36 resultados para Closed-Loop Systems


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Nowadays robots have made their way into real applications that were prohibitive and unthinkable thirty years ago. This is mainly due to the increase in power computations and the evolution in the theoretical field of robotics and control. Even though there is plenty of information in the current literature on this topics, it is not easy to find clear concepts of how to proceed in order to design and implement a controller for a robot. In general, the design of a controller requires of a complete understanding and knowledge of the system to be controlled. Therefore, for advanced control techniques the systems must be first identified. Once again this particular objective is cumbersome and is never straight forward requiring of great expertise and some criteria must be adopted. On the other hand, the particular problem of designing a controller is even more complex when dealing with Parallel Manipulators (PM), since their closed-loop structures give rise to a highly nonlinear system. Under this basis the current work is developed, which intends to resume and gather all the concepts and experiences involve for the control of an Hydraulic Parallel Manipulator. The main objective of this thesis is to provide a guide remarking all the steps involve in the designing of advanced control technique for PMs. The analysis of the PM under study is minced up to the core of the mechanism: the hydraulic actuators. The actuators are modeled and experimental identified. Additionally, some consideration regarding traditional PID controllers are presented and an adaptive controller is finally implemented. From a macro perspective the kinematic and dynamic model of the PM are presented. Based on the model of the system and extending the adaptive controller of the actuator, a control strategy for the PM is developed and its performance is analyzed with simulation.

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La diabetes mellitus es un trastorno del metabolismo de los carbohidratos producido por la insuficiente o nula producción de insulina o la reducida sensibilidad a esta hormona. Es una enfermedad crónica con una mayor prevalencia en los países desarrollados debido principalmente a la obesidad, la vida sedentaria y disfunciones en el sistema endocrino relacionado con el páncreas. La diabetes Tipo 1 es una enfermedad autoinmune en la que son destruidas las células beta del páncreas, que producen la insulina, y es necesaria la administración de insulina exógena. Un enfermo de diabetes Tipo 1 debe seguir una terapia con insulina administrada por la vía subcutánea que debe estar adaptada a sus necesidades metabólicas y a sus hábitos de vida, esta terapia intenta imitar el perfil insulínico de un páncreas no patológico. La tecnología actual permite abordar el desarrollo del denominado “páncreas endocrino artificial”, que aportaría precisión, eficacia y seguridad para los pacientes, en cuanto a la normalización del control glucémico y reducción del riesgo de hipoglucemias. Permitiría que el paciente no estuviera tan pendiente de su enfermedad. El páncreas artificial consta de un sensor continuo de glucosa, una bomba de infusión de insulina y un algoritmo de control, que calcula la insulina a infusionar usando la glucosa como información principal. Este trabajo presenta un método de control en lazo semi-cerrado mediante un sistema borroso experto basado en reglas. La regulación borrosa se fundamenta en la ambigüedad del lenguaje del ser humano. Esta incertidumbre sirve para la formación de una serie de reglas que representan el pensamiento humano, pero a la vez es el sistema que controla un proceso, en este caso el sistema glucorregulatorio. Este proyecto está enfocado en el diseño de un controlador borroso que haciendo uso de variables como la glucosa, insulina y dieta, sea capaz de restaurar la función endocrina del páncreas de forma tecnológica. La validación del algoritmo se ha realizado principalmente mediante experimentos en simulación utilizando una población de pacientes sintéticos, evaluando los resultados con estadísticos de primer orden y algunos más específicos como el índice de riesgo de Kovatchev, para después comparar estos resultados con los obtenidos por otros métodos de control anteriores. Los resultados demuestran que el control borroso (FBPC) mejora el control glucémico con respecto a un sistema predictivo experto basado en reglas booleanas (pBRES). El FBPC consigue reducir siempre la glucosa máxima y aumentar la mínima respecto del pBRES pero es en terapias desajustadas, donde el FBPC es especialmente robusto, hace descender la glucosa máxima 8,64 mg/dl, el uso de insulina es 3,92 UI menor, aumenta la glucosa mínima 3,32 mg/dl y lleva al rango de glucosa 80 – 110 mg/dl 15,33 muestras más. Por lo tanto se puede concluir que el FBPC realiza un mejor control glucémico que el controlador pBRES haciéndole especialmente efectivo, robusto y seguro en condiciones de desajustes de terapia basal y con gran capacidad de mejora futura. SUMMARY The diabetes mellitus is a metabolic disorder caused by a poor or null insulin secretion or a reduced sensibility to insulin. Diabetes is a chronic disease with a higher prevalence in the industrialized countries, mainly due to obesity, the sedentary life and endocrine disfunctions connected with the pancreas. Type 1 diabetes is a self-immune disease where the beta cells of the pancreas, which are the responsible of secreting insulin, are damaged. Hence, it is necessary an exogenous delivery of insulin. The Type 1 diabetic patient has to follow a therapy with subcutaneous insulin administration which should be adjusted to his/her metabolic needs and life style. This therapy tries to mimic the insulin profile of a non-pathological pancreas. Current technology lets the development of the so-called endocrine artificial pancreas that would provide accuracy, efficiency and safety to patients, in regards to the glycemic control normalization and reduction of the risk of hypoglycemic. In addition, it would help the patient not to be so concerned about his disease. The artificial pancreas has a continuous glucose sensor, an insulin infusion pump and a control algorithm, that calculates the insulin infusion using the glucose as main information. This project presents a method of control in semi-closed-loop, through an expert fuzzy system based on rules. The fuzzy regulation is based on the human language ambiguity. This uncertainty serves for construction of some rules that represent the human language besides it is the system that controls a process, in this case the glucoregulatory system. This project is focus on the design of a fuzzy controller that, using variables like glucose insulin and diet, will be able to restore the pancreas endocrine function with technology. The algorithm assessment has mainly been done through experiments in simulation using a population of synthetic patients, evaluating the results with first order statistical parameters and some other more specific such as the Kovatchev risk index, to compare later these results with the ones obtained in others previous methods of control. The results demonstrate that the fuzzy control (FBPC) improves the glycemic control connected with a predictive expert system based on Booleans rules (pBRES). The FBPC is always able to reduce the maximum level of glucose and increase the minimum level as compared with pBRES but it is in unadjusted therapies where FBPC is especially strong, it manages to decrease the maximum level of glucose and insulin used by 8,64 mg/dl and 3,92 UI respectively, also increases the value of minimum glucose by 3,32 mg/dl, getting 15,33 samples more inside the 80-110 mg/dl glucose rank. Therefore we can conclude that FBPC achieves a better glycemic control than the controller pBRES doing it especially effective, robust and safe in conditions of mismatch basal therapy and with a great capacity for future improvements.

