequencies is observed when the misorientation angle increases.

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A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,…) combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the governing equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism

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El proyecto trata del estudio de la tasa de absorción específica (SAR). En él se estudia la SAR que desprenden distintos dispositivos de comunicaciones inalámbricos. Se ha llevado a cabo en las instalaciones de la SETSI, en el laboratorio de radiofrecuencia situado en El Casar, Guadalajara, que pertenece al Ministerio de Industria Comercio y Turismo. La SAR es una relación entre la energía electromagnética acumulada en una masa de un material o tejido concreto. Por tanto, lo primero es definir la SAR, en la que se exponen sus parámetros. Además, se recogen los límites de exposición fijados por las normas internacionales IEC 62209-1 e IEC 62209-2 en relación a SAR. Posteriormente, acorde con las normas, se realiza una definición detallada de un banco de medidas de SAR, en donde se explica cada uno de los componentes del banco de manera detallada así como los sistemas que intervienen previamente a la realización de la medida, tipos de los sistemas para realizar las verificaciones pertinentes, y también las incertidumbres de ciertos parámetros. También se realiza un proceso completo de medida de SAR en el laboratorio de la SETSI, donde se realizan las comprobaciones necesarias para la realización de una serie de medidas sobre dispositivos de comunicaciones móviles. Éstas medidas se realizan primero sobre un teléfono móvil en las frecuencias de GSM, UMTS y WIFI, en las configuraciones estipuladas por la norma; “tocando” e “inclinada 15°” comparando los valores obtenidos con los límites marcados por las normas internacionales. Por último, en este apartado se realizan ciertas medidas con otras configuraciones que no están recogidas en la norma para intentar obtener los máximos valores de SAR posibles. Después se realiza una comparación entre dos dispositivos tipo “tablet”, para ello se realizan medidas en la banda de WIFI y se comentan los resultados obtenidos, relacionado con el diseño de cada uno de ellos. Posteriormente se realiza un presupuesto de un banco de SAR, donde se detallan todos los componentes que intervienen en la realización de las medidas de SAR, pero no se incluyen en él, los costes de mantenimiento o los costes relacionados con su uso. Por último se explican las conclusiones finales desprendidas de la realización de este proyecto de fin de carrera así como la bibliografía utilizada. ABTRACT This project consists on the study of the specific absorption rate (SAR).It studies the different SAR of several wireless communications devices. It has been held in SETSI’S facilities, in its radio frecuency laboratory located in El Casar, Guadalajara, which belongs to the Ministy of Industry, Trade and Tourism. The SAR is a ratio between the electromagnetic energy accumulated in a mass of concrete material or tissue. Therefore, the SAR is defined first, which sets its parameters. Also lists the exposure limits set by international standards IEC 62209-1 and IEC 62209-2 regarding SAR. Subsequently, according to the guidelines, performing a detailed definition of a SAR measures bench, which explains each of the components in detail of the bench and involved systems prior to the realization of the extent and types of systems to perform the necessary checks, and certain parameters uncertainties. Also performed a complete process for SAR in the SETSI laboratory, located in El Casar, Guadalajara, where the necessary checks are made to carry out a serie of measures on mobile communications devices. These will be carried out first on a mobile phone at frequencies of GSM, UMTS and WiFi, in the configurations set by the standard, "touch" and "tilt 15 °" comparing the values obtained with the limits set by international standards. Finally, this section will perform certain actions with other configurations that are not included in the standard to try to get the maximum possible SAR values. Then a comparison is made between two devices, such as "tablet", this will make measurements in the band WIFI and discussed the results, related to the design of each. Subsequently, a budget of a SAR bench, detailing all components involved in SAR measures, but not included in it, maintenance costs or the costs associated with its use. Finally conclusions are explained detached from the realization of this project as well as the bibliography used on it.

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The electron-retarding range of the current-voltage characteristic of a flat Langmuir probe perpendicular to a strong magnetic field in a fully ionized plasma is analysed allowing for anomalous (Bohm) cross-field transport and temperature changes in the collection process. With probe size and ion thermal gyroradius comparable, and smaller than the electron mean free path, there is an outer quasineutral region with ion viscosity determinant in allowing nonambipolar parallel and cross flow. A potential overshoot lying either at the base or inside the quasineutral region both makes ions follow Boltzmann's law at negative bias and extends the electron-retarding range to probe bias e(j)p ~ +2Too. Electron heating and cooling occur roughly at positive and negative bias, with a re-minimum around efa ~ - 2 7 ^ ; far from the probe heat conduction cools and heats electrons at and radially away from the probe axis, respectively. The potential overshoot with no thermal effects would reduce the electron current Ie, making the In Ie versus 4>p graph downwards-concave,but cooling further reduces Ie substantially, and may tilt the slope upwards past the temperature minimum. The domain of strict validity of our analysis is narrow in case of low ion mass (deuterium), breaking down with the ion Boltzmann law.

