This thesis presents the multivariable controller design and implementation for a high-precision 6-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner. The positioner is a triangular single-moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. The three planar levitation motors not only generate the vertical force to levitate the triangular platen but control the platen's position in the horizontal plane. All 6-DOF motions are controlled by magnetic forces only. The positioner moves over a Halbach magnet matrix using three sets of two-axis Hall-effect sensors to measure the planar motion and three Nanogage laser distance sensors for the vertical motion. However, the Hall-effect sensors and the Nanogage laser distance sensors can only provide measurements of the displacement of all 6-axis. Since we do not have full-state feedback, I designed two Linear Quadratic Gaussian (LQG) multivariable controllers using a recursive discrete-time observer. A discrete hybrid H2/H(infinity) filter is implemented to obtain optimal estimates of position and orientation, as well as additional estimates of velocity and angular velocity for all 6 axes. In addition, an analysis was done on the signals measured by the Hall-effect sensors, and from there several digital filters were tested to optimize the readings of the sensors and obtain the best estimates possible. One of the multivariable controllers was designed to close the control loop for the three-planar-DOF motion, and the other to close the loop for the vertical motion, all at a sampling frequency of 800 Hz. Experimental results show a position resolution of 1.5 micrometers with position noise of 0.545 micrometers rms in the x-and y-directions and a resolution of less than 110 nm with position noise of 49.3 nm rms in z.

Les normes sur les émissions de polluants des automobiles sont de plus en plus sévères. Les moteurs à injection directe à rampe commune permettent d'atteindre ces exigences notamment grâce à l'injection du carburant à très haute pression. Cette pression varie de 200 à 1600 bar selon le point de fonctionnement du véhicule. L'objectif des travaux de thèse est de réaliser le contrôle de la pression du carburant avec deux contraintes principales : proposer une méthodologie de calibration du contrôleur à partir des caractéristiques techniques du système d'injection et améliorer à la fois la performance et la robustesse du contrôle. Les travaux réalisés se décomposent comme suit : étude du système d'injection et développement d'un modèle de connaissance ; développement des stratégies et des lois de commande ; mise en application sur véhicule. Les essais réalisés sur véhicule ont montré une amélioration des performances et de la robustesse du contrôle de la pression du carburant obtenue par la proposition d'une nouvelle méthodologie de calibration. Celle-ci est basée par l'obtention du contrôleur à partir des caractéristiques techniques du système d'injection et par l'utilisation de lois de commande avancées (commande H8 pour les systèmes Linéaires à Paramètres Variants (LPV)). En particulier l'approche basée sur l'utilisation des Transformations Linéaires Fractionnelles (LFT) a été considérée.

Quantitative Feedback Theory (QFT) is a control system design methodology founded on the premise that feedback is necessary only because of system uncertainty. Articulating flexible structures, such as flexible manipulators, present a difficult closed-loop control problem. In such servo systems, the coupling of the rigid and flexible modes and the non-minimum phase dynamics severely limit system stability and performance. The difficulties in controlling these structures is exacerbated by the denumerably infinite number of flexible modes and associated difficulties in developing accurate dynamic models for controller design. As such, the control of articulating flexible structures presents a non-trivial testbed for the design of QFT based robust control systems. This dissertation examines the multi-input multi-output (MIMO) QFT based control of an articulating flexible structure and presents an enhancement of the theoretical basis for the MIMO QFT design methodologies. The control problem under consideration is the active vibration control of an articulating single-link flexible manipulator. This is facilitated by an actuation scheme comprised of a combination of spatially discrete actuation, in the form of a DC motor to perform articulation, and spatially distributed actuation, in the form of a piezoelectric transducer for active vibration control. In the process of developing and experimentally validating the QFT based control system, shortcomings in the theoretical basis for the MIMO QFT design methodologies are addressed. Robust stability theorems are developed for the two main MIMO QFT design methodologies, namely the sequential and non-sequential MIMO QFT design methodologies. The theorems complement and extend the existing theoretical basis for the MIMO QFT design methodologies. The dissertation results expose salient features of the MIMO QFT design methodologies and provide connections to other multivariable design methodologies.

