In this thesis a class of robust non-linear controllers for a gantry crane system are discussed. The gantry crane has three degrees of freedom, all of which are interrelated. These are the horizontal traverse of the cart, the vertical motion of the goods (i.e. rope length) and the swing angle made by the goods during the movement of the cart. The objective is to control all three degrees of freedom. This means achieving setpoint control for the cart and the rope length and cancellation of the swing oscillations. A mathematical model of the gantry crane system is developed using Lagrangian dynamics. In this thesis it is shown that a model of the gantry crane system can be represented as two sub models which are coupled by a term which includes the rope length as a parameter. The first system will consist of the cart and swing dynamics and the other system is the hoist dynamics. The mathematical model of these two systems will be derived independent of the other system. The model that is comprised of the two sub models is verified as an accurate model of a gantry crane system and it will be used to simulate the performance of the controllers using Matlab. For completeness a fully coupled mathematical model of the gantry crane system is also developed. A detailed design of a gain scheduled sliding mode controller is presented. This will guarantee the controller's robustness in the presence of uncertainties and bounded matched disturbances. This controller is developed to achieve cart setpoint and swing control while achieving rope length setpoint control. A non gain scheduled sliding mode controller is also developed to determine if the more complex gain scheduled sliding mode controller gives any significant improvement in performance. In the implementation of both sliding mode controllers, all system states must be available. In the real-time gantry crane system used in this thesis, the cart velocity and the swing angle velocity are not directly available from the system. They will be estimated using an alpha-beta state estimator. To overcome this limitation and provide a more practical solution an optimal output feedback model following controller is designed. It is demonstrated that by expressing the system and the model for which the system is to follow in a non-minimal state space representation, LQR techniques can be used to design the controller. This produces a dynamic controller that has a proper transfer function, and negates the need for the availability of all system states. This thesis presents an alternative method of solving the LQR problem by using a generic eigenvalue solution to solve the Riccati equation and thus determine the optimal feedback gains. In this thesis it is shown that by using a combination of sliding mode and H??? control techniques, a non-linear controller is achieved which is robust in the presence of a wide variety of uncertainties and disturbances. A supervisory controller is also described in this thesis. The supervisory control is made up of a feedforward and a feedback component. It is shown that the feedforward component is the crane operator's action, and the feedback component is a sliding mode controller which compensates as the system's output deviates from the desired trajectory because of the operator's inappropriate actions or external disturbances such as wind gusts and noise. All controllers are simulated using Matlab and implemented in real-time on a scale model of the gantry crane system using the program RTShell. The real-time results are compared against simulated results to determine the controller's performance in a real-time environment.

More stringent requirements on nitrogen removal from wastewater are the motivation for this thesis. In order to improve treatment results and enhance cost-efficient operation of wastewater treatment plants, model based control strategies are presented. A Java based simulator for activated sludge processes (JASS) is presented. The graphical user interface, educational experiences and implemented control strategies are discussed. Controlling the addition of an external carbon source is the next topic discussed. A simple model based feedforward controller is derived and evaluated in a simulation study. The controller attenuates process disturbances quickly. Further, two feedforward controllers for adjusting the aeration volume in activated sludge processes are derived. The aim of the volume control strategies was to efficiently dampen the impact of process disturbances without using an excessively high dissolved oxygen concentration. The simulation results are promising and show that the aeration volume may be a feasible control variable. A linearisation method for static input non-linearities is presented. The method gives essentially the same result as the existing standard method, but possesses some implementational advantages. The method is used to linearise the non-linear oxygen transfer function of an activated sludge process in an application study. Multivariable interactions in a process model describing nitrate removal in an activated sludge process are studied using the well known RGA method as well as a relatively novel tool based on Hankel norms. The results of the analysis are compared to conclusions drawn from common process knowledge and are used to design a multivariable control strategy. It was found that process disturbances may be rejected faster using multivariable control. Finally, the operational costs of the denitrification process are investigated and visualised graphically. Cost optimal regions are found by a numerical grid search. Procedures for controlling the denitrification process in a cost-efficient way are described.

