Book Review: Elastic Beams and Frames, by J. D. Renton

The book represents a very interesting example of the possibility to combine in a single publication basic theory of structures and quite advanced topics on the same subject. The author fulfills this objective in a reasonable size book, less than 400 pages divided into 15 chapters averaging 20 pages each plus 9 short appendices. A diskette is also included in the book. This diskette contains training as well practical executable programs on different aspects of structural analysis, such as cross-sections properties,general-purpose computer programs for the static, dynamic and stability analysis of simple bar structures, etc. The book figures are didactic and have been carefully drawn.

Variable threshold algorithm for division of labor analyzed as a dynamical system

Division of labor is a widely studied aspect of colony behavior of social insects. Division of labor models indicate how individuals distribute themselves in order to perform different tasks simultaneously. However, models that study division of labor from a dynamical system point of view cannot be found in the literature. In this paper, we define a division of labor model as a discrete-time dynamical system, in order to study the equilibrium points and their properties related to convergence and stability. By making use of this analytical model, an adaptive algorithm based on division of labor can be designed to satisfy dynamic criteria. In this way, we have designed and tested an algorithm that varies the response thresholds in order to modify the dynamic behavior of the system. This behavior modification allows the system to adapt to specific environmental and collective situations, making the algorithm a good candidate for distributed control applications. The variable threshold algorithm is based on specialization mechanisms. It is able to achieve an asymptotically stable behavior of the system in different environments and independently of the number of individuals. The algorithm has been successfully tested under several initial conditions and number of individuals.

State of the Art and Future Trends in Grid Codes Applicable to Isolated Electrical Systems

Electrical power systems are changing their traditional structure, which was based on a little number of large generating power plants placed at great distances from loads by new models that tend to split the big production nodes in many smaller ones. The set of small groups which are located close to consumers and provide safe and quality energy is called distributed generation (DG). The proximity of the sources to the loads reduces losses associated with transportation and increases overall system efficiency. DG also favors the inclusion of renewable energy sources in isolated electrical systems or remote microgrids, because they can be installed where the natural resource is located. In both cases, as weak grids unable to get help from other nearby networks, it is essential to ensure appropriate behavior of DG sources to guarantee power system safety and stability. The grid codes sets out the technical requirements to be fulfilled for the sources connected in these electrical networks. In technical literature it is rather easy to find and compare grid codes for interconnected electrical systems. However, the existing literature is incomplete and sparse regarding isolated electrical systems and this happens due to the difficulties inherent in the pursuit of codes. Some countries have developed their own legislation only for their island territory (as Spain or France), others apply the same set of rules as in mainland, another group of island countries have elaborated a complete grid code for all generating sources and some others lack specific regulation. This paper aims to make a complete review of the state of the art in grid codes applicable to isolated systems, setting the comparison between them and defining the guidelines predictably followed by the upcoming regulations in these particular systems.

Design and Simulation of Deep Nanometer SRAM Cells under Energy, Mismatch, and Radiation Constraints