Quantitative Feedback Theory (QFT) is a control system design methodology founded on the premise that feedback is necessary only because of system uncertainty. Articulating flexible structures, such as flexible manipulators, present a difficult closed-loop control problem. In such servo systems, the coupling of the rigid and flexible modes and the non-minimum phase dynamics severely limit system stability and performance. The difficulties in controlling these structures is exacerbated by the denumerably infinite number of flexible modes and associated difficulties in developing accurate dynamic models for controller design. As such, the control of articulating flexible structures presents a non-trivial testbed for the design of QFT based robust control systems. This dissertation examines the multi-input multi-output (MIMO) QFT based control of an articulating flexible structure and presents an enhancement of the theoretical basis for the MIMO QFT design methodologies. The control problem under consideration is the active vibration control of an articulating single-link flexible manipulator. This is facilitated by an actuation scheme comprised of a combination of spatially discrete actuation, in the form of a DC motor to perform articulation, and spatially distributed actuation, in the form of a piezoelectric transducer for active vibration control. In the process of developing and experimentally validating the QFT based control system, shortcomings in the theoretical basis for the MIMO QFT design methodologies are addressed. Robust stability theorems are developed for the two main MIMO QFT design methodologies, namely the sequential and non-sequential MIMO QFT design methodologies. The theorems complement and extend the existing theoretical basis for the MIMO QFT design methodologies. The dissertation results expose salient features of the MIMO QFT design methodologies and provide connections to other multivariable design methodologies.

Controladores PID são largamente utilizados no controle de processos industriais, tanto em sistemas monovariáveis como em sistemas multivariáveis. No entanto, muitos dos controladores encontrados na indústria são mal sintonizados. Um dos métodos mais simples de sintonia de controladores PID consiste em identificar algumas grandezas, as quais se relacionam com características do processo a controlar, e em seguida aplicar fórmulas para os parâmetros dos controladores baseadas nestas grandezas. Estas grandezas são o ganho e o período críticos do processo, os quais se relacionam diretamente com o limite de estabilidade do sistema. Uma característica bastante interessante deste método é que o mesmo pode facilmente ser implementado por um controle auto-ajustável. Por este fato, métodos de auto-ajuste destes controladores têm sido bastante utilizados em sistemas monovariáveis, através do uso do método do relé como procedimento de obtenção das grandezas críticas, necessárias à sintonia dos controladores. O método do relé consiste em aplicar um controle bang-bang em malha fechada com o processo do qual se quer identificar as grandezas críticas. Este procedimento, dentro de certas condições, provoca uma oscilação sustentada na saída do processo, da qual as grandezas críticas são obtidas. Tendo como objetivo o auto-ajuste de controladores PID em sistemas multivariáveis, o método do relé também pode ser utilizado para obtenção das grandezas críticas, devidamente adequado de maneira a obter as grandezas críticas multivariáveis do processo. Diferentes procedimentos de ensaios com relés podem ser aplicados em sistemas multivariáveis, porém somente um destes procedimentos é capaz de identificar as grandezas críticas multivariáveis do processo diretamente: o ensaio descentralizado com relés. Mesmo assim, a sintonia proposta na literatura é baseada nas fórmulas monovariáveis de Ziegler-Nichols e afins, mostrando-se, muitas vezes, inadequada. Desta forma, este trabalho tem o objetivo de apresentar um método de ajuste multivariável para controladores PID descentralizados, baseado nas grandezas críticas do processo. Este método estende o método do ponto crítico para sistemas monovariáveis aos sistemas multivariáveis, através da análise multivariável do problema. A análise do método do ponto crítico para sistemas monovariáveis mostra que um controlador PI ou PID sintonizado pelas fórmulas baseadas nas grandezas críticas do processo sempre irá deslocar o ponto crítico do processo para um outro ponto no plano complexo, determinado pelas fórmulas utilizadas. Da mesma forma, o método de sintonia proposto neste trabalho desloca o ponto crítico do processo para outro ponto no plano complexo, escolhido a priori, alterando a freqüência crítica do sistema. / PID controllers are widely used in process control, in singlevariable systems as well as in multivariable ones. Yet, many of the controllers found in industry are poorly tuned. One of the simplest tuning method of PID controllers consists in identifying some values which are related to the process characteristics, and simply apply some