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Objective: This study assessed the efficacy of a closed-loop (CL) system consisting of a predictive rule-based algorithm (pRBA) on achieving nocturnal and postprandial normoglycemia in patients with type 1 diabetes mellitus (T1DM). The algorithm is personalized for each patient’s data using two different strategies to control nocturnal and postprandial periods. Research Design and Methods: We performed a randomized crossover clinical study in which 10 T1DM patients treated with continuous subcutaneous insulin infusion (CSII) spent two nonconsecutive nights in the research facility: one with their usual CSII pattern (open-loop [OL]) and one controlled by the pRBA (CL). The CL period lasted from 10 p.m. to 10 a.m., including overnight control, and control of breakfast. Venous samples for blood glucose (BG) measurement were collected every 20 min. Results: Time spent in normoglycemia (BG, 3.9–8.0 mmol/L) during the nocturnal period (12 a.m.–8 a.m.), expressed as median (interquartile range), increased from 66.6% (8.3–75%) with OL to 95.8% (73–100%) using the CL algorithm (P<0.05). Median time in hypoglycemia (BG, <3.9 mmol/L) was reduced from 4.2% (0–21%) in the OL night to 0.0% (0.0–0.0%) in the CL night (P<0.05). Nine hypoglycemic events (<3.9 mmol/L) were recorded with OL compared with one using CL. The postprandial glycemic excursion was not lower when the CL system was used in comparison with conventional preprandial bolus: time in target (3.9–10.0 mmol/L) 58.3% (29.1–87.5%) versus 50.0% (50–100%). Conclusions: A highly precise personalized pRBA obtains nocturnal normoglycemia, without significant hypoglycemia, in T1DM patients. There appears to be no clear benefit of CL over prandial bolus on the postprandial glycemia

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High power density is strongly preferable for the on-board battery charger of Plug-in Hybrid Electric Vehicle (PHEV). Wide band gap devices, such as Gallium Nitride HEMTs are being explored to push to higher switching frequency and reduce passive component size. In this case, the bulk DC link capacitor of AC-DC Power Factor Correction (PFC) stage, which is usually necessary to store ripple power of two times the line frequency in a DC current charging system, becomes a major barrier on power density. If low frequency ripple is allowed in the battery, the DC link capacitance can be significantly reduced. This paper focuses on the operation of a battery charging system, which is comprised of one Full Bridge (FB) AC-DC stage and one Dual Active Bridge (DAB) DC-DC stage, with charging current containing low frequency ripple at two times line frequency, designated as sinusoidal charging. DAB operation under sinusoidal charging is investigated. Two types of control schemes are proposed and implemented in an experimental prototype. It is proved that closed loop current control is the better. Full system test including both FB AC-DC stage and DAB DC-DC stage verified the concept of sinusoidal charging, which may lead to potentially very high power density battery charger for PHEV.

