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En aquesta Tesi es proposa una nova estructura de control amb l'objectiu de solucionar el conflicte entre rendiment i robustesa en l'esquema de realimentació tradicional. La teoria matemàtica de la factorització coprimera permet proposar un configuració de control basada en observador. És el que es denomina configuració Observador-Controlador i es fa servir de diferents maneres. La primera proposta enfoca la millorar les prestacions de robustesa com a una alternativa al disseny d'un controlador robust. Amb la intenció d'aconseguir un bon rendiment en presència de pertorbacions i d'incerteses procedim de la següent manera: en primer lloc, dissenyem un sistema de control per realimentació estàndard per tal de satisfer els requeriments de seguiment a referència; en segon lloc, millorem les propietats de robustesa sense alterar les propietats de seguiment del sistema de control inicial. Aquesta estratègia es basa en la generació d'un complement pel sistema de control nominal mitjançant una estructura fonamentada en la configuració Observador-Controlador. Els sistema de control resultant funciona de tal manera que la planta estarà controlada només pel controlador per realimentació nominal quan no hi hagi ni incerteses ni pertorbacions externes i el controlador per a la robustificació estarà actiu només en presencia de incerteses i/o pertorbacions externes.La segona proposta afronta l'objectiu d'aconseguir un bon rendiment en presència de pertorbacions i d'incerteses. En aquest cas, desenvolupen un controlador de dos graus de llibertat (2-DOF) i procedim de la següent manera: primer, dissenyem un sistema de control per realimentació basat en observador per tal de garantir un nivell mínim d'estabilitat robusta; segon, dissenyem un prefiltre per tal de garantir robustesa en les propietats de llaç obert. Malgrat les dues propostes no es basen en una reformulació en termes del factor de Youla, es possible fer una parametrització basada en Youla per tal de caracteritzar el conjunt de tots els observadors per una planta nominal. En essència, les dues propostes es poden veure com a estructures de dos graus de llibertat. Tot i que l'esquema de la primera proposta no s'adapta a una estructura de 2-DOF clàssica, amb un prefiltre i una part per realimentació, podem considerar-la com a tal pel fet que aconsegueix una complerta separació de propietats. En aquest cas, el controlador inicial s'ocupa de les especificacions de seguiment a referència per a la planta nominal i el controlador per a la robustificació s'encarrega de la millora, si cal, les prestacions de robustesa nominals. / In this Thesis, we shall propose a new controller architecture to try to completely overcome the conflict between performance and robustness in the traditional feedback framework. The proposed control configuration comes from the coprime factorization approach and, in such a context, a somewhat uncommon observer-based control configuration is derived. It is the Observer-Controller configuration and it is used in different arrangements.The first proposal deals with the robustness enhancement problem as an alternative to the design of a robust control system. With the lofty goal of achieving high performance in the face of disturbances and uncertainties we proceed as follows: first, an initial feedback control system is set for the nominal plant to satisfy tracking requirements and second, the resulting robustness properties are conveniently enhanced while leaving unaltered the tracking responses provided by the initial controller. The approach is based on the generation of a complement for the nominal control system by means of an structure based on the Observer-Controller configuration. The final control system works in such a way that the plant will be solely controlled by the initial nominal feedback controller when there is neither model uncertainties nor external disturbances and the robustification controller will only be active when there is model uncertainties and/or external disturbances. The second proposal also addresses the goal of high performance in the face of disturbances and uncertainties. In this case, a two degrees-of-freedom (2-DOF) control configuration is developed. We proceed as follows: first, an observer-based feedback control scheme is designed to guarantee some levels of stability robustness and second, a prefilter controller is computed to guarantee robust open-loop processing of the reference commands. Despite both proposals are not based on a reformulation in terms of the Youla parameter, it is possible to perform a Youla parametrization to characterize the set of all observers for the nominal plant. Essentially, both proposals can be considered as 2-DOF control configurations. The first presented proposal do not fit the standard 2-DOF control scheme made up with a feedback controller and a prefilter controller. Nevertheless, it can also be seen to lie in the 2-DOF control configuration in the sense that a complete separation of properties is achieved. In such case, the tracking properties of the nominal plant are attained by a controller and the robustness properties are considered and enhanced if necessary by the Observer-Controller configuration.