formulae based on these quantities to determine the parameters of the controllers. Theses quantities are the ultimate gain and the ultimate period of the process, which are directly related to the system stability limit. A very interesting characteristic of this method is that it is easily implemented by an auto-tuning control. Thus, auto-tuning methods of this kind of controllers have been largely used in singlevariable systems, using the relay feedback experiment in order to obtain the ultimate quantities, which are needed to tune the controllers. The relay feedback experiment consists in applying a bang-bang control to the process from which the ultimate quantities are to be identified. This procedure, under some conditions, provides a sustained oscillation in the process’ output, from which the ultimate quantities are obtained. Aiming at auto-tuning of PID controllers in multivariable systems, the relay feedback experiment can also be used in order to get the ultimate quantities. Different relay feedback procedures can be applied to multivariable processes, but only one of these can identify the real multivariable ultimate quantities, formally considering the multivariable nature of the process: the decentralized relay feedback (DRF). However, the tuning of the controllers proposed in the literature is based on Ziegler-Nichols like formulae, what seems to be, many times, inappropriate. This work presents a multivariable tuning method of decentralized PID controllers, based on the process’ ultimate quantities. This method extends the ultimate point method used in SISO systems to multivariable ones, through multivariable analysis of the problem. The analysis of the ultimate point method used in singlevariable systems shows that a PI or PID controller tuned through formulae based on the process’ ultimate quantities will always dislocate the ultimate point to another point in the complex plane, determined by the used formulae. The tuning method proposed in this work dislocates the process’ ultimate point of a multivariable process to another point in the complex plane, chosen a priori, modifying the system’s ultimate frequency.

Geographic research on the Corn Belt and other regional landscapes of the central U.S. has not to date identified quantitatively the climatic, edaphic, topographic, and economic characteristics that determine rural land cover, and that therefore govern land cover change. Using the USDA/NASS Cropland Data Layer, this study identifies these characteristics using Multivariable Fractional Polynomials within a logistic regression framework. It maps the suitability distribution for corn, soybeans, spring and winter wheat, cotton, grassland, and forest land covers that dominate the central U.S., at a 56m resolution across 16 central U.S. states. The non-linear logistic regression models are successful in identifying determinants of land cover with relative operating characteristic (ROC) scores that range from 0.769 for soybeans to 0.888 for forest, with a combined corn/soybean model achieving an ROC of 0.871. For corn and soybean models, when prior land cover of a pixel is added, predictability and ROC scores increase substantially (0.07-0.10), indicating a strong temporal feedback in land cover dynamics. This process also aids in the delineation of fields from pixels. Adding neighboring land covers, however, improves predictability and ROC scores only slightly (0.014-0.019), indicating a weak spatial feedback mechanism. By including annual crop prices within the logit models, economically marginal cropland that comes into crop production only when prices are high is identified in a spatially-explicit manner. This capacity improves further analyses of economic and environmental impacts of policies that affect crop prices. The sustainability of current rural land use trends in the central U.S. is highly dependent on the ability to adapt to changing climatic conditions of the 21st century. As the climate begins to shift towards longer growing seasons, more erratic rainfall patterns, and overall warmer temperatures, there is potential for major impacts on seven major land covers of the central U.S. Suitability landscapes of individual land covers (corn, soybeans, spring and winter wheat, cotton, grasslands, and forests) were utilized to determine the influence of climate change on these landscapes. Twenty-seven climate change projection scenarios based on three global climate models, three representative concentration pathways, and three time periods were applied to the land cover suitability maps utilizing raster regression. The area now identified as the Corn Belt is projected to see a dramatic shift in the suitable climate with a potential for a 30 percent increase in summer growing degree days. While the area where conditions are suitable for corn, soybeans and spring wheat are all expected to decrease, winter wheat has the potential to increase in suitable area. In order to maintain current geographic patterns of crop production, corn would need to be adapted to higher temperatures.

