An Actor-Critic based controller for glucose regulation in type 1 diabetes

A novel adaptive approach for glucose control in individuals with type 1 diabetes under sensor-augmented pump therapy is proposed. The controller, is based on Actor-Critic (AC) learning and is inspired by the principles of reinforcement learning and optimal control theory. The main characteristics of the proposed controller are (i) simultaneous adjustment of both the insulin basal rate and the bolus dose, (ii) initialization based on clinical procedures, and (iii) real-time personalization. The effectiveness of the proposed algorithm in terms of glycemic control has been investigated in silico in adults, adolescents and children under open-loop and closed-loop approaches, using announced meals with uncertainties in the order of ±25% in the estimation of carbohydrates. The results show that glucose regulation is efficient in all three groups of patients, even with uncertainties in the level of carbohydrates in the meal. The percentages in the A+B zones of the Control Variability Grid Analysis (CVGA) were 100% for adults, and 93% for both adolescents and children. The AC based controller seems to be a promising approach for the automatic adjustment of insulin infusion in order to improve glycemic control. After optimization of the algorithm, the controller will be tested in a clinical trial.

eIF4E-bound mRNPs are substrates for nonsense-mediated mRNA decay in mammalian cells

Eukaryotic mRNAs with premature translation-termination codons (PTCs) are recognized and degraded by a process referred to as nonsense-mediated mRNA decay (NMD). The evolutionary conservation of the core NMD factors UPF1, UPF2 and UPF3 would imply a similar basic mechanism of PTC recognition in all eukaryotes. However, unlike NMD in yeast, which targets PTC-containing mRNAs irrespectively of whether their 5' cap is bound by the cap-binding complex (CBC) or by the eukaryotic initiation factor 4E (eIF4E), mammalian NMD has been claimed to be restricted to CBC-bound mRNAs during the pioneer round of translation. In our recent study we compared decay kinetics of two NMD reporter systems in mRNA fractions bound to either CBC or eIF4E in human cells. Our findings reveal that NMD destabilizes eIF4E bound transcripts as efficiently as those associated with CBC. These results corroborate an emerging unified model for NMD substrate recognition, according to which NMD can ensue at every aberrant translation termination event. Additionally, our results indicate that the closed loop structure of mRNA forms only after the replacement of CBC with eIF4E at the 5' cap.

eIF4E‐bound mRNPs are substrates for nonsense‐mediated mRNA decay in mammalian cells

Eukaryotic mRNAs with premature translation-termination codons (PTCs) are recognized and degraded by a process referred to as nonsense-mediated mRNA decay (NMD). The evolutionary conservation of the core NMD factors UPF1, UPF2 and UPF3 would imply a similar basic mechanism of PTC recognition in all eukaryotes. However, unlike NMD in yeast, which targets PTC-containing mRNAs irrespectively of whether their 5' cap is bound by the cap-binding complex (CBC) or by the eukaryotic initiation factor 4E (eIF4E), mammalian NMD has been claimed to be restricted to CBC-bound mRNAs during the pioneer round of translation. In our recent study we compared decay kinetics of two NMD reporter systems in mRNA fractions bound to either CBC or eIF4E in human cells. Our findings reveal that NMD destabilizes eIF4E bound transcripts as efficiently as those associated with CBC. These results corroborate an emerging unified model for NMD substrate recognition, according to which NMD can ensue at every aberrant translation termination event. Additionally, our results indicate that the closed loop structure of mRNA forms only after the replacement of CBC with eIF4E at the 5' cap.

eIF4E-bound mRNPs are substrates for nonsense-mediated mRNA decay in mammalian cells