In this master’s thesis, a turbine model and a common control structure for theturbocharger for SI and CI-engines is developed. To design the control structure,simulations are done on an existing diesel engine model with VGT. In order tobe able to make simulations for engines with a wastegated turbine, the model isextended to include mass flow and turbine efficiency for that configuration. Thedeveloped model has a mean absolute relative error of 3.6 % for the turbine massflow and 7.4 % for the turbine efficiency. The aim was to control the intake manifoldpressure with good transients and to use the same control structure for VGTand wastegate. By using a common structure, development and calibration timecan be reduced. The non-linearities have been reduced by using an inverted turbinemodel in the control structure, which consists of a PI-controller with feedforward.The controller can be tuned to give a fast response for CI engines and a slowerresponse but with less overshoot for SI engines, which is preferable.

Fuzzy set is a generalization of the classical set. A classical set is distinguished from another by a sharp boundary at some threshold value and therefore, they are also known as crisp set. In fuzzy theory, sharp boundary and crisp set are replaced by partial truth and fuzzy sets. The idea of partial truth facilitates information description especially those communicated through natural language whose transition between descriptive terms are not abrupt discontinuities. Instead, the transition is a smooth change over a range corresponding to the degree of fulfillment each intermediate elements has according to the operating definition of the concept. The shape of a fuzzy set is defined by its membership function. This, by far, has been the common extent of concern regarding the membership function. Different applications may use the membership function to describe different variables such as speed, position, temperature, dirtiness, traffic conditions etc. But the underlying application of fuzzy sets remains the same: to describe information whose membership function, created in an initial setting, preserve the same size and shape throughout its entire application. In other word, fuzzy sets are utilized as if they are static entities. Nothing has been said about how an initially defined membership function can develop over time with respect to a system. The current research proposes a new framework that concerns the evolution of membership functions. We introduce the concept of membership function propagation as a dynamic description of uncertainty. Given a dynamical system with a set of uncertain initial states which can be represented by membership functions, the membership function propagation describes how these membership functions evolve over time with respect to the system. The evolution produces a set of propagated membership functions that have different size and shape from their predecessors. They represent the uncertainty associated with the states of the system at a given time. This new description also confers new definitions for two important concepts in control theory, namely controllability and observability. These two concepts are re-introduced in a fuzzy sense, based on the concept of membership function propagation. By assuming convexity of the fuzzy set, criterions for controllability and observability can be derived. These criterions are illustrated by MATLAB and SIMULINK simulations of an inverted pendulum and a 2 degree of freedom mechanical manipulator.

A typical wastewater effluent of a chemical process can contain several strong acids/bases, weak acids/bases as well as their salts. They must be neutralized before being discharged to the environment in order to protect aquatic life and human welfare. However, neutralization process is highly non&ndash / linear and has time&ndash / varying characteristics. Therefore, the control of pH is a challenging problem where advanced control strategies are often considered. In this study, the aim is to design a pH control system that will be capable of controlling the pH-value of a plant waste-water effluent stream having unknown acids with unknown concentrations using an on&ndash / line identification procedure. A Model Predictive Controller, MPC, and a Fuzzy Logic Controller, FLC, are designed and used in a laboratory scale pH neutralization system. The characteristic of the upstream flow is obtained by a small identification reactor which has ten times faster dynamics and which is working parallel to actual neutralization tank. In the control strategy, steady&ndash / state titration curve of the process stream is obtained using the data collected in terms of pH value from the response of the identification reactor to a pulse input in base flow rate and using the simulated response of the identification reactor for the same input. After obtaining the steady&ndash / state titration curve, it is used in the design of a Proportional&ndash / Integral, PI, and of an Adaptive Model Predictive Controller, AMPC. On the other hand, identification reactor is not used in the FLC scheme. The performances of the designed controllers are tested mainly for disturbance rejection, set&ndash / point tracking and robustness issues theoretically and experimentally. The superiority of the FLC is verified.