A utilização de controladores preditivos multivariáveis na indústria de processos cresceu significativamente nos últimos anos principalmente devido à versatilidade e a confiabilidade que essa ferramenta proporciona em termos de controle avançado. No entanto, aspectos relacionados à aplicação prática do que vem sendo desenvolvido no meio acadêmico possui pouca difusão na indústria devido às configurações clássicas adotadas, como sistemas quadrados (com o mesmo número de variáveis controladas e manipuladas), modelos lineares, utilização de setpoint e etc. diferindo daquilo que está disponível e é amplamente utilizado industrialmente: sistemas não-quadrados (geralmente com mais variáveis controladas do que manipuladas), modelos não-lineares e utilização de soft-constraints. Esse trabalho propõe uma metodologia para ajuste dos parâmetros presentes em um controlador preditivo, atento à variedade de algoritmos presentes na indústria de processos. Essa metodologia se baseia na obtenção do melhor desempenho alcançável para cada cenário de um modelo global do processo, atendendo as restrições de Número de Desempenho Robusto relativo (rRPN), Máxima Sensibilidade e restrições nas ações de controle. Baseado em um desempenho que é alcançável, o modelo linear global é escalonado (assim como a planta não-linear) e os pesos que levam o sistema para a melhor condição operacional são estimados. Essa técnica abrange controladores operando em faixas e/ou setpoint e configurações não-quadradas, i.e., com mais variáveis controladas do que manipuladas. A abordagem proposta foi testada em uma planta de quatro tanques esféricos com aquecimento apresentando resultados coerentes, corroborando seu potencial de aplicação industrial. / Due to their versatility and reliability, Model Predictive Controllers (MPCs) are the standard solution for advanced process control in the process industry. However, there is a gap between the academic developments and the actual industrial applications, since the most academic studies focus on systems working with set-points and same number of manipulated and controlled variables, whereas the industrial application cope with non-squared configuration usually with several controlled variables in ranging and a reduced number of manipulated variables. This work proposes a tuning methodology for the countable parameters presents in a typical industrial predictive controller, considering the variety of the algorithms presents commercially in the process industry. This methodology is based on the estimation of the best attainable performance for each scenario of the global model of the process, constrained by the relative Robust Performance Number (rRPN), Maximal Sensitivity and restrictions in the control actions. Based on a performance that is attainable, the linear global model is scaled (and the non-linear) and the weights that lead the system to the best operational condition are estimated. This technique covers controllers operating in zones of control and/or set-point tracking and non-square configurations, i.e., with more controlled variables than manipulated. The proposed approach was tested in a Quadruple-Spherical tanks heating system presenting coherent results indicating its potential for industrial applications.

A escolha do modelo de referência é a principal tarefa a ser executada pelo projetista em um projeto de controle por modelo de referência. Uma má escolha do modelo de referência pode resultar em um desempenho de malha fechada que tem pouca semelhança com o especificado e a malha fechada pode até ser instável. Neste trabalho, esse problema será discutido no controle de plantas multivariáveis. O resultado experimental em uma planta de controle de nível de três tanques mostra uma aparentemente correta, ainda que ingênua, escolha do modelo de referência levando a um desempenho muito pobre em malha fechada. O problema é, então, analisado, expondo a ingenuidade do exemplo. Começa-se por reconhecer as restrições fundamentais impostas pelo sistema e, em seguida, deriva-se diretrizes gerais que respeitam essas restrições, para uma escolha eficaz do modelo de referência em sistemas multivariáveis. Também é proporcionada uma nova formulação para calcular o grau relativo mínimo de cada elemento do modelo de referência sem a necessidade de um modelo completo da planta. A aplicação destas orientações em simulações e na planta de três tanques ilustra sua eficácia. / The choice of the reference model is the main task to be performed by the designer in a model reference control design. A poor choice of the reference model may result in a closed-loop performance that bears no resemblance to the specifications and the closedloop may even be unstable. In this work we discuss this issue in the control of multivariable plants. Experimental results in a three tank level control plant show a seemingly correct, yet naive, choice of reference model leading to very poor closed-loop performance. The problem is then analyzed, exposing the naivete of the design example. We start by recognizing the fundamental constraints imposed by the system and then deriving general guidelines respecting these contraints for the effective choice of the reference model in multivariable systems. We also provide a novel formulation to compute the minimal relative degree of each element of the reference model without needing a complete model of the plant. The application of these guidelines to simulations and the three tank plant illustrates their effectiveness.