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El presente Trabajo fin Fin de Máster, versa sobre una caracterización preliminar del comportamiento de un robot de tipo industrial, configurado por 4 eslabones y 4 grados de libertad, y sometido a fuerzas de mecanizado en su extremo. El entorno de trabajo planteado es el de plantas de fabricación de piezas de aleaciones de aluminio para automoción. Este tipo de componentes parte de un primer proceso de fundición que saca la pieza en bruto. Para series medias y altas, en función de las propiedades mecánicas y plásticas requeridas y los costes de producción, la inyección a alta presión (HPDC) y la fundición a baja presión (LPC) son las dos tecnologías más usadas en esta primera fase. Para inyección a alta presión, las aleaciones de aluminio más empleadas son, en designación simbólica según norma EN 1706 (entre paréntesis su designación numérica); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). Para baja presión, EN AC AlSi7Mg0,3 (EN AC 42100). En los 3 primeros casos, los límites de Silicio permitidos pueden superan el 10%. En el cuarto caso, es inferior al 10% por lo que, a los efectos de ser sometidas a mecanizados, las piezas fabricadas en aleaciones con Si superior al 10%, se puede considerar que son equivalentes, diferenciándolas de la cuarta. Las tolerancias geométricas y dimensionales conseguibles directamente de fundición, recogidas en normas como ISO 8062 o DIN 1688-1, establecen límites para este proceso. Fuera de esos límites, las garantías en conseguir producciones con los objetivos de ppms aceptados en la actualidad por el mercado, obligan a ir a fases posteriores de mecanizado. Aquellas geometrías que, funcionalmente, necesitan disponer de unas tolerancias geométricas y/o dimensionales definidas acorde a ISO 1101, y no capaces por este proceso inicial de moldeado a presión, deben ser procesadas en una fase posterior en células de mecanizado. En este caso, las tolerancias alcanzables para procesos de arranque de viruta se recogen en normas como ISO 2768. Las células de mecanizado se componen, por lo general, de varios centros de control numérico interrelacionados y comunicados entre sí por robots que manipulan las piezas en proceso de uno a otro. Dichos robots, disponen en su extremo de una pinza utillada para poder coger y soltar las piezas en los útiles de mecanizado, las mesas de intercambio para cambiar la pieza de posición o en utillajes de equipos de medición y prueba, o en cintas de entrada o salida. La repetibilidad es alta, de centésimas incluso, definida según norma ISO 9283. El problema es que, estos rangos de repetibilidad sólo se garantizan si no se hacen esfuerzos o éstos son despreciables (caso de mover piezas). Aunque las inercias de mover piezas a altas velocidades hacen que la trayectoria intermedia tenga poca precisión, al inicio y al final (al coger y dejar pieza, p.e.) se hacen a velocidades relativamente bajas que hacen que el efecto de las fuerzas de inercia sean menores y que permiten garantizar la repetibilidad anteriormente indicada. No ocurre así si se quitara la garra y se intercambia con un cabezal motorizado con una herramienta como broca, mandrino, plato de cuchillas, fresas frontales o tangenciales… Las fuerzas ejercidas de mecanizado generarían unos pares en las uniones tan grandes y tan variables que el control del robot no sería capaz de responder (o no está preparado, en un principio) y generaría una desviación en la trayectoria, realizada a baja velocidad, que desencadenaría en un error de posición (ver norma ISO 5458) no asumible para la funcionalidad deseada. Se podría llegar al caso de que la tolerancia alcanzada por un pretendido proceso más exacto diera una dimensión peor que la que daría el proceso de fundición, en principio con mayor variabilidad dimensional en proceso (y por ende con mayor intervalo de tolerancia garantizable). De hecho, en los CNCs, la precisión es muy elevada, (pudiéndose despreciar en la mayoría de los casos) y no es la responsable de, por ejemplo la tolerancia de posición al taladrar un agujero. Factores como, temperatura de la sala y de la pieza, calidad constructiva de los utillajes y rigidez en el amarre, error en el giro de mesas y de colocación de pieza, si lleva agujeros previos o no, si la herramienta está bien equilibrada y el cono es el adecuado para el tipo de mecanizado… influyen más. Es interesante que, un elemento no específico tan común en una planta industrial, en el entorno anteriormente descrito, como es un robot, el cual no sería necesario añadir por disponer de él ya (y por lo tanto la inversión sería muy pequeña), puede mejorar la cadena de valor disminuyendo el costo de fabricación. Y si se pudiera conjugar que ese robot destinado a tareas de manipulación, en los muchos tiempos de espera que va a disfrutar mientras el CNC arranca viruta, pudiese coger un cabezal y apoyar ese mecanizado; sería doblemente interesante. Por lo tanto, se antoja sugestivo poder conocer su comportamiento e intentar explicar qué sería necesario para llevar esto a cabo, motivo de este trabajo. La arquitectura de robot seleccionada es de tipo SCARA. La búsqueda de un robot cómodo de modelar y de analizar cinemática y dinámicamente, sin limitaciones relevantes en la multifuncionalidad de trabajos solicitados, ha llevado a esta elección, frente a otras arquitecturas como por ejemplo los robots antropomórficos de 6 grados de libertad, muy populares a nivel industrial. Este robot dispone de 3 uniones, de las cuales 2 son de tipo par de revolución (1 grado de libertad cada una) y la tercera es de tipo corredera o par cilíndrico (2 grados de libertad). La primera unión, de tipo par de revolución, sirve para unir el suelo (considerado como eslabón número 1) con el eslabón número 2. La segunda unión, también de ese tipo, une el eslabón número 2 con el eslabón número 3. Estos 2 brazos, pueden describir un movimiento horizontal, en el plano X-Y. El tercer eslabón, está unido al eslabón número 4 por la unión de tipo corredera. El movimiento que puede describir es paralelo al eje Z. El robot es de 4 grados de libertad (4 motores). En relación a los posibles trabajos que puede realizar este tipo de robot, su versatilidad abarca tanto operaciones típicas de manipulación como operaciones de arranque de viruta. Uno de los mecanizados más usuales es el taladrado, por lo cual se elige éste para su modelización y análisis. Dentro del taladrado se elegirá para acotar las fuerzas, taladrado en macizo con broca de diámetro 9 mm. El robot se ha considerado por el momento que tenga comportamiento de sólido rígido, por ser el mayor efecto esperado el de los pares en las uniones. Para modelar el robot se utiliza el método de los sistemas multicuerpos. Dentro de este método existen diversos tipos de formulaciones (p.e. Denavit-Hartenberg). D-H genera una cantidad muy grande de ecuaciones e incógnitas. Esas incógnitas son de difícil comprensión y, para cada posición, hay que detenerse a pensar qué significado tienen. Se ha optado por la formulación de coordenadas naturales. Este sistema utiliza puntos y vectores unitarios para definir la posición de los distintos cuerpos, y permite compartir, cuando es posible y se quiere, para definir los pares cinemáticos y reducir al mismo tiempo el número de variables. Las incógnitas son intuitivas, las ecuaciones de restricción muy sencillas y se reduce considerablemente el número de ecuaciones e incógnitas. Sin embargo, las coordenadas naturales “puras” tienen 2 problemas. El primero, que 2 elementos con un ángulo de 0 o 180 grados, dan lugar a puntos singulares que pueden crear problemas en las ecuaciones de restricción y por lo tanto han de evitarse. El segundo, que tampoco inciden directamente sobre la definición o el origen de los movimientos. Por lo tanto, es muy conveniente complementar esta formulación con ángulos y distancias (coordenadas relativas). Esto da lugar a las coordenadas naturales mixtas, que es la formulación final elegida para este TFM. Las coordenadas naturales mixtas no tienen el problema de los puntos singulares. Y la ventaja más importante reside en su utilidad a la hora de aplicar fuerzas motrices, momentos o evaluar errores. Al incidir sobre la incógnita origen (ángulos o distancias) controla los motores de manera directa. El algoritmo, la simulación y la obtención de resultados se ha programado mediante Matlab. Para realizar el modelo en coordenadas naturales mixtas, es preciso modelar en 2 pasos el robot a estudio. El primer modelo se basa en coordenadas naturales. Para su validación, se plantea una trayectoria definida y se analiza cinemáticamente si el robot satisface el movimiento solicitado, manteniendo su integridad como sistema multicuerpo. Se cuantifican los puntos (en este caso inicial y final) que configuran el robot. Al tratarse de sólidos rígidos, cada eslabón queda definido por sus respectivos puntos inicial y final (que son los más interesantes para la cinemática y la dinámica) y por un vector unitario no colineal a esos 2 puntos. Los vectores unitarios se colocan en los lugares en los que se tenga un eje de rotación o cuando se desee obtener información de un ángulo. No son necesarios vectores unitarios para medir distancias. Tampoco tienen por qué coincidir los grados de libertad con el número de vectores unitarios. Las longitudes de cada eslabón quedan definidas como constantes geométricas. Se establecen las restricciones que definen la naturaleza del robot y las relaciones entre los diferentes elementos y su entorno. La trayectoria se genera por una nube de puntos continua, definidos en coordenadas independientes. Cada conjunto de coordenadas independientes define, en un instante concreto, una posición y postura de robot determinada. Para conocerla, es necesario saber qué coordenadas dependientes hay en ese instante, y se obtienen resolviendo por el método de Newton-Rhapson las ecuaciones de restricción en función de las coordenadas independientes. El motivo de hacerlo así es porque las coordenadas dependientes deben satisfacer las restricciones, cosa que no ocurre con las coordenadas independientes. Cuando la validez del modelo se ha