Eukaryotic mRNAs with premature translation-termination codons (PTCs) are recognized and degraded by a process referred to as nonsense-mediated mRNA decay (NMD). The evolutionary conservation of the core NMD factors UPF1, UPF2 and UPF3 would imply a similar basic mechanism of PTC recognition in all eukaryotes. However, unlike NMD in yeast, which targets PTC-containing mRNAs irrespectively of whether their 5' cap is bound by the cap-binding complex (CBC) or by the eukaryotic initiation factor 4E (eIF4E), mammalian NMD has been claimed to be restricted to CBC-bound mRNAs during the pioneer round of translation. In our recent study we compared decay kinetics of two NMD reporter systems in mRNA fractions bound to either CBC or eIF4E in human cells. Our findings reveal that NMD destabilizes eIF4E bound transcripts as efficiently as those associated with CBC. These results corroborate an emerging unified model for NMD substrate recognition, according to which NMD can ensue at every aberrant translation termination event. Additionally, our results indicate that the closed loop structure of mRNA forms only after the replacement of CBC with eIF4E at the 5' cap.

eIF4E‐bound mRNPs are substrates for nonsense‐mediated mRNA decay in mammalian cells

Eukaryotic mRNAs with premature translation-termination codons (PTCs) are recognized and degraded by a process referred to as nonsense-mediated mRNA decay (NMD). The evolutionary conservation of the core NMD factors UPF1, UPF2 and UPF3 would imply a similar basic mechanism of PTC recognition in all eukaryotes. However, unlike NMD in yeast, which targets PTC-containing mRNAs irrespectively of whether their 5' cap is bound by the cap-binding complex (CBC) or by the eukaryotic initiation factor 4E (eIF4E), mammalian NMD has been claimed to be restricted to CBC-bound mRNAs during the pioneer round of translation. In our recent study we compared decay kinetics of two NMD reporter systems in mRNA fractions bound to either CBC or eIF4E in human cells. Our findings reveal that NMD destabilizes eIF4E bound transcripts as efficiently as those associated with CBC. These results corroborate an emerging unified model for NMD substrate recognition, according to which NMD can ensue at every aberrant translation termination event. Additionally, our results indicate that the closed loop structure of mRNA forms only after the replacement of CBC with eIF4E at the 5' cap.

ON THE EXISTENCE OF SHOCKS IN IRRADIATED EXOPLANETARY ATMOSPHERES

Supersonic flows are expected to exist in the atmospheres of irradiated exoplanets, but the question of whether shocks develop lingers. Specifically, it reduces to whether continuous flow in a closed loop may become supersonic and if some portions of the supersonic flow steepen into shocks. We first demonstrate that continuous, supersonic flow may exist in two flavors: isentropic and non-isentropic, with shocks being included in the latter class of solutions. Supersonic flow is a necessary but insufficient condition for shocks to develop. The development of a shock requires the characteristics of neighboring points in a flow to intersect. We demonstrate that the intersection of characteristics may be quantified via the knowledge of the Mach number. Finally, we examine three-dimensional simulations of hot Jovian atmospheres and demonstrate that shock formation is expected to occur mostly on the dayside hemisphere, upstream of the substellar point, because the enhanced temperatures near the substellar point provide a natural pressure barrier for the returning flow. Understanding the role of shocks in irradiated exoplanetary atmospheres is relevant to correctly modeling observables such as the peak offsets of infrared phase curves.

GoCARB in the Context of an Artificial Pancreas

Background: In an artificial pancreas (AP), the meals are either manually announced or detected and their size estimated from the blood glucose level. Both methods have limitations, which result in suboptimal postprandial glucose control. The GoCARB system is designed to provide the carbohydrate content of meals and is presented within the AP framework. Method: The combined use of GoCARB with a control algorithm is assessed in a series of 12 computer simulations. The simulations are defined according to the type of the control (open or closed loop), the use or not-use of GoCARB and the diabetics’ skills in carbohydrate estimation. Results: For bad estimators without GoCARB, the percentage of the time spent in target range (70-180 mg/dl) during the postprandial period is 22.5% and 66.2% for open and closed loop, respectively. When the GoCARB is used, the corresponding percentages are 99.7% and 99.8%. In case of open loop, the time spent in severe hypoglycemic events (<50 mg/dl) is 33.6% without the GoCARB and is reduced to 0.0% when the GoCARB is used. In case of closed loop, the corresponding percentage is 1.4% without the GoCARB and is reduced to 0.0% with the GoCARB. Conclusion: The use of GoCARB improves the control of postprandial response and glucose profiles especially in the case of open loop. However, the most efficient regulation is achieved by the combined use of the control algorithm and the GoCARB.