La fiabilidad está pasando a ser el principal problema de los circuitos integrados según la tecnología desciende por debajo de los 22nm. Pequeñas imperfecciones en la fabricación de los dispositivos dan lugar ahora a importantes diferencias aleatorias en sus características eléctricas, que han de ser tenidas en cuenta durante la fase de diseño. Los nuevos procesos y materiales requeridos para la fabricación de dispositivos de dimensiones tan reducidas están dando lugar a diferentes efectos que resultan finalmente en un incremento del consumo estático, o una mayor vulnerabilidad frente a radiación. Las memorias SRAM son ya la parte más vulnerable de un sistema electrónico, no solo por representar más de la mitad del área de los SoCs y microprocesadores actuales, sino también porque las variaciones de proceso les afectan de forma crítica, donde el fallo de una única célula afecta a la memoria entera. Esta tesis aborda los diferentes retos que presenta el diseño de memorias SRAM en las tecnologías más pequeñas. En un escenario de aumento de la variabilidad, se consideran problemas como el consumo de energía, el diseño teniendo en cuenta efectos de la tecnología a bajo nivel o el endurecimiento frente a radiación. En primer lugar, dado el aumento de la variabilidad de los dispositivos pertenecientes a los nodos tecnológicos más pequeños, así como a la aparición de nuevas fuentes de variabilidad por la inclusión de nuevos dispositivos y la reducción de sus dimensiones, la precisión del modelado de dicha variabilidad es crucial. Se propone en la tesis extender el método de inyectores, que modela la variabilidad a nivel de circuito, abstrayendo sus causas físicas, añadiendo dos nuevas fuentes para modelar la pendiente sub-umbral y el DIBL, de creciente importancia en la tecnología FinFET. Los dos nuevos inyectores propuestos incrementan la exactitud de figuras de mérito a diferentes niveles de abstracción del diseño electrónico: a nivel de transistor, de puerta y de circuito. El error cuadrático medio al simular métricas de estabilidad y prestaciones de células SRAM se reduce un mínimo de 1,5 veces y hasta un máximo de 7,5 a la vez que la estimación de la probabilidad de fallo se mejora en varios ordenes de magnitud. El diseño para bajo consumo es una de las principales aplicaciones actuales dada la creciente importancia de los dispositivos móviles dependientes de baterías. Es igualmente necesario debido a las importantes densidades de potencia en los sistemas actuales, con el fin de reducir su disipación térmica y sus consecuencias en cuanto al envejecimiento. El método tradicional de reducir la tensión de alimentación para reducir el consumo es problemático en el caso de las memorias SRAM dado el creciente impacto de la variabilidad a bajas tensiones. Se propone el diseño de una célula que usa valores negativos en la bit-line para reducir los fallos de escritura según se reduce la tensión de alimentación principal. A pesar de usar una segunda fuente de alimentación para la tensión negativa en la bit-line, el diseño propuesto consigue reducir el consumo hasta en un 20 % comparado con una célula convencional. Una nueva métrica, el hold trip point se ha propuesto para prevenir nuevos tipos de fallo debidos al uso de tensiones negativas, así como un método alternativo para estimar la velocidad de lectura, reduciendo el número de simulaciones necesarias. Según continúa la reducción del tamaño de los dispositivos electrónicos, se incluyen nuevos mecanismos que permiten facilitar el proceso de fabricación, o alcanzar las prestaciones requeridas para cada nueva generación tecnológica. Se puede citar como ejemplo el estrés compresivo o extensivo aplicado a los fins en tecnologías FinFET, que altera la movilidad de los transistores fabricados a partir de dichos fins. Los efectos de estos mecanismos dependen mucho del layout, la posición de unos transistores afecta a los transistores colindantes y pudiendo ser el efecto diferente en diferentes tipos de transistores. Se propone el uso de una célula SRAM complementaria que utiliza dispositivos pMOS en los transistores de paso, así reduciendo la longitud de los fins de los transistores nMOS y alargando los de los pMOS, extendiéndolos a las células vecinas y hasta los límites de la matriz de células. Considerando los efectos del STI y estresores de SiGe, el diseño propuesto mejora los dos tipos de transistores, mejorando las prestaciones de la célula SRAM complementaria en más de un 10% para una misma probabilidad de fallo y un mismo consumo estático, sin que se requiera aumentar el área. Finalmente, la radiación ha sido un problema recurrente en la electrónica para aplicaciones espaciales, pero la reducción de las corrientes y tensiones de los dispositivos actuales los está volviendo vulnerables al ruido generado por radiación, incluso a nivel de suelo. Pese a que tecnologías como SOI o FinFET reducen la cantidad de energía colectada por el circuito durante el impacto de una partícula, las importantes variaciones de proceso en los nodos más pequeños va a