probado (primera validación), se pasa al modelo 2. El modelo número 2, incorpora a las coordenadas naturales del modelo número 1, las coordenadas relativas en forma de ángulos en los pares de revolución (3 ángulos; ϕ1, ϕ 2 y ϕ3) y distancias en los pares prismáticos (1 distancia; s). Estas coordenadas relativas pasan a ser las nuevas coordenadas independientes (sustituyendo a las coordenadas independientes cartesianas del modelo primero, que eran coordenadas naturales). Es necesario revisar si el sistema de vectores unitarios del modelo 1 es suficiente o no. Para este caso concreto, se han necesitado añadir 1 vector unitario adicional con objeto de que los ángulos queden perfectamente determinados con las correspondientes ecuaciones de producto escalar y/o vectorial. Las restricciones habrán de ser incrementadas en, al menos, 4 ecuaciones; una por cada nueva incógnita. La validación del modelo número 2, tiene 2 fases. La primera, al igual que se hizo en el modelo número 1, a través del análisis cinemático del comportamiento con una trayectoria definida. Podrían obtenerse del modelo 2 en este análisis, velocidades y aceleraciones, pero no son necesarios. Tan sólo interesan los movimientos o desplazamientos finitos. Comprobada la coherencia de movimientos (segunda validación), se pasa a analizar cinemáticamente el comportamiento con trayectorias interpoladas. El análisis cinemático con trayectorias interpoladas, trabaja con un número mínimo de 3 puntos máster. En este caso se han elegido 3; punto inicial, punto intermedio y punto final. El número de interpolaciones con el que se actúa es de 50 interpolaciones en cada tramo (cada 2 puntos máster hay un tramo), resultando un total de 100 interpolaciones. El método de interpolación utilizado es el de splines cúbicas con condición de aceleración inicial y final constantes, que genera las coordenadas independientes de los puntos interpolados de cada tramo. Las coordenadas dependientes se obtienen resolviendo las ecuaciones de restricción no lineales con el método de Newton-Rhapson. El método de las splines cúbicas es muy continuo, por lo que si se desea modelar una trayectoria en el que haya al menos 2 movimientos claramente diferenciados, es preciso hacerlo en 2 tramos y unirlos posteriormente. Sería el caso en el que alguno de los motores se desee expresamente que esté parado durante el primer movimiento y otro distinto lo esté durante el segundo movimiento (y así sucesivamente). Obtenido el movimiento, se calculan, también mediante fórmulas de diferenciación numérica, las velocidades y aceleraciones independientes. El proceso es análogo al anteriormente explicado, recordando la condición impuesta de que la aceleración en el instante t= 0 y en instante t= final, se ha tomado como 0. Las velocidades y aceleraciones dependientes se calculan resolviendo las correspondientes derivadas de las ecuaciones de restricción. Se comprueba, de nuevo, en una tercera validación del modelo, la coherencia del movimiento interpolado. La dinámica inversa calcula, para un movimiento definido -conocidas la posición, velocidad y la aceleración en cada instante de tiempo-, y conocidas las fuerzas externas que actúan (por ejemplo el peso); qué fuerzas hay que aplicar en los motores (donde hay control) para que se obtenga el citado movimiento. En la dinámica inversa, cada instante del tiempo es independiente de los demás y tiene una posición, una velocidad y una aceleración y unas fuerzas conocidas. En este caso concreto, se desean aplicar, de momento, sólo las fuerzas debidas al peso, aunque se podrían haber incorporado fuerzas de otra naturaleza si se hubiese deseado. Las posiciones, velocidades y aceleraciones, proceden del cálculo cinemático. El efecto inercial de las fuerzas tenidas en cuenta (el peso) es calculado. Como resultado final del análisis dinámico inverso, se obtienen los pares que han de ejercer los cuatro motores para replicar el movimiento prescrito con las fuerzas que estaban actuando. La cuarta validación del modelo consiste en confirmar que el movimiento obtenido por aplicar los pares obtenidos en la dinámica inversa, coinciden con el obtenido en el análisis cinemático (movimiento teórico). Para ello, es necesario acudir a la dinámica directa. La dinámica directa se encarga de calcular el movimiento del robot, resultante de aplicar unos pares en motores y unas fuerzas en el robot. Por lo tanto, el movimiento real resultante, al no haber cambiado ninguna condición de las obtenidas en la dinámica inversa (pares de motor y fuerzas inerciales debidas al peso de los eslabones) ha de ser el mismo al movimiento teórico. Siendo así, se considera que el robot está listo para trabajar. Si se introduce una fuerza exterior de mecanizado no contemplada en la dinámica inversa y se asigna en los motores los mismos pares resultantes de la resolución del problema dinámico inverso, el movimiento real obtenido no es igual al movimiento teórico. El control de lazo cerrado se basa en ir comparando el movimiento real con el deseado e introducir las correcciones necesarias para minimizar o anular las diferencias. Se aplican ganancias en forma de correcciones en posición y/o velocidad para eliminar esas diferencias. Se evalúa el error de posición como la diferencia, en cada punto, entre el movimiento teórico deseado en el análisis cinemático y el movimiento real obtenido para cada fuerza de mecanizado y una ganancia concreta. Finalmente, se mapea el error de posición obtenido para cada fuerza de mecanizado y las diferentes ganancias previstas, graficando la mejor precisión que puede dar el robot para cada operación que se le requiere, y en qué condiciones. -------------- This Master´s Thesis deals with a preliminary characterization of the behaviour for an industrial robot, configured with 4 elements and 4 degrees of freedoms, and subjected to machining forces at its end. Proposed working conditions are those typical from manufacturing plants with aluminium alloys for automotive industry. This type of components comes from a first casting process that produces rough parts. For medium and high volumes, high pressure die casting (HPDC) and low pressure die casting (LPC) are the most used technologies in this first phase. For high pressure die casting processes, most used aluminium alloys are, in simbolic designation according EN 1706 standard (between brackets, its numerical designation); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). For low pressure, EN AC AlSi7Mg0,3 (EN AC 42100). For the 3 first alloys, Si allowed limits can exceed 10% content. Fourth alloy has admisible limits under 10% Si. That means, from the point of view of machining, that components made of alloys with Si content above 10% can be considered as equivalent, and the fourth one must be studied separately. Geometrical and dimensional tolerances directly achievables from casting, gathered in standards such as ISO 8062 or DIN 1688-1, establish a limit for this process. Out from those limits, guarantees to achieve batches with objetive ppms currently accepted by market, force to go to subsequent machining process. Those geometries that functionally require a geometrical and/or dimensional tolerance defined according ISO 1101, not capable with initial moulding process, must be obtained afterwards in a machining phase with machining cells. In this case, tolerances achievables with cutting processes are gathered in standards such as ISO 2768. In general terms, machining cells contain several CNCs that they are interrelated and connected by robots that handle parts in process among them. Those robots have at their end a gripper in order to take/remove parts in machining fixtures, in interchange tables to modify position of part, in measurement and control tooling devices, or in entrance/exit conveyors. Repeatibility for robot is tight, even few hundredths of mm, defined according ISO 9283. Problem is like this; those repeatibilty ranks are only guaranteed when there are no stresses or they are not significant (f.e. due to only movement of parts). Although inertias due to moving parts at a high speed make that intermediate paths have little accuracy, at the beginning and at the end of trajectories (f.e, when picking part or leaving it) movement is made with very slow speeds that make lower the effect of inertias forces and allow to achieve repeatibility before mentioned. It does not happens the same if gripper is removed and it is exchanged by an spindle with a machining tool such as a drilling tool, a pcd boring tool, a face or a tangential milling cutter… Forces due to machining would create such big and variable torques in joints that control from the robot would not be able to react (or it is not prepared in principle) and would produce a deviation in working trajectory, made at a low speed, that would trigger a position error (see ISO 5458 standard) not assumable for requested function. Then it could be possible that tolerance achieved by a more exact expected process would turn out into a worst dimension than the one that could be achieved with casting process, in principle with a larger dimensional variability in process (and hence with a larger tolerance range reachable). As a matter of fact, accuracy is very tight in CNC, (its influence can be ignored in most cases) and it is not the responsible of, for example position tolerance when drilling a hole. Factors as, room and part temperature, manufacturing quality of machining fixtures, stiffness at clamping system, rotating error in 4th axis and part positioning error, if there are previous holes, if machining tool is properly balanced, if shank is suitable for that machining type… have more influence. It is interesting to know that, a non specific element as common, at a manufacturing plant in the enviroment above described, as a robot (not needed to be added, therefore with an additional minimum investment), can improve value chain decreasing manufacturing costs. And when it would be possible to combine that the robot dedicated to handling works could support CNCs´ works in its many waiting time while CNCs cut, and could take an spindle and help to cut; it would be double