MA336exam01

Exam questions and solutions in LaTex

MA336exam01pdf

Exam questions and solutions in PDF

MA336exam00

Exam questions and solutions in LaTex

Semiactive control strategies for vibration mitigation in adaptronic structures equipped with magnetorheological dampers

Los sistemas tales como edificios y veh¨ªculos est¨¢n sujetos a vibraciones que pueden causar mal funcionamiento, incomodidad o colapso. Para mitigar estas vibraciones, se suelen instalar amortiguadores. Estas estructuras se convierten en sistemas adaptr¨®nicos cuando los amortiguadores son controlables. Esta tesis se enfoca en la soluci¨®n del problema de vibraciones en edificios y veh¨ªculos usando amortiguadores magnetoreol¨®gicos (MR). Estos son unos amortiguadores controlables caracterizados por una din¨¢mica altamente no lineal. Adem¨¢s, los sistemas donde se instalan se caracterizan por la incertidumbre param¨¦trica, la limitaci¨®n de medidas y las perturbaciones desconocidas, lo que obliga al uso de t¨¦cnicas complejas de control. En esta tesis se usan Backstepping, QFT y H2/H¡Þ mixto para resolver el problema. Las leyes de control se verifican mediante simulaci¨®n y experimentaci¨®n.

Aplicació d'algoritmes genètics en l'optimització dels processos de fabricació del paper

La creciente preocupación y concienciación de la sociedad respecto el medio ambiente, y en consecuencia la legislación y regulaciones generadas inducen a la modificación de los procesos productivos existentes en la industria química. Las configuraciones iniciales deben modificarse para conseguir una mayor integración de procesos. Para este fin se han creado y desarrollado diferentes metodologías que deben facilitar la tarea a los responsables del rediseño. El desarrollo de una metodología y herramientas complementarias es el principal objetivo de la investigación aquí presentada, especialmente centrada en el desarrollo y la aplicación de una metodología de optimización de procesos. Esta metodología de optimización se aplica sobre configuraciones de proceso existentes y pretende encontrar nuevas configuraciones viables según los objetivos de optimización fijados. La metodología tiene dos partes diferenciadas: la primera se basa en un simulador de procesos comercial y la segunda es la técnica de optimización propiamente dicha. La metodología se inicia con la elaboración de una simulación convenientemente validada que reproduzca el proceso existente, en este caso una papelera no integrada que produce papel estucado de calidad, para impresión. A continuación la técnica de optimización realiza una búsqueda dentro del dominio de los posibles resultados, en busca de los mejores resultados que satisfazcan plenamente los objetivos planteados. Dicha técnica de optimización está basada en los algoritmos genéticos como herramienta de búsqueda, junto a un subprograma basado en técnicas de programación matemática para el cálculo de resultados. Un número reducido de resultados son finalmente escogidos y utilizados para modificar la simulación existente fijando la redistribución de los flujos del proceso. Los resultados de la simulación del proceso determinan en último caso la viabilidad técnica de cada reconfiguración planteada. En el proceso de optimización, los objetivos están definidos en una función objetivo dentro de la técnica de optimización. Dicha función rige la búsqueda de resultados. La función objetivo puede ser individual o una combinación de objetivos. En el presente caso, la función persigue una minimización del consumo de agua y una minimización de la pérdida de materia prima. La optimización se realiza bajo restricciones para alcanzar este objetivo combinado en forma de una solución de compromiso. Producto de la aplicación de esta metodología se han obtenido resultados interesantes que significan una mejora del cierre de circuitos y un ahorro de materia prima, sin comprometer al mismo tiempo la operabilidad del proceso producto ni la calidad del papel.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Biologically motivated model for object detection and identification in real-world scenes

The classical computer vision methods can only weakly emulate some of the multi-level parallelisms in signal processing and information sharing that takes place in different parts of the primates’ visual system thus enabling it to accomplish many diverse functions of visual perception. One of the main functions of the primates’ vision is to detect and recognise objects in natural scenes despite all the linear and non-linear variations of the objects and their environment. The superior performance of the primates’ visual system compared to what machine vision systems have been able to achieve to date, motivates scientists and researchers to further explore this area in pursuit of more efficient vision systems inspired by natural models. In this paper building blocks for a hierarchical efficient object recognition model are proposed. Incorporating the attention-based processing would lead to a system that will process the visual data in a non-linear way focusing only on the regions of interest and hence reducing the time to achieve real-time performance. Further, it is suggested to modify the visual cortex model for recognizing objects by adding non-linearities in the ventral path consistent with earlier discoveries as reported by researchers in the neuro-physiology of vision.

Modeling small-scale dairy farms in central Mexico using multi-criteria programming

Milk supply from Mexican dairy farms does not meet demand and small-scale farms can contribute toward closing the gap. Two multi-criteria programming techniques, goal programming and compromise programming, were used in a study of small-scale dairy farms in central Mexico. To build the goal and compromise programming models, 4 ordinary linear programming models were also developed, which had objective functions to maximize metabolizable energy for milk production, to maximize margin of income over feed costs, to maximize metabolizable protein for milk production, and to minimize purchased feedstuffs. Neither multicriteria approach was significantly better than the other; however, by applying both models it was possible to perform a more comprehensive analysis of these small-scale dairy systems. The multi-criteria programming models affirm findings from previous work and suggest that a forage strategy based on alfalfa, rye-grass, and corn silage would meet nutrient requirements of the herd. Both models suggested that there is an economic advantage in rescheduling the calving season to the second and third calendar quarters to better synchronize higher demand for nutrients with the period of high forage availability.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Climate model calculations of the impact of aerosols from road transport and shipping

Road transport and shipping are copious sources of aerosols, which exert a 9 significant radiative forcing, compared to, for example, the CO2 emitted by these sectors. An 10 advanced atmospheric general circulation model, coupled to a mixed-layer ocean, is used to 11 calculate the climate response to the direct radiative forcing from such aerosols. The cases 12 considered include imposed distributions of black carbon and sulphate aerosols from road 13 transport, and sulphate aerosols from shipping; these are compared to the climate response 14 due to CO2 increases. The difficulties in calculating the climate response due to small 15 forcings are discussed, as the actual forcings have to be scaled by large amounts to enable a 16 climate response to be easily detected. Despite the much greater geographical inhomogeneity 17 in the sulphate forcing, the patterns of zonal and annual-mean surface temperature response 18 (although opposite in sign) closely resembles that resulting from homogeneous changes in 19 CO2. The surface temperature response to black carbon aerosols from road transport is shown 20 to be notably non-linear in scaling applied, probably due to the semi-direct response of clouds 21 to these aerosols. For the aerosol forcings considered here, the most widespread method of 22 calculating radiative forcing significantly overestimates their effect, relative to CO2, 23 compared to surface temperature changes calculated using the climate model.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Testing for non-linearity in daily sterling exchange rates

A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire post Bretton-Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH effects clearly demonstrated in a large number of papers, but with the tests for non-linearity which are currently available being unable to classify any additional non-linear structure.