En esta Tesis se tratan varios aspectos relacionados con la linealización de sistemas no lineales. Las dificultades inherentes al empleo de técnicas de análisis, modelado y control de sistemas no lineales, son debidas en gran parte a lo poco sistemáticas que son. Además, respecto a los métodos de linealización basados en técnicas de control cabe decir que los que usan realimentación de estado, en general, son difíciles de realizar en la práctica ya que el diseño de observadores de estado no lineales es problemático. Asimismo, también lo es el diseño y realización de controladores no lineales. El método de linealización propuesto en esta Tesis consiste en determinar el tipo de realimentación a aplicar a un sistema no lineal, de modo que, según un cierto criterio de medida, el efecto de las no linealidades se reduzca frente al de las linealidades. El sistema no lineal se descompondrá en dos bloques, uno lineal y otro no lineal. El bloque lineal será el que caracterizará el funcionamiento deseado, es decir el funcionamiento linealizado, y es por esto que se considera un sistema modelo. Este sistema modelo se le denominará modelo de referencia, y será la guía de cual es el funcionamiento deseado. Una de las alternativas para descomponer el sistema no lineal en los dos bloques comentados es haciendo uso del desarrollo en serie de Volterra del mismo, de modo que el primer término de la expansión, término lineal, se corresponderá con el modelo de referencia a seguir.Haciendo uso del modelo matemático del sistema no lineal y del modelo de referencia se obtendrá la caracterización de un sistema error, que modela las diferencias de funcionamiento entre el sistema no lineal y el lineal deseado. De este modo, el objetivo consiste en conseguir que la salida del sistema error sea nula, o en su defecto que sea lo menor posible. Esta reducción del sistema error se plantea como un problema de atenuación de perturbaciones vía realimentación, de acuerdo a un criterio óptimo medido con la norma H-infinita: se buscará la minimización de la norma H-infinita de la parte lineal del sistema error, pero vigilando al mismo tiempo la estabilidad del sistema global en lazo cerrado. Para ello el criterio de estabilidad empleado es el de la pequeña ganancia. / In this Thesis some aspects related to the linearization of nonlinear systems are considered. When working with nonlinear systems it is difficult the analysis, modelling and control of such kind of systems. Moreover the linearization methods based on control theory using state feedback are difficult to use, in a practical point of view, due to the difficult to design nonlinear state observers.The linearization method proposed in this Thesis consist in determining what kind of linear feedback must be applied to a nonlinear system in order to reduce the error, according to a certain norm, between nonlinear and linear terms. The nonlinear systems will be decomposed in two blocks, one linear and the other nonlinear. The linear part corresponds to the desired behaviour: it can be considered as a model. This model system is called reference model. One option, proposed in this work, for doing this decomposition is by using a Volterra series decomposition, being the first Volterra kernel the desired linear part.By using the mathematical model of the nonlinear system and the reference model it can be obtained an error model, able for describing the error between nonlinear and model (linear) systems. So, the goal to achieve is the reduction of this error. It consists in a problem of optimization (minimization) of the H-infinity norm by using output feedback. Moreover, the overall stability of the closed loop system must be accomplished and tested by means of the small gain stability theory.

An approach for robust design based on stochastic expansions is investigated. The research consists of two parts : 1) stochastic expansions for uncertainty propagation and 2) adaptive sampling for Pareto front approximation. For the first part, a strategy based on the generalized polynomial chaos (gPC) expansion method is developed. Second, in order to alleviate the computational cost of approximating the Pareto front, two strategies based on adaptive sampling for multi-objective problems are presented. The first one is based on the two aforementioned methods, whereas the second one considers, in addition, two levels of fidelity of the uncertainty propagation method.

Designers use simulations to observe the behaviour of a system and to make design decisions to improve dynamic performance. However, for complex dynamic systems, these simulations are often time-consuming and, for robust design purposes, numerous simulations are required as a range of design variables is investigated. Furthermore, the optimum set is desired to meet specifications at particular instances in time. In this thesis, the dynamic response of a system is broken into discrete time instances and recorded into a matrix. Each column of this matrix corresponds to a discrete time instance and each row corresponds to the response at a particular design variable set. Singular Value Decomposition (SVD) is then used to separate this matrix into two matrices: one that consists of information in parameter-space and the other containing information in time-space. Metamodels are then used to efficiently and accurately calculate the response at some arbitrary set of design variables at any time. This efficiency is especially useful in Monte Carlo simulation where the responses are required at a very large sample of design variable sets. This work is then extended where the normalized sensitivities along with the first and second moments of the response are required at specific times. Later, the procedure of calculating the metamodel at specific times and how this metamodel is used in parameter design or integrated design for finding the optimum parameters given specifications at specific time steps is shown. In conclusion, this research shows that SVD and metamodelling can be used to apply probabilistic robust design tools where specifications at certain times are required for the optimum performance of a system.