interesting. So according to all this, it would be interesting to be able to know its behaviour and try to explain what would be necessary to make this possible, reason of this work. Selected robot architecture is SCARA type. The search for a robot easy to be modeled and kinematically and dinamically analyzed, without significant limits in the multifunctionality of requested operations, has lead to this choice. Due to that, other very popular architectures in the industry, f.e. 6 DOFs anthropomorphic robots, have been discarded. This robot has 3 joints, 2 of them are revolute joints (1 DOF each one) and the third one is a cylindrical joint (2 DOFs). The first joint, a revolute one, is used to join floor (body 1) with body 2. The second one, a revolute joint too, joins body 2 with body 3. These 2 bodies can move horizontally in X-Y plane. Body 3 is linked to body 4 with a cylindrical joint. Movement that can be made is paralell to Z axis. The robt has 4 degrees of freedom (4 motors). Regarding potential works that this type of robot can make, its versatility covers either typical handling operations or cutting operations. One of the most common machinings is to drill. That is the reason why it has been chosen for the model and analysis. Within drilling, in order to enclose spectrum force, a typical solid drilling with 9 mm diameter. The robot is considered, at the moment, to have a behaviour as rigid body, as biggest expected influence is the one due to torques at joints. In order to modelize robot, it is used multibodies system method. There are under this heading different sorts of formulations (f.e. Denavit-Hartenberg). D-H creates a great amount of equations and unknown quantities. Those unknown quatities are of a difficult understanding and, for each position, one must stop to think about which meaning they have. The choice made is therefore one of formulation in natural coordinates. This system uses points and unit vectors to define position of each different elements, and allow to share, when it is possible and wished, to define kinematic torques and reduce number of variables at the same time. Unknown quantities are intuitive, constrain equations are easy and number of equations and variables are strongly reduced. However, “pure” natural coordinates suffer 2 problems. The first one is that 2 elements with an angle of 0° or 180°, give rise to singular positions that can create problems in constrain equations and therefore they must be avoided. The second problem is that they do not work directly over the definition or the origin of movements. Given that, it is highly recommended to complement this formulation with angles and distances (relative coordinates). This leads to mixed natural coordinates, and they are the final formulation chosen for this MTh. Mixed natural coordinates have not the problem of singular positions. And the most important advantage lies in their usefulness when applying driving forces, torques or evaluating errors. As they influence directly over origin variable (angles or distances), they control motors directly. The algorithm, simulation and obtaining of results has been programmed with Matlab. To design the model in mixed natural coordinates, it is necessary to model the robot to be studied in 2 steps. The first model is based in natural coordinates. To validate it, it is raised a defined trajectory and it is kinematically analyzed if robot fulfils requested movement, keeping its integrity as multibody system. The points (in this case starting and ending points) that configure the robot are quantified. As the elements are considered as rigid bodies, each of them is defined by its respectively starting and ending point (those points are the most interesting ones from the point of view of kinematics and dynamics) and by a non-colinear unit vector to those points. Unit vectors are placed where there is a rotating axis or when it is needed information of an angle. Unit vectors are not needed to measure distances. Neither DOFs must coincide with the number of unit vectors. Lengths of each arm are defined as geometrical constants. The constrains that define the nature of the robot and relationships among different elements and its enviroment are set. Path is generated by a cloud of continuous points, defined in independent coordinates. Each group of independent coordinates define, in an specific instant, a defined position and posture for the robot. In order to know it, it is needed to know which dependent coordinates there are in that instant, and they are obtained solving the constraint equations with Newton-Rhapson method according to independent coordinates. The reason to make it like this is because dependent coordinates must meet constraints, and this is not the case with independent coordinates. When suitability of model is checked (first approval), it is given next step to model 2. Model 2 adds to natural coordinates from model 1, the relative coordinates in the shape of angles in revoluting torques (3 angles; ϕ1, ϕ 2 and ϕ3) and distances in prismatic torques (1 distance; s). These relative coordinates become the new independent coordinates (replacing to cartesian independent coordinates from model 1, that they were natural coordinates). It is needed to review if unit vector system from model 1 is enough or not . For this specific case, it was necessary to add 1 additional unit vector to define perfectly angles with their related equations of dot and/or cross product. Constrains must be increased in, at least, 4 equations; one per each new variable. The approval of model 2 has two phases. The first one, same as made with model 1, through kinematic analysis of behaviour with a defined path. During this analysis, it could be obtained from model 2, velocities and accelerations, but they are not needed. They are only interesting movements and finite displacements. Once that the consistence of movements has been checked (second approval), it comes when the behaviour with interpolated trajectories must be kinematically analyzed. Kinematic analysis with interpolated trajectories work with a minimum number of 3 master points. In this case, 3 points have been chosen; starting point, middle point and ending point. The number of interpolations has been of 50 ones in each strecht (each 2 master points there is an strecht), turning into a total of 100 interpolations. The interpolation method used is the cubic splines one with condition of constant acceleration both at the starting and at the ending point. This method creates the independent coordinates of interpolated points of each strecht. The dependent coordinates are achieved solving the non-linear constrain equations with Newton-Rhapson method. The method of cubic splines is very continuous, therefore when it is needed to design a trajectory in which there are at least 2 movements clearly differents, it is required to make it in 2 steps and join them later. That would be the case when any of the motors would keep stopped during the first movement, and another different motor would remain stopped during the second movement (and so on). Once that movement is obtained, they are calculated, also with numerical differenciation formulas, the independent velocities and accelerations. This process is analogous to the one before explained, reminding condition that acceleration when t=0 and t=end are 0. Dependent velocities and accelerations are calculated solving related derivatives of constrain equations. In a third approval of the model it is checked, again, consistence of interpolated movement. Inverse dynamics calculates, for a defined movement –knowing position, velocity and acceleration in each instant of time-, and knowing external forces that act (f.e. weights); which forces must be applied in motors (where there is control) in order to obtain requested movement. In inverse dynamics, each instant of time is independent of the others and it has a position, a velocity, an acceleration and known forces. In this specific case, it is intended to apply, at the moment, only forces due to the weight, though forces of another nature could have been added if it would have been preferred. The positions, velocities and accelerations, come from kinematic calculation. The inertial effect of forces taken into account (weight) is calculated. As final result of the inverse dynamic analysis, the are obtained torques that the 4 motors must apply to repeat requested movement with the forces that were acting. The fourth approval of the model consists on confirming that the achieved movement due to the use of the torques obtained in the inverse dynamics, are in accordance with movements from kinematic analysis (theoretical movement). For this, it is necessary to work with direct dynamics. Direct dynamic is in charge of calculating the movements of robot that results from applying torques at motors and forces at the robot. Therefore, the resultant real movement, as there was no change in any condition of the ones obtained at the inverse dynamics (motor torques and inertial forces due to weight of elements) must be the same than theoretical movement. When these results are achieved, it is considered that robot is ready to work. When a machining external force is introduced and it was not taken into account before during the inverse dynamics, and torques at motors considered are the ones of the inverse dynamics, the real movement obtained is not the same than the theoretical movement. Closed loop control is based on comparing real movement with expected movement and introducing required corrrections to minimize or cancel differences. They are applied gains in the way of corrections for position and/or tolerance to remove those differences. Position error is evaluated as the difference, in each point, between theoretical movemment (calculated in the kinematic analysis) and the real movement achieved for each machining force and for an specific gain. Finally, the position error obtained for each machining force and gains are mapped, giving a chart with the best accuracy that the robot can give for each operation that has been requested and which conditions must be provided.