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The excitation of Fast Magnetosonic (FMS)waves by a cylindrical array of parallel tethers carrying timemodulated current is discussed. The tethers would fly vertical in the equatorial plane, which is perpendicular to the geomagnetic field when its tilt is ignored, and would be stabilized by the gravity gradient. The tether array would radiate a single FMS wave. In the time-dependent background made of geomagnetic field plus radiated wave, plasma FMS perturbations are excited in the array vicinity through a parametric instability. The growth rate is estimated by truncating the evolution equation for FMS perturbations to the two azimuthal modes of lowest order. Design parameters such as tether length and number, required power and mass are discussed for Low Earth Orbit conditions. The array-attached wave structure would have the radiated wave controlled by the intensity and modulation frequency of the currents, making an active experiment on non-linear low frequency waves possible in real space plasma conditions.

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Magnetic excitation of whistlers by a square array of electrodynamic tethers is discussed. The array is made of perpendicular rows of tethers that carry equal, uniform, and time-modulated currents at equal frequency with a 90° phase shift. The array would fly vertical in the orbital equatorial plane, which is perpendicular to the geomagnetic field B0 when its tilt is ignored. The array radiates a whistler wave along B0. A parametric instability due to pumping by the background magnetic field through the radiated wave gives rise to two unstable coupled whistler perturbations. The growth rate is maximum for perturbations with wave vector at angles 38.36° and 75.93° from B0. For an experiment involving a wavefront that moves with the orbiting array, which might serve to study nonlinear wave interactions and turbulence in space plasmas, characteristic values of growth rate and parameters, such as the number of tethers and their dimensions and distances in the array, are discussed for low Earth orbit ambient conditions.

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Laparoscopic instrument tracking systems are a key element in image-guided interventions, which requires high accuracy to be used in a real surgical scenario. In addition, these systems are a suitable option for objective assessment of laparoscopic technical skills based on instrument motion analysis. This study presents a new approach that improves the accuracy of a previously presented system, which applies an optical pose tracking system to laparoscopic practice. A design enhancement of the artificial markers placed on the laparoscopic instrument as well as an improvement of the calibration process are presented as a means to achieve more accurate results. A technical evaluation has been performed in order to compare the accuracy between the previous design and the new approach. Results show a remarkable improvement in the fluctuation error throughout the measurement platform. Moreover, the accumulated distance error and the inclination error have been improved. The tilt range covered by the system is the same for both approaches, from 90º to 7.5º. The relative position error is better for the new approach mainly at close distances to the camera system

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An electrodynamic tether system for power generation at Jupiter is presented that allows extracting energy from Jupiter's corotating plasmasphere while leaving the system orbital energy unaltered to first order. The spacecraft is placed in a polar orbit with the tether spinning in the orbital plane so that the resulting Lorentz force, neglecting Jupiter's magnetic dipole tilt, is orthogonal to the instantaneous velocity vector and orbital radius, hence affecting orbital inclination rather than orbital energy. In addition, the electrodynamic tether subsystem, which consists of two radial tether arms deployed from the main central spacecraft, is designed in such a way as to extract maximum power while keeping the resulting Lorentz torque constantly null. The power-generation performance of the system and the effect on the orbit inclination is evaluated analytically for different orbital conditions and verified numerically. Finally, a thruster-based inclination-compensation maneuver at apoapsis is added, resulting in an efficient scheme to extract energy from the plasmasphere of the planet with minimum propellant consumption and no inclination change. A tradeoff analysis is conducted showing that, depending on tether size and orbit characteristics, the system performance can be considerably higher than conventional power-generation methods.

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We demonstrate the capability of a laser micromachining workstation for cost-effective manufacturing of a variety of microfluidic devices, including SU-8 microchannels on silicon wafers and 3D complex structures made on polyimide Kapton® or poly carbonate (PC). The workstation combines a KrF excimer laser at 248 nm and a Nd3+:YVO4 DPSS with a frequency tripled at 355 nm with a lens magnification 10X, both lasers working at a pulsed regime with nanoseconds (ns) pulse duration. Workstation also includes a high-resolution motorized XYZ-tilt axis (~ 1 um / axis) and a Through The Lens (TTL) imaging system for a high accurate positioning over a 120 x 120 mm working area. We have surveyed different fabrication techniques: direct writing lithography,mask manufacturing for contact lithography and polymer laser ablation for complex 3D devices, achieving width channels down to 13μ m on 50μ m SU-8 thickness using direct writing lithography, and width channels of 40 μm for polyimide on SiO2 plate. Finally, we have tested the use of some devices for capillary chips measuring the flow speed for liquids with different viscosities. As a result, we have characterized the presence of liquid in the channel by interferometric microscopy.