In this thesis a class of robust non-linear controllers for a gantry crane system are discussed. The gantry crane has three degrees of freedom, all of which are interrelated. These are the horizontal traverse of the cart, the vertical motion of the goods (i.e. rope length) and the swing angle made by the goods during the movement of the cart. The objective is to control all three degrees of freedom. This means achieving setpoint control for the cart and the rope length and cancellation of the swing oscillations. A mathematical model of the gantry crane system is developed using Lagrangian dynamics. In this thesis it is shown that a model of the gantry crane system can be represented as two sub models which are coupled by a term which includes the rope length as a parameter. The first system will consist of the cart and swing dynamics and the other system is the hoist dynamics. The mathematical model of these two systems will be derived independent of the other system. The model that is comprised of the two sub models is verified as an accurate model of a gantry crane system and it will be used to simulate the performance of the controllers using Matlab. For completeness a fully coupled mathematical model of the gantry crane system is also developed. A detailed design of a gain scheduled sliding mode controller is presented. This will guarantee the controller's robustness in the presence of uncertainties and bounded matched disturbances. This controller is developed to achieve cart setpoint and swing control while achieving rope length setpoint control. A non gain scheduled sliding mode controller is also developed to determine if the more complex gain scheduled sliding mode controller gives any significant improvement in performance. In the implementation of both sliding mode controllers, all system states must be available. In the real-time gantry crane system used in this thesis, the cart velocity and the swing angle velocity are not directly available from the system. They will be estimated using an alpha-beta state estimator. To overcome this limitation and provide a more practical solution an optimal output feedback model following controller is designed. It is demonstrated that by expressing the system and the model for which the system is to follow in a non-minimal state space representation, LQR techniques can be used to design the controller. This produces a dynamic controller that has a proper transfer function, and negates the need for the availability of all system states. This thesis presents an alternative method of solving the LQR problem by using a generic eigenvalue solution to solve the Riccati equation and thus determine the optimal feedback gains. In this thesis it is shown that by using a combination of sliding mode and H??? control techniques, a non-linear controller is achieved which is robust in the presence of a wide variety of uncertainties and disturbances. A supervisory controller is also described in this thesis. The supervisory control is made up of a feedforward and a feedback component. It is shown that the feedforward component is the crane operator's action, and the feedback component is a sliding mode controller which compensates as the system's output deviates from the desired trajectory because of the operator's inappropriate actions or external disturbances such as wind gusts and noise. All controllers are simulated using Matlab and implemented in real-time on a scale model of the gantry crane system using the program RTShell. The real-time results are compared against simulated results to determine the controller's performance in a real-time environment.