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La diabetes mellitus es una enfermedad que se caracteriza por la nula o insuficiente producción de insulina, o la resistencia del organismo a la misma. La insulina es una hormona que ayuda a que la glucosa llegue a los tejidos periféricos y al sistema nervioso para suministrar energía. Actualmente existen dos tipos de terapias aplicada en tejido subcutáneo: mediante inyección múltiple realizada con plumas, y la otra es mediante infusión continua de insulina por bomba (CSII). El mayor problema de esta terapia son los retardos por la absorción, tanto de los carbohidratos como de la insulina, y los retardos introducidos por el sensor subcutáneo de glucosa que mide la glucosa del líquido intersticial, lo deseable es controlar la glucosa en sangre. Para intentar independizar al paciente de su enfermedad se está trabajando en el desarrollo del páncreas endocrino artificial (PEA) que dotaría al paciente de una bomba de insulina, un sensor de glucosa y un controlador, el cual se encargaría de la toma de decisiones de las infusiones de insulina. Este proyecto persigue el diseño de un regulador en modo de funcionamiento en CL, con el objetivo de conseguir una regulación óptima del nivel de glucosa en sangre. El diseño de dicho regulador va a ser acometido utilizando la teoría del control por modelo interno (IMC). Esta teoría se basa en la idea de que es necesario realimentar la respuesta de un modelo aproximado del proceso que se quiere controlar. La salida del modelo, comparada con la del proceso real nos da la incertidumbre del modelo de la planta, frente a la planta real. Dado que según la teoría del modelo interno, estas diferencias se dan en las altas frecuencias, la teoría IMC propone un filtro paso bajo como regulador en serie con la inversa del modelo de la planta para conseguir el comportamiento deseado. Además se pretende implementar un Predictor Smith para minimizar los efectos del retardo de la medida del sensor. En el proyecto para conseguir la viabilidad del PEA se ha adaptado el controlador IMC clásico utilizando las ganancias estáticas de un modelo de glucosa, a partir de la ruta subcutánea de infusión y la vía subcutánea de medida. El modo de funcionamiento del controlador en SCL mejora el rango de normoglucemia, necesitando la intervención del paciente indicando anticipadamente el momento de las ingestas al controlador. El uso de un control SCL con el Predictor de Smith mejora los resultados pues se añade al controlador una variable sobre las ingestas con la participación del paciente. ABSTRACT. Diabetes mellitus is a group of metabolic diseases in which a person has high blood sugar, due to the body does not produce enough insulin, or because cells do not respond to the insulin produced. The insulin is a hormone that helps the glucose to reach to outlying tissues and the nervous system to supply energy. There are currently two types of therapies applied in subcutaneous tissue: the first one consists in using the intensive therapy with an insulin pen, and the other one is by continuous subcutaneous insulin infusion (CSII). The biggest problems of this therapy are the delays caused by the absorption of carbohydrates and insulin, and the delays introduced by the subcutaneous glucose sensor that measures glucose from interstitial fluid, it is suitable to control glucose blood. To try to improve these patients quality of life, work is being done on the development of an artificial endocrine pancreas (PEA) consisting of a subcutaneous insulin pump, a subcutaneous glucose sensor and an algorithm of glucose control, which would calculate the bolus that the pump would infuse to patient. This project aims to design a controller for closed-loop therapy, with the objective of obtain an optimal regulation of blood glucose level. The design of this controller will be formed using the theory of internal model control (IMC). This theory is based on the uncertainties given by a model to feedback the system control. Output model, in comparison with the actual process gives the uncertainty of the plant model, compared to the real plant. Since the theory of the internal model, these differences occur at high frequencies, the theory proposes IMC as a low pass filter regulator in series with the inverse model of the plant to get the required behavior. In addition, it will implement a Smith Predictor to minimize the effects of the delay measurement sensor. The project for the viability of PEA has adapted the classic IMC controller using the gains static of glucose model from the subcutaneous infusion and subcutaneous measuring. In simulation the SemiClosed-Loop controller get on the normoglycemia range, requiring patient intervention announce the bolus priming connected to intakes. Using an SCL control with the Smith Predictor improves the outcome because a variable about intakes is added to the controller through patient intervention.