O escopo desta dissertação é o desenvolvimento de um método para detectar os modelos da matriz dinâmica que estejam degradando o desempenho de controladores preditivos baseados em modelos. O método proposto se baseia na análise de correlação cruzada entre o erro nominal do controlador em malha fechada e a uma estimativa da contribuição de cada canal para o cálculo da saída, filtrada pela função de sensibilidade do controlador. Esse método pode ser empregado na auditoria de controladores com variáveis controladas em setpoints e/ou com variáveis que operem entre faixas, como é usual de se encontrar na indústria. Esta dissertação apresenta os resultados da aplicação bem sucedida do método no sistema de quatro tanques (JOHANSSON, 2000), para o qual três cenários foram avaliados. No primeiro cenário, o método localizou corretamente discrepâncias de ganho e de dinâmica de modelos de um controlador preditivo baseado em modelos (Model-based Predictive Controller, ou controlador MPC). No segundo, o método foi utilizado para avaliar a influência de uma variável externa para melhorar o desempenho de um controlador afetado por distúrbios não medidos. No terceiro cenário, o método localizou canais com modelos nulos que deveriam ser incluídos na matriz de controle de um controlador MPC de estrutura descentralizada. Os resultados deste estudo de caso foram comparados com aqueles obtidos pelo método proposto por BADWE, GUDI e PATWARDHAN (2009), constatando-se que o método proposto é mais robusto que o método usado na comparação, não demandando ajustes de parâmetros por parte do usuário para fornecer bons resultados. A dissertação inclui também um estudo de caso da aplicação industrial do método na auditoria de desempenho de um controlador preditivo linear de estrutura descentralizada, com doze variáveis controladas, oito manipuladas e quatro distúrbios não medidos, aplicado a um sistema de fracionamento de propeno e propano em uma indústria petroquímica. A auditoria permitiu reduzir o escopo de revisão do controlador a dezenove canais da matriz, sendo que quatorze destes correspondiam a canais com modelos nulos que deveriam ser incluídos na matriz. A eficácia do método foi comprovada repetindo-se a avaliação da qualidade de modelo para todas as variáveis controladas. / The scope of this dissertation is the development of a method to detect the models of the dynamic matrix that are affecting the performance of model-based predictive controllers. The proposed method is based on the cross correlation analysis between the nominal controller error and an estimate of the contribution of each channel to the controller output, filtered by the controller nominal sensitivity function. The method can be used in the performance assessment of controllers employing variables controlled at the setpoint and/or those controlled within ranges. This dissertation presents the results of the successful application of the method to the quadruple-tank process (JOHANSSON, 2000), for which three scenarios were evaluated. In the first scenario, the method correctly located gain and dynamic mismatches on a model-based predictive controller (MPC controller). In the second one, the method was used to evaluate the influence of an external variable to improve the performance of a controller affected by unmeasured disturbances. In the third scenario, the method located null models that should be included in the dynamic matrix of a decentralized MPC controller. The results of the three scenarios were compared with the ones obtained through the method proposed by BADWE, GUDI e PATWARDHAN (2009). The proposed method was considered more robust than the reference one for not requiring parameters estimation performed by the user to provide good results. This dissertation also includes a case study about the application of the method on the performance assessment of an industrial linear predictive controller of decentralized structure. The controller has twelve controlled variables, eight manipulated variables, and four unmeasured disturbances and is applied to a propylene-propane fractionation system of a petrochemical industry. The performance assessment allowed reducing the scope of the controller revision to nineteen channels of the models matrix, fourteen of which were null models that should be included in the controller. The efficacy of the proposed method was confirmed by repeating the model quality evaluation for all the controlled variables.