Specificities of Caenorhabditis elegans and human hairpin binding proteins for the first nucleotide in the histone mRNA hairpin loop.

The 3' ends of animal replication-dependent histone mRNAs are formed by endonucleolytic cleavage of the primary transcripts downstream of a highly conserved RNA hairpin. The hairpin-binding protein (HBP) binds to this RNA element and is involved in histone RNA 3' processing. A minimal RNA-binding domain (RBD) of approximately 73 amino acids that has no similarity with other known RNA-binding motifs was identified in human HBP [Wang Z-F et al., Genes & Dev, 1996, 10:3028-3040]. The primary sequence identity between human and Caenorhabditis elegans RBDs is 55% compared to 38% for the full-length proteins. We analyzed whether differences between C. elegans and human HBP and hairpins are reflected in the specificity of RNA binding. The C. elegans HBP and its RBD recognize only their cognate RNA hairpins, whereas the human HBP or RBD can bind both the mammalian and the C. elegans hairpins. This selectivity of C. elegans HBP is mostly mediated by the first nucleotide in the loop, which is C in C. elegans and U in all other metazoans. By converting amino acids in the human RBD to the corresponding C. elegans residues at places where the latter deviates from the consensus, we could identify two amino acid segments that contribute to selectivity for the first nucleotide of the hairpin loop.

Inorganic carbon and geochemistry measurements from landfast sea ice in Resolute Passage, Nunavut, Canada, as part of the Arctic-ICE project, May - June 2010

We conducted a six-week investigation of the sea ice inorganic carbon system during the winter-spring transition in the Canadian Arctic Archipelago. Samples for the determination of sea ice geochemistry were collected in conjunction with physical and biological parameters as part of the 2010 Arctic-ICE (Arctic - Ice-Covered Ecosystem in a Rapidly Changing Environment) program, a sea ice-based process study in Resolute Passage, Nunavut. The goal of Arctic-ICE was to determine the physical-biological processes controlling the timing of primary production in Arctic landfast sea ice and to better understand the influence of these processes on the drawdown and release of climatically active gases. The field study was conducted from 1 May to 21 June, 2010.

Experiences on the specification of algorithms for fire and smoke control in road tunnels

The main objective of ventilation systems in case of fire is the reduction of the possible consequences by achieving the best possible conditions for the evacuation of the users and the intervention of the emergency services. The required immediate transition, from normal to emergency functioning of the ventilation equipments, is being strengthened by the use of automatic and semi-automatic control systems, what reduces the response times through the help to the operators, and the use of pre-defined strategies. A further step consists on the use of closed-loop algorithms, which takes into account not only the initial conditions but their development (air velocity, traffic situation, etc.), optimizing smoke control capacity.

Artificial pancreas using a personalized rule-based controller achieves overnight normoglycemia in patients with type 1 diabetes

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

Role of superconducting shields in electrodynamic propulsion

An electrodynamic tether can propel a spacecraft through a planetary magnetized plasma without using propellant. In the classical embodiment of an electrodynamic tether, the ambient magnetic fleld exerts a Lorentz force on the current along the tether, the ambient plasma providing circuit closure for the current A suggested propulsion scheme would hypothetically eliminate tether performance dependence on the plasma density by using a full wire loop to close the current circuit, and a superconductor to shield a loop segment from the external uniform magnetic fleld and cancel the Lorentz force on that segment. Here, we use basic electromagnetic laws to explain how such a scheme cannot produce a net force. Because there is no net current in the superconducting shield, the circulation of the magnetic field along a closed line outside the full cross section, in its plane, is just due to the current flowing in the loop segment. The presence of the superconducting shield simply moves the Lorentz force from the shielded loop segment to the shield itself and, as a result, the total magnetic force, acting on full loop plus shield, remains zero.