afectar su inmunidad frente a la radiación. Se demuestra que los errores inducidos por radiación pueden aumentar hasta en un 40 % en el nodo de 7nm cuando se consideran las variaciones de proceso, comparado con el caso nominal. Este incremento es de una magnitud mayor que la mejora obtenida mediante el diseño de células de memoria específicamente endurecidas frente a radiación, sugiriendo que la reducción de la variabilidad representaría una mayor mejora. ABSTRACT Reliability is becoming the main concern on integrated circuit as the technology goes beyond 22nm. Small imperfections in the device manufacturing result now in important random differences of the devices at electrical level which must be dealt with during the design. New processes and materials, required to allow the fabrication of the extremely short devices, are making new effects appear resulting ultimately on increased static power consumption, or higher vulnerability to radiation SRAMs have become the most vulnerable part of electronic systems, not only they account for more than half of the chip area of nowadays SoCs and microprocessors, but they are critical as soon as different variation sources are regarded, with failures in a single cell making the whole memory fail. This thesis addresses the different challenges that SRAM design has in the smallest technologies. In a common scenario of increasing variability, issues like energy consumption, design aware of the technology and radiation hardening are considered. First, given the increasing magnitude of device variability in the smallest nodes, as well as new sources of variability appearing as a consequence of new devices and shortened lengths, an accurate modeling of the variability is crucial. We propose to extend the injectors method that models variability at circuit level, abstracting its physical sources, to better model sub-threshold slope and drain induced barrier lowering that are gaining importance in FinFET technology. The two new proposed injectors bring an increased accuracy of figures of merit at different abstraction levels of electronic design, at transistor, gate and circuit levels. The mean square error estimating performance and stability metrics of SRAM cells is reduced by at least 1.5 and up to 7.5 while the yield estimation is improved by orders of magnitude. Low power design is a major constraint given the high-growing market of mobile devices that run on battery. It is also relevant because of the increased power densities of nowadays systems, in order to reduce the thermal dissipation and its impact on aging. The traditional approach of reducing the voltage to lower the energy consumption if challenging in the case of SRAMs given the increased impact of process variations at low voltage supplies. We propose a cell design that makes use of negative bit-line write-assist to overcome write failures as the main supply voltage is lowered. Despite using a second power source for the negative bit-line, the design achieves an energy reduction up to 20% compared to a conventional cell. A new metric, the hold trip point has been introduced to deal with new sources of failures to cells using a negative bit-line voltage, as well as an alternative method to estimate cell speed, requiring less simulations. With the continuous reduction of device sizes, new mechanisms need to be included to ease the fabrication process and to meet the performance targets of the successive nodes. As example we can consider the compressive or tensile strains included in FinFET technology, that alter the mobility of the transistors made out of the concerned fins. The effects of these mechanisms are very dependent on the layout, with transistor being affected by their neighbors, and different types of transistors being affected in a different way. We propose to use complementary SRAM cells with pMOS pass-gates in order to reduce the fin length of nMOS devices and achieve long uncut fins for the pMOS devices when the cell is included in its corresponding array. Once Shallow Trench isolation and SiGe stressors are considered the proposed design improves both kinds of transistor, boosting the performance of complementary SRAM cells by more than 10% for a same failure probability and static power consumption, with no area overhead. While radiation has been a traditional concern in space electronics, the small currents and voltages used in the latest nodes are making them more vulnerable to radiation-induced transient noise, even at ground level. Even if SOI or FinFET technologies reduce the amount of energy transferred from the striking particle to the circuit, the important process variation that the smallest nodes will present will affect their radiation hardening capabilities. We demonstrate that process variations can increase the radiation-induced error rate by up to 40% in the 7nm node compared to the nominal case. This increase is higher than the improvement achieved by radiation-hardened cells suggesting that the reduction of process variations would bring a higher improvement.