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In this paper a Glucose-Insulin regulator for Type 1 Diabetes using artificial neural networks (ANN) is proposed. This is done using a discrete recurrent high order neural network in order to identify and control a nonlinear dynamical system which represents the pancreas? beta-cells behavior of a virtual patient. The ANN which reproduces and identifies the dynamical behavior system, is configured as series parallel and trained on line using the extended Kalman filter algorithm to achieve a quickly convergence identification in silico. The control objective is to regulate the glucose-insulin level under different glucose inputs and is based on a nonlinear neural block control law. A safety block is included between the control output signal and the virtual patient with type 1 diabetes mellitus. Simulations include a period of three days. Simulation results are compared during the overnight fasting period in Open-Loop (OL) versus Closed- Loop (CL). Tests in Semi-Closed-Loop (SCL) are made feedforward in order to give information to the control algorithm. We conclude the controller is able to drive the glucose to target in overnight periods and the feedforward is necessary to control the postprandial period.

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La Diabetes mellitus es una enfermedad caracterizada por la insuficiente o nula producción de insulina por parte del páncreas o la reducida sensibilidad del organismo a esta hormona, que ayuda a que la glucosa llegue a los tejidos y al sistema nervioso para suministrar energía. La Diabetes tiene una mayor prevalencia en los países desarrollados debido a múltiples factores, entre ellos la obesidad, la vida sedentaria, y disfunciones en el sistema endocrino relacionadas con el páncreas. La Diabetes Tipo 1 es una enfermedad crónica e incurable, en la que son destruidas las células beta del páncreas, que producen la insulina, haciéndose necesaria la administración de insulina de forma exógena para controlar los niveles de glucosa en sangre. El paciente debe seguir una terapia con insulina administrada por vía subcutánea, que debe estar adaptada a sus necesidades metabólicas y a sus hábitos de vida. Esta terapia intenta imitar el perfil insulínico de un páncreas sano. La tecnología actual permite abordar el desarrollo del denominado “páncreas endocrino artificial” (PEA), que aportaría precisión, eficacia y seguridad en la aplicación de las terapias con insulina y permitiría una mayor independencia de los pacientes frente a su enfermedad, que en la actualidad están sujetos a una constante toma de decisiones. El PEA consta de un sensor continuo de glucosa, una bomba de infusión de insulina y un algoritmo de control, que calcula la insulina a infusionar utilizando los niveles de glucosa del paciente como información principal. Este trabajo presenta una modificación en el método de control en lazo cerrado propuesto en un proyecto previo. El controlador del que se parte está compuesto por un controlador basal booleano y un controlador borroso postprandial basado en reglas borrosas heredadas del controlador basal. El controlador postprandial administra el 50% del bolo manual (calculado a partir de la cantidad de carbohidratos que el paciente va a consumir) en el instante del aviso de la ingesta y reparte el resto en instantes posteriores. El objetivo es conseguir una regulación óptima del nivel de glucosa en el periodo postprandial. Con el objetivo de reducir las hiperglucemias que se producen en el periodo postprandial se realiza un transporte de insulina, que es un adelanto de la insulina basal del periodo postprandial que se suministrará junto con un porcentaje variable del bolo manual. Este porcentaje estará relacionado con el estado metabólico del paciente previo a la ingesta. Además se modificará la base de conocimiento para adecuar el comportamiento del controlador al periodo postprandial. Este proyecto está enfocado en la mejora del controlador borroso postprandial previo, modificando dos aspectos: la inferencia del controlador postprandial y añadiendo una toma de decisiones automática sobre el % del bolo manual y el transporte. Se ha propuesto un controlador borroso con una nueva inferencia, que no hereda las características del controlado basal, y ha sido adaptado al periodo postprandial. Se ha añadido una inferencia borrosa que modifica la cantidad de insulina a administrar en el momento del aviso de ingesta y la cantidad de insulina basal a transportar del periodo postprandial al bolo manual. La validación del algoritmo se ha realizado mediante experimentos en simulación utilizando una población de diez pacientes sintéticos pertenecientes al Simulador de Padua/Virginia, evaluando los resultados con estadísticos para después compararlos con los obtenidos con el método de control anterior. Tras la evaluación de los resultados se puede concluir que el nuevo controlador postprandial, acompañado de la toma de decisiones automática, realiza un mejor control glucémico en el periodo postprandial, disminuyendo los niveles de las hiperglucemias. ABSTRACT. Diabetes mellitus is a disease characterized by the insufficient or null production of insulin from the pancreas or by a reduced sensitivity to this hormone, which helps glucose get to the tissues and the nervous system to provide energy. Diabetes has more prevalence in developed countries due to multiple factors, including obesity, sedentary lifestyle and endocrine dysfunctions related to the pancreas. Type 1 Diabetes is a chronic, incurable disease in which beta cells in the pancreas that produce insulin are destroyed, and exogenous insulin delivery is required to control blood glucose levels. The patient must follow a therapy with insulin administered by the subcutaneous route that should be adjusted to the metabolic needs and lifestyle of the patient. This therapy tries to imitate the insulin profile of a non-pathological pancreas. Current technology can adress the development of the so-called “endocrine artificial pancreas” (EAP) that would provide accuracy, efficacy and safety in the application of insulin therapies and will allow patients a higher level of independence from their disease. Patients are currently tied to constant decision making. The EAP consists of a continuous glucose sensor, an insulin infusion pump and a control algorithm that computes the insulin amount that has to be infused using the glucose as the main source of information. This work shows modifications to the control method in closed loop proposed in a previous project. The reference controller is composed by a boolean basal controller and a postprandial rule-based fuzzy controller which inherits the rules from the basal controller. The postprandial controller administrates 50% of the bolus (calculated from the amount of carbohydrates that the patient is going to ingest) in the moment of the intake warning, and distributes the remaining in later instants. The goal is to achieve an optimum regulation of the glucose level in the postprandial period. In order to reduce hyperglycemia in the postprandial period an insulin transport is carried out. It consists on a feedforward of the basal insulin from the postprandial period, which will be administered with a variable percentage of the manual bolus. This percentage would be linked with the metabolic state of the patient in moments previous to the intake. Furthermore, the knowledge base is going to be modified in order to fit the controller performance to the postprandial period. This project is focused on the improvement of the previous controller, modifying two aspects: the postprandial controller inference, and the automatic decision making on the percentage of the manual bolus and the transport. A fuzzy controller with a new inference has been proposed and has been adapted to the postprandial period. A fuzzy inference has been added, which modifies both the amount of manual bolus to administrate at the intake warning and the amount of basal insulin to transport to the prandial bolus. The algorithm assessment has been done through simulation experiments using a synthetic population of 10 patients in the UVA/PADOVA simulator, evaluating the results with statistical parameters for further comparison with those obtained with the previous control method. After comparing results it can be concluded that the new postprandial controller, combined with the automatic decision making, carries out a better glycemic control in the postprandial period, decreasing levels of hyperglycemia.