Dual Active Bridge based Battery Charger for Plug-in Hybrid Electric Vehicle with Charging Current Containing Low Frequency Ripple

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.

Modelling and Control of Stepper Motors for High Accuracy Positioning Systems Used in Radioactive Environments

Hybrid Stepper Motors are widely used in open-loop position applications. They are the choice of actuation for the collimators in the Large Hadron Collider, the largest particle accelerator at CERN. In this case the positioning requirements and the highly radioactive operating environment are unique. The latter forces both the use of long cables to connect the motors to the drives which act as transmission lines and also prevents the use of standard position sensors. However, reliable and precise operation of the collimators is critical for the machine, requiring the prevention of step loss in the motors and maintenance to be foreseen in case of mechanical degradation. In order to make the above possible, an approach is proposed for the application of an Extended Kalman Filter to a sensorless stepper motor drive, when the motor is separated from its drive by long cables. When the long cables and high frequency pulse width modulated control voltage signals are used together, the electrical signals difer greatly between the motor and drive-side of the cable. Since in the considered case only drive-side data is available, it is therefore necessary to estimate the motor-side signals. Modelling the entire cable and motor system in an Extended Kalman Filter is too computationally intensive for standard embedded real-time platforms. It is, in consequence, proposed to divide the problem into an Extended Kalman Filter, based only on the motor model, and separated motor-side signal estimators, the combination of which is less demanding computationally. The efectiveness of this approach is shown in simulation. Then its validity is experimentally demonstrated via implementation in a DSP based drive. A testbench to test its performance when driving an axis of a Large Hadron Collider collimator is presented along with the results achieved. It is shown that the proposed method is capable of achieving position and load torque estimates which allow step loss to be detected and mechanical degradation to be evaluated without the need for physical sensors. These estimation algorithms often require a precise model of the motor, but the standard electrical model used for hybrid stepper motors is limited when currents, which are high enough to produce saturation of the magnetic circuit, are present. New model extensions are proposed in order to have a more precise model of the motor independently of the current level, whilst maintaining a low computational cost. It is shown that a significant improvement in the model It is achieved with these extensions, and their computational performance is compared to study the cost of model improvement versus computation cost. The applicability of the proposed model extensions is demonstrated via their use in an Extended Kalman Filter running in real-time for closed-loop current control and mechanical state estimation. An additional problem arises from the use of stepper motors. The mechanics of the collimators can wear due to the abrupt motion and torque profiles that are applied by them when used in the standard way, i.e. stepping in open-loop. Closed-loop position control, more specifically Field Oriented Control, would allow smoother profiles, more respectful to the mechanics, to be applied but requires position feedback. As mentioned already, the use of sensors in radioactive environments is very limited for reliability reasons. Sensorless control is a known option but when the speed is very low or zero, as is the case most of the time for the motors used in the LHC collimator, the loss of observability prevents its use. In order to allow the use of position sensors without reducing the long term reliability of the whole system, the possibility to switch from closed to open loop is proposed and validated, allowing the use of closed-loop control when the position sensors function correctly and open-loop when there is a sensor failure. A different approach to deal with the switched drive working with long cables is also presented. Switched mode stepper motor drives tend to have poor performance or even fail completely when the motor is fed through a long cable due to the high oscillations in the drive-side current. The design of a stepper motor output fillter which solves this problem is thus proposed. A two stage filter, one devoted to dealing with the diferential mode and the other with the common mode, is designed and validated experimentally. With this ?lter the drive performance is greatly improved, achieving a positioning repeatability even better than with the drive working without a long cable, the radiated emissions are reduced and the overvoltages at the motor terminals are eliminated.

Caracterización de un robot para aplicaciones de mecanizado con requerimientos de tolerancias

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.