A methodology to analyze, design and implement very fast and robust controls of Buck-type converters

La electrónica digital moderna presenta un desafío a los diseñadores de sistemas de potencia. El creciente alto rendimiento de microprocesadores, FPGAs y ASICs necesitan sistemas de alimentación que cumplan con requirimientos dinámicos y estáticos muy estrictos. Específicamente, estas alimentaciones son convertidores DC-DC de baja tensión y alta corriente que necesitan ser diseñados para tener un pequeño rizado de tensión y una pequeña desviación de tensión de salida bajo transitorios de carga de una alta pendiente. Además, dependiendo de la aplicación, se necesita cumplir con otros requerimientos tal y como proveer a la carga con ”Escalado dinámico de tensión”, donde el convertidor necesitar cambiar su tensión de salida tan rápidamente posible sin sobreoscilaciones, o ”Posicionado Adaptativo de la Tensión” donde la tensión de salida se reduce ligeramente cuanto más grande sea la potencia de salida. Por supuesto, desde el punto de vista de la industria, las figuras de mérito de estos convertidores son el coste, la eficiencia y el tamaño/peso. Idealmente, la industria necesita un convertidor que es más barato, más eficiente, más pequeño y que aún así cumpla con los requerimienos dinámicos de la aplicación. En este contexto, varios enfoques para mejorar la figuras de mérito de estos convertidores se han seguido por la industria y la academia tales como mejorar la topología del convertidor, mejorar la tecnología de semiconducores y mejorar el control. En efecto, el control es una parte fundamental en estas aplicaciones ya que un control muy rápido hace que sea más fácil que una determinada topología cumpla con los estrictos requerimientos dinámicos y, consecuentemente, le da al diseñador un margen de libertar más amplio para mejorar el coste, la eficiencia y/o el tamaño del sistema de potencia. En esta tesis, se investiga cómo diseñar e implementar controles muy rápidos para el convertidor tipo Buck. En esta tesis se demuestra que medir la tensión de salida es todo lo que se necesita para lograr una respuesta casi óptima y se propone una guía de diseño unificada para controles que sólo miden la tensión de salida Luego, para asegurar robustez en controles muy rápidos, se proponen un modelado y un análisis de estabilidad muy precisos de convertidores DC-DC que tienen en cuenta circuitería para sensado y elementos parásitos críticos. También, usando este modelado, se propone una algoritmo de optimización que tiene en cuenta las tolerancias de los componentes y sensados distorsionados. Us ando este algoritmo, se comparan controles muy rápidos del estado del arte y su capacidad para lograr una rápida respuesta dinámica se posiciona según el condensador de salida utilizado. Además, se propone una técnica para mejorar la respuesta dinámica de los controladores. Todas las propuestas se han corroborado por extensas simulaciones y prototipos experimentales. Con todo, esta tesis sirve como una metodología para ingenieros para diseñar e implementar controles rápidos y robustos de convertidores tipo Buck. ABSTRACT Modern digital electronics present a challenge to designers of power systems. The increasingly high-performance of microprocessors, FPGAs (Field Programmable Gate Array) and ASICs (Application-Specific Integrated Circuit) require power supplies to comply with very demanding static and dynamic requirements. Specifically, these power supplies are low-voltage/high-current DC-DC converters that need to be designed to exhibit low voltage ripple and low voltage deviation under high slew-rate load transients. Additionally, depending on the application, other requirements need to be met such as to provide to the load ”Dynamic Voltage Scaling” (DVS), where the converter needs to change the output voltage as fast as possible without underdamping, or ”Adaptive Voltage Positioning” (AVP) where the output voltage is slightly reduced the greater the output power. Of course, from the point of view of the industry, the figures of merit of these converters are the cost, efficiency and size/weight. Ideally, the industry needs a converter that is cheaper, more efficient, smaller and that can still meet the dynamic requirements of the application. In this context, several approaches to improve the figures of merit of these power supplies are followed in the industry and academia such as improving the topology of the converter, improving the semiconductor technology and improving the control. Indeed, the control is a fundamental part in these applications as a very fast control makes it easier for the topology to comply with the strict dynamic requirements and, consequently, gives the designer a larger margin of freedom to improve the cost, efficiency and/or size of the power supply. In this thesis, how to design and implement very fast controls for the Buck converter is investigated. This thesis proves that sensing the output voltage is all that is needed to achieve an almost time-optimal response and a unified design guideline for controls that only sense the output voltage is proposed. Then, in order to assure robustness in very fast controls, a very accurate modeling and stability analysis of DC-DC converters is proposed that takes into account sensing networks and critical parasitic elements. Also, using this modeling approach, an optimization algorithm that takes into account tolerances of components and distorted measurements is proposed. With the use of the algorithm, very fast analog controls of the state-of-the-art are compared and their capabilities to achieve a fast dynamic response are positioned de pending on the output capacitor. Additionally, a technique to improve the dynamic response of controllers is also proposed. All the proposals are corroborated by extensive simulations and experimental prototypes. Overall, this thesis serves as a methodology for engineers to design and implement fast and robust controls for Buck-type converters.

Magnetic Attitude Control for Satellites in Polar or Sun-Synchronous Orbits

In this work, a new law for magnetic control of satellites in near-polar orbits is presented. This law has been developed for the UMPSat-2 microsatellite, which has been designed and manufactured by Universidad Politécnica de Madrid, Madrid. The control law is a modification of the B-dot strategy that enables the satellite to control the rotation rate. Besides, the satellite?s equilibrium state is characterized by having the rotation axis perpendicular to the orbit?s plane. The control law described in the present work only needs magnetometers and magnetorquers, as sensors and actuators, respectively, to carry out a successful attitude control on the spacecraft. A description of the analysis is included. Performance and applicability of the proposed method have been demonstrated by control dynamics together with Monte Carlo techniques and by implementing the control law in the UPMSat-2 mission simulator. Results show good performance in terms of acquisition and stability of the satellite rotation rate and orientation with respect to its orbit?s plane.

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

Accurate Analysis of Subharmonic Oscillations of V^2 and V^2Ic Controls Applied to Buck Converter

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.