Reducing variation in key product features is a very important goal in process improvement. Finding and trying to control the cause(s) of variation is one way to reduce variability, but is not cost effective or even possible in some situations. In such cases, Robust Parameter Design (RPD) is an alternative. The goal in RPD is to reduce variation by reducing the sensitivity of the process to the sources of variation, rather than controlling these sources directly. That is, the goal is to find levels of the control inputs that minimize the output variation imposed on the process via the noise variables (causes). In the literature, a variety of experimental plans have been proposed for RPD, including Robustness, Desensitization and Taguchi’s method. In this thesis, the efficiency of the alternative plans is compared in the situation where the most important source of variation, called the “Dominant Cause”, is known. It is shown that desensitization is the most appropriate approach for applying the RPD method to an existing process.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality. Such tests are often non-robust to departures from normality, which eventually leads to unreliable conclusions. In this thesis, we propose a combination of a robust Levene-type test and a finite-intersection method, which relaxes the assumption of normality. The new combined procedure yields a more accurate estimate of sizes of the test and provides competitive powers. In addition, we discuss various modifications of the proposed test for unbalanced design cases. We present theoretical justifications of the new test and illustrate its applications by simulations and case studies.

In the chemical or biochemical industry most processes are modeled by nonlinear equations. It is of a great significance to design high-performance nonlinear controllers for efficient control of these nonlinear processes to achieve closed-loop system's stability and high performance. However, there are many difficulties which hinder the design of such controllers due mainly to the process nonlinearity. In this work, comprehensive design procedures based on robust control have been proposed to efficiently deal with the design of gain-scheduled controllers for nonlinear systems. Since all the design procedures proposed in this work rely strongly on the process model, the first difficulty addressed in this thesis is the identification of a relatively simple model of the nonlinear processes under study. The nonlinearity of the processes makes it often difficult to obtain a first-principles model which can be used for analysis and design of the controller. As a result, relatively simple empirical models, Volterra series model and state-affine model, are chosen in this work to represent the nonlinear process for the design of controllers. The second major difficulty is that although the nonlinear models used in this thesis are easy to identify, the analysis of stability and performance for such models using nonlinear control theory is not straightforward. Instead, it is proposed in this study to investigate the stability and performance using a robust control approach. In this approach, the nonlinear model is approximated by a nominal linear model combined with a mathematical description of model error to be referred to, in this work, as model uncertainty. In the current work it was assumed that the main source of uncertainty with respect to the nominal linear model is due to the system nonlinearity. Then, in this study, robust control theoretical tools have been especially developed and applied for the design of gain-scheduled Proportional-Integral (PI) control and gain-scheduled Model Predictive Control (MPC). Gain-scheduled controllers are chosen because for nonlinear processes operated over a wide range of operation, gain-scheduling has proven to be a successful control design technique (Bequette, 1997) for nonlinear processes. To guarantee the closed-loop system's robust stability and performance with the designed controllers, a systematic approach has been proposed for the design of robust gain-scheduled controllers for nonlinear processes. The design procedure is based on robust stability and performance conditions proposed in this work. For time-varying uncertain parameters, robust stability and performance conditions using fixed Lyapunov functions and parameter-dependent Lyapunov functions, were used. Then, comprehensive procedures for the design and optimization of robust gain-scheduled PI and MPC controllers tuning parameters based on the robust stability and performance tests are then proposed. Since the closed-loop system represented by the combination of a state-affine process model and the gain-scheduled controller is found to have an affine dependence on the uncertain parameters, robust stability and performance conditions can be tested by a finite number of Linear Matrix Inequalities (LMIs). Thus, the final problems are numerically solvable. One of the inherent problems with robust control is that the design is conservative. Two approaches have been proposed in this work to reduce the conservatism. The first one is based on parameter-dependent Lyapunov functions, and it is applied when the rate of change of the time-varying uncertainty parameters is <i>a priori</i> available. The second one is based on the relaxation of an input-saturation factor defined in the thesis to deal with the issue of actuator saturation. Finally, to illustrate the techniques discussed in the thesis, robust gain-scheduled PI and MPC controllers are designed for a continuous stirred tank reactor (CSTR) process. A simple MIMO example with two inputs and two outputs controlled by a multivariable gain-scheduled MPC controller is also discussed to illustrate the applicability of the methods to multivariable situations. All the designed controllers are simulated and the simulations show that the proposed design procedures are efficient in designing and comparing robust gain-scheduled controllers for nonlinear processes.