Controladores PID são largamente utilizados no controle de processos industriais, tanto em sistemas monovariáveis como em sistemas multivariáveis. No entanto, muitos dos controladores encontrados na indústria são mal sintonizados. Um dos métodos mais simples de sintonia de controladores PID consiste em identificar algumas grandezas, as quais se relacionam com características do processo a controlar, e em seguida aplicar fórmulas para os parâmetros dos controladores baseadas nestas grandezas. Estas grandezas são o ganho e o período críticos do processo, os quais se relacionam diretamente com o limite de estabilidade do sistema. Uma característica bastante interessante deste método é que o mesmo pode facilmente ser implementado por um controle auto-ajustável. Por este fato, métodos de auto-ajuste destes controladores têm sido bastante utilizados em sistemas monovariáveis, através do uso do método do relé como procedimento de obtenção das grandezas críticas, necessárias à sintonia dos controladores. O método do relé consiste em aplicar um controle bang-bang em malha fechada com o processo do qual se quer identificar as grandezas críticas. Este procedimento, dentro de certas condições, provoca uma oscilação sustentada na saída do processo, da qual as grandezas críticas são obtidas. Tendo como objetivo o auto-ajuste de controladores PID em sistemas multivariáveis, o método do relé também pode ser utilizado para obtenção das grandezas críticas, devidamente adequado de maneira a obter as grandezas críticas multivariáveis do processo. Diferentes procedimentos de ensaios com relés podem ser aplicados em sistemas multivariáveis, porém somente um destes procedimentos é capaz de identificar as grandezas críticas multivariáveis do processo diretamente: o ensaio descentralizado com relés. Mesmo assim, a sintonia proposta na literatura é baseada nas fórmulas monovariáveis de Ziegler-Nichols e afins, mostrando-se, muitas vezes, inadequada. Desta forma, este trabalho tem o objetivo de apresentar um método de ajuste multivariável para controladores PID descentralizados, baseado nas grandezas críticas do processo. Este método estende o método do ponto crítico para sistemas monovariáveis aos sistemas multivariáveis, através da análise multivariável do problema. A análise do método do ponto crítico para sistemas monovariáveis mostra que um controlador PI ou PID sintonizado pelas fórmulas baseadas nas grandezas críticas do processo sempre irá deslocar o ponto crítico do processo para um outro ponto no plano complexo, determinado pelas fórmulas utilizadas. Da mesma forma, o método de sintonia proposto neste trabalho desloca o ponto crítico do processo para outro ponto no plano complexo, escolhido a priori, alterando a freqüência crítica do sistema. / PID controllers are widely used in process control, in singlevariable systems as well as in multivariable ones. Yet, many of the controllers found in industry are poorly tuned. One of the simplest tuning method of PID controllers consists in identifying some values which are related to the process characteristics, and simply apply some formulae based on these quantities to determine the parameters of the controllers. Theses quantities are the ultimate gain and the ultimate period of the process, which are directly related to the system stability limit. A very interesting characteristic of this method is that it is easily implemented by an auto-tuning control. Thus, auto-tuning methods of this kind of controllers have been largely used in singlevariable systems, using the relay feedback experiment in order to obtain the ultimate quantities, which are needed to tune the controllers. The relay feedback experiment consists in applying a bang-bang control to the process from which the ultimate quantities are to be identified. This procedure, under some conditions, provides a sustained oscillation in the process’ output, from which the ultimate quantities are obtained. Aiming at auto-tuning of PID controllers in multivariable systems, the relay feedback experiment can also be used in order to get the ultimate quantities. Different relay feedback procedures can be applied to multivariable processes, but only one of these can identify the real multivariable ultimate quantities, formally considering the multivariable nature of the process: the decentralized relay feedback (DRF). However, the tuning of the controllers proposed in the literature is based on Ziegler-Nichols like formulae, what seems to be, many times, inappropriate. This work presents a multivariable tuning method of decentralized PID controllers, based on the process’ ultimate quantities. This method extends the ultimate point method used in SISO systems to multivariable ones, through multivariable analysis of the problem. The analysis of the ultimate point method used in singlevariable systems shows that a PI or PID controller tuned through formulae based on the process’ ultimate quantities will always dislocate the ultimate point to another point in the complex plane, determined by the used formulae. The tuning method proposed in this work dislocates the process’ ultimate point of a multivariable process to another point in the complex plane, chosen a priori, modifying the system’s ultimate frequency.