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El autor ha trabajado como parte del equipo de investigación en mediciones de viento en el Centro Nacional de Energías Renovables (CENER), España, en cooperación con la Universidad Politécnica de Madrid y la Universidad Técnica de Dinamarca. El presente reporte recapitula el trabajo de investigación realizado durante los últimos 4.5 años en el estudio de las fuentes de error de los sistemas de medición remota de viento, basados en la tecnología lidar, enfocado al error causado por los efectos del terreno complejo. Este trabajo corresponde a una tarea del paquete de trabajo dedicado al estudio de sistemas remotos de medición de viento, perteneciente al proyecto de intestigación europeo del 7mo programa marco WAUDIT. Adicionalmente, los datos de viento reales han sido obtenidos durante las campañas de medición en terreno llano y terreno complejo, pertenecientes al también proyecto de intestigación europeo del 7mo programa marco SAFEWIND. El principal objetivo de este trabajo de investigación es determinar los efectos del terreno complejo en el error de medición de la velocidad del viento obtenida con los sistemas de medición remota lidar. Con este conocimiento, es posible proponer una metodología de corrección del error de las mediciones del lidar. Esta metodología está basada en la estimación de las variaciones del campo de viento no uniforme dentro del volumen de medición del lidar. Las variaciones promedio del campo de viento son predichas a partir de los resultados de las simulaciones computacionales de viento RANS, realizadas para el parque experimental de Alaiz. La metodología de corrección es verificada con los resultados de las simulaciones RANS y validadas con las mediciones reales adquiridas en la campaña de medición en terreno complejo. Al inicio de este reporte, el marco teórico describiendo el principio de medición de la tecnología lidar utilizada, es presentado con el fin de familiarizar al lector con los principales conceptos a utilizar a lo largo de este trabajo. Posteriormente, el estado del arte es presentado en donde se describe los avances realizados en el desarrollo de la la tecnología lidar aplicados al sector de la energía eólica. En la parte experimental de este trabajo de investigación se ha estudiado los datos adquiridos durante las dos campañas de medición realizadas. Estas campañas has sido realizadas en terreno llano y complejo, con el fin de complementar los conocimiento adquiridos en casa una de ellas y poder comparar los efectos del terreno en las mediciones de viento realizadas con sistemas remotos lidar. La primer campaña experimental se desarrollo en terreno llano, en el parque de ensayos de aerogeneradores H0vs0re, propiedad de DTU Wind Energy (anteriormente Ris0). La segunda campaña experimental se llevó a cabo en el parque de ensayos de aerogeneradores Alaiz, propiedad de CENER. Exactamente los mismos dos equipos lidar fueron utilizados en estas campañas, haciendo de estos experimentos altamente relevantes en el contexto de evaluación del recurso eólico. Un equipo lidar está basado en tecnología de onda continua, mientras que el otro está basado en tecnología de onda pulsada. La velocidad del viento fue medida, además de con los equipos lidar, con anemómetros de cazoletas, veletas y anemómetros verticales, instalados en mástiles meteorológicos. Los sensores del mástil meteorológico son considerados como las mediciones de referencia en el presente estudio. En primera instancia, se han analizado los promedios diez minútales de las medidas de viento. El objetivo es identificar las principales fuentes de error en las mediciones de los equipos lidar causadas por diferentes condiciones atmosféricas y por el flujo no uniforme de viento causado por el terreno complejo. El error del lidar ha sido estudiado como función de varias propiedades estadísticas del viento, como lo son el ángulo vertical de inclinación, la intensidad de turbulencia, la velocidad vertical, la estabilidad atmosférica y las características del terreno. El propósito es usar este conocimiento con el fin de definir criterios de filtrado de datos. Seguidamente, se propone una metodología para corregir el error del lidar causado por el campo de viento no uniforme, producido por la presencia de terreno complejo. Esta metodología está basada en el análisis matemático inicial sobre el proceso de cálculo de la velocidad de viento por los equipos lidar de onda continua. La metodología de corrección propuesta hace uso de las variaciones de viento calculadas a partir de las simulaciones RANS realizadas para el parque experimental de Alaiz. Una ventaja importante que presenta esta metodología es que las propiedades el campo de viento real, presentes en las mediciones instantáneas del lidar de onda continua, puede dar paso a análisis adicionales como parte del trabajo a futuro. Dentro del marco del proyecto, el trabajo diario se realizó en las instalaciones de CENER, con supervisión cercana de la UPM, incluyendo una estancia de 1.5 meses en la universidad. Durante esta estancia, se definió el análisis matemático de las mediciones de viento realizadas por el equipo lidar de onda continua. Adicionalmente, los efectos del campo de viento no uniforme sobre el error de