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V2Ic control provides very fast dynamic performance to the Buck converter both under load steps and under voltage reference steps. However, the design of this control is complex since it is prone to subharmonic oscillations and several parameters affect the stability of the system. This paper derives and validates a very accurate modeling and stability analysis of a closed-loop V2Ic control using the Floquet theory. This allows the derivation of sensitivity analysis to design a robust converter. The proposed methodology is validated on a 5-MHz Buck converter. The work is also extended to V2 control using the same methodology, showing high accuracy and robustness. The paper also demonstrates, on the V2 control, that even a low bandwidth-linear controller can affect the stability of a ripple-based control.

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This paper studies the impact that different approaches of modeling the real-time use of the secondary regulation reserves have in the joint energy and reserve hourly scheduling of a price-taker pumped-storage hydropower plant. The unexpected imbalance costs due to the error between the forecasted real-time use of the reserves and the actual value are also studied and evaluated for the different approaches. The proposed methodology is applied to a daily-cycle and closed-loop pumped-storage hydropower plant. Preliminary results show that the deviations in the water volume at the end of the day are important when the percentage of the real-time use of reserves is unknown in advance, and also that the total income in all approaches after correcting these deviations is significantly lower than the maximum theoretical income.

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The runtime management of the infrastructure providing service-based systems is a complex task, up to the point where manual operation struggles to be cost effective. As the functionality is provided by a set of dynamically composed distributed services, in order to achieve a management objective multiple operations have to be applied over the distributed elements of the managed infrastructure. Moreover, the manager must cope with the highly heterogeneous characteristics and management interfaces of the runtime resources. With this in mind, this paper proposes to support the configuration and deployment of services with an automated closed control loop. The automation is enabled by the definition of a generic information model, which captures all the information relevant to the management of the services with the same abstractions, describing the runtime elements, service dependencies, and business objectives. On top of that, a technique based on satisfiability is described which automatically diagnoses the state of the managed environment and obtains the required changes for correcting it (e.g., installation, service binding, update, or configuration). The results from a set of case studies extracted from the banking domain are provided to validate the feasibility of this proposa

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Modern FPGAs with Dynamic and Partial Reconfiguration (DPR) feature allow the implementation of complex, yet flexible, hardware systems. Combining this flexibility with evolvable hardware techniques, real adaptive systems, able to reconfigure themselves according to environmental changes, can be envisaged. In this paper, a highly regular and modular architecture combined with a fast reconfiguration mechanism is proposed, allowing the introduction of dynamic and partial reconfiguration in the evolvable hardware loop. Results and use case show that, following this approach, evolvable processing IP Cores can be built, providing intensive data processing capabilities, improving data and delay overheads with respect to previous proposals. Results also show that, in the worst case (maximum mutation rate), average reconfiguration time is 5 times lower than evaluation time.

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In parallel to the effort of creating Open Linked Data for the World Wide Web there is a number of projects aimed for developing the same technologies but in the context of their usage in closed environments such as private enterprises. In the paper, we present results of research on interlinking structured data for use in Idea Management Systems - a still rare breed of knowledge management systems dedicated to innovation management. In our study, we show the process of extending an ontology that initially covers only the Idea Management System structure towards the concept of linking with distributed enterprise data and public data using Semantic Web technologies. Furthermore we point out how the established links can help to solve the key problems of contemporary Idea Management Systems

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Functional validation of complex digital systems is a hard and critical task in the design flow. In particular, when dealing with communication systems, like Multiband Orthogonal Frequency Division Multiplexing Ultra Wideband (MB-OFDM UWB), the design decisions taken during the process have to be validated at different levels in an easy way. In this work, a unified algorithm-architecture-circuit co-design environment for this type of systems, to be implemented in FPGA, is presented. The main objective is to find an efficient methodology for designing a configurable optimized MB-OFDM UWB system by using as few efforts as possible in verification stage, so as to speed up the development period. Although this efficient design methodology is tested and considered to be suitable for almost all types of complex FPGA designs, we propose a solution where both the circuit and the communication channel are tested at different levels (algorithmic, RTL, hardware device) using a common testbench.

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This paper studies the problem of determining the position of beacon nodes in Local Positioning Systems (LPSs), for which there are no inter-beacon distance measurements available and neither the mobile node nor any of the stationary nodes have positioning or odometry information. The common solution is implemented using a mobile node capable of measuring its distance to the stationary beacon nodes within a sensing radius. Many authors have implemented heuristic methods based on optimization algorithms to solve the problem. However, such methods require a good initial estimation of the node positions in order to find the correct solution. In this paper we present a new method to calculate the inter-beacon distances, and hence the beacons positions, based in the linearization of the trilateration equations into a closed-form solution which does not require any approximate initial estimation. The simulations and field evaluations show a good estimation of the beacon node positions.