medición del lidar fueron analíticamente definidos, después de asumir algunas simplificaciones. Adicionalmente, durante la etapa inicial de este proyecto se desarrollo una importante trabajo de cooperación con DTU Wind Energy. Gracias a esto, el autor realizó una estancia de 1.5 meses en Dinamarca. Durante esta estancia, el autor realizó una visita a la campaña de medición en terreno llano con el fin de aprender los aspectos básicos del diseño de campañas de medidas experimentales, el estudio del terreno y los alrededores y familiarizarse con la instrumentación del mástil meteorológico, el sistema de adquisición y almacenamiento de datos, así como de el estudio y reporte del análisis de mediciones. ABSTRACT The present report summarizes the research work performed during last 4.5 years of investigation on the sources of lidar bias due to complex terrain. This work corresponds to one task of the remote sensing work package, belonging to the FP7 WAUDIT project. Furthermore, the field data from the wind velocity measurement campaigns of the FP7 SafeWind project have been used in this report. The main objective of this research work is to determine the terrain effects on the lidar bias in the measured wind velocity. With this knowledge, it is possible to propose a lidar bias correction methodology. This methodology is based on an estimation of the wind field variations within the lidar scan volume. The wind field variations are calculated from RANS simulations performed from the Alaiz test site. The methodology is validated against real scale measurements recorded during an eight month measurement campaign at the Alaiz test site. Firstly, the mathematical framework of the lidar sensing principle is introduced and an overview of the state of the art is presented. The experimental part includes the study of two different, but complementary experiments. The first experiment was a measurement campaign performed in flat terrain, at DTU Wind Energy H0vs0re test site, while the second experiment was performed in complex terrain at CENER Alaiz test site. Exactly the same two lidar devices, based on continuous wave and pulsed wave systems, have been used in the two consecutive measurement campaigns, making this a relevant experiment in the context of wind resource assessment. The wind velocity was sensed by the lidars and standard cup anemometry and wind vanes (installed on a met mast). The met mast sensors are considered as the reference wind velocity measurements. The first analysis of the experimental data is dedicated to identify the main sources of lidar bias present in the 10 minute average values. The purpose is to identify the bias magnitude introduced by different atmospheric conditions and by the non-uniform wind flow resultant of the terrain irregularities. The lidar bias as function of several statistical properties of the wind flow like the tilt angle, turbulence intensity, vertical velocity, atmospheric stability and the terrain characteristics have been studied. The aim of this exercise is to use this knowledge in order to define useful lidar bias data filters. Then, a methodology to correct the lidar bias caused by non-uniform wind flow is proposed, based on the initial mathematical analysis of the lidar measurements. The proposed lidar bias correction methodology has been developed focusing on the the continuous wave lidar system. In a last step, the proposed lidar bias correction methodology is validated with the data of the complex terrain measurement campaign. The methodology makes use of the wind field variations obtained from the RANS analysis. The results are presented and discussed. The advantage of this methodology is that the wind field properties at the Alaiz test site can be studied with more detail, based on the instantaneous measurements of the CW lidar. Within the project framework, the daily basis work has been done at CENER, with close guidance and support from the UPM, including an exchange period of 1.5 months. During this exchange period, the mathematical analysis of the lidar sensing of the wind velocity was defined. Furthermore, the effects of non-uniform wind fields on the lidar bias were analytically defined, after making some assumptions for the sake of simplification. Moreover, there has been an important cooperation with DTU Wind Energy, where a secondment period of 1.5 months has been done as well. During the secondment period at DTU Wind Energy, an important introductory learning has taken place. The learned aspects include the design of an experimental measurement campaign in flat terrain, the site assessment study of obstacles and terrain conditions, the data acquisition and processing, as well as the study and reporting of the measurement analysis.

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Vertical Alignment Nematics (VANs) displays are a form of LCDs in which the liquid crystals naturally align vertically to the glass substrates. In spite of their name, the liquid crystal (LC) director is never exactly vertical, rather it always show a small angle with the normal to the sample plane called tilt that may vary throughout the cell bulk. Its values are ultimately determined by the pretilt, defined as the tilt angle on the surfaces in the absence of voltage.