Neste trabalho, aborda-se o problema de estabilização de sistemas lineares com atrasos nos estados e sujeitos a ação de atuadores saturantes. Em particular, são propostos métodos para a síntese de leis de controle estabilizantes do tipo realimentação de estados, realimentação dinâmica de saída, bem como para a síntese de compensadores de "anti-windup" estáticos e dinâmicos. Como objetivo de síntese consideram-se duas possibilidades, que o sistema esteja livre ou não de perturbações. No primeiro caso, determina-se uma lei de controle estabilizante de tal forma a maximizar um conjunto de condições iniciais admissíveis D. No caso do conjunto D ser dado, a lei de controle estabilizante que se determina, deve garantir estabilidade assintótica do sistema em malha-fechada para toda condição inicial pertencente a D. No segundo caso, considerando-se os problemas de atenuação e tolerância à perturbação, as leis de controle são obtidas com o intuito de minimizar o ganho-L2 entre a perturbação e a saída regulada do sistema ou de maximizar o limite superior da norma L2 das perturbações admissíveis, para as quais garante-se que as trajetórias do sistema em malha-fechada permaneçam limitadas. Condições locais e globais de estabilização são obtidas a partir da teoria de Lyapunov e da modelagem por zona-morta da saturação, com a conseqüente aplicação de uma condição de setor generalizada. Em se tratando de sistemas contínuos, para que as condições obtidas sejam dependentes do atraso, combinam-se estas ferramentas com a representação do sistema através de sistema descritor. Já no caso de sistemas discretos, combinam-se estas duas ferramentas com a utilização do Lema de Finsler. A utilização destas ferramentas possibilita que as condições obtidas sejam na forma de desigualdades matriciais lineares (LMI's) ou quase lineares, permitindo assim, a formulação de problemas de otimização convexos. / In this work, we deal with the problem of stabilization of linear systems with delayed state and saturating inputs. Specifically, methods are proposed for the synthesis of stabilizing control laws of state feedback and dynamic output feedback types, as well as for the synthesis of static and dynamic anti-windup compensators. Regarding synthesis objectives two possibilities were considered, that the system is free or not of disturbances. In the first case, the stabilizing control law is computed considering the maximization of the set of admissible initial conditions D. In the case the set D is given, this stabilizing control law should guarantee asymptotic stability of the closed-loop system. In the second case, considering the problems of tolerance and disturbance attenuation, the control laws are proposed in order to minimize the L2 gain between to disturbance and the regulated output of system, or in order to maximize the bound on the admissible disturbances for which the trajectories are bounded. Local and global conditions for stabilization are obtained from the theory of Lyapunov and the modeling of the saturation by means of deadzone nonlinearities and the consequent application of a modified sector condition. For continuous systems, in order to obtain delay dependent conditions, these tools are combined with descriptor approach. In the case of discrete-time systems, these two tools are combined with the utilization of Finsler's Lemma. The use of these leads to the conditions in the form of Linear Matrix Inequalities (LMI's) or almost linear, allowing the formulation of convex optimization problems.

Neste trabalho, aborda-se o problema de estabilização de sistemas lineares com atrasos nos estados e sujeitos a ação de atuadores saturantes. Em particular, são propostos métodos para a síntese de leis de controle estabilizantes do tipo realimentação de estados, realimentação dinâmica de saída, bem como para a síntese de compensadores de "anti-windup" estáticos e dinâmicos. Como objetivo de síntese consideram-se duas possibilidades, que o sistema esteja livre ou não de perturbações. No primeiro caso, determina-se uma lei de controle estabilizante de tal forma a maximizar um conjunto de condições iniciais admissíveis D. No caso do conjunto D ser dado, a lei de controle estabilizante que se determina, deve garantir estabilidade assintótica do sistema em malha-fechada para toda condição inicial pertencente a D. No segundo caso, considerando-se os problemas de atenuação e tolerância à perturbação, as leis de controle são obtidas com o intuito de minimizar o ganho-L2 entre a perturbação e a saída regulada do sistema ou de maximizar o limite superior da norma L2 das perturbações admissíveis, para as quais garante-se que as trajetórias do sistema em malha-fechada permaneçam limitadas. Condições locais e globais de estabilização são obtidas a partir da teoria de Lyapunov e da modelagem por zona-morta da saturação, com a conseqüente aplicação de uma condição de setor generalizada. Em se tratando de sistemas contínuos, para que as condições obtidas sejam dependentes do atraso, combinam-se estas ferramentas com a representação do sistema através de sistema descritor. Já no caso de sistemas discretos, combinam-se estas duas ferramentas com a utilização do Lema de Finsler. A utilização destas ferramentas possibilita que as condições obtidas sejam na forma de desigualdades matriciais lineares (LMI's) ou quase lineares, permitindo assim, a formulação de problemas de otimização convexos. / In this work, we deal with the problem of stabilization of linear systems with delayed state and saturating inputs. Specifically, methods are proposed for the synthesis of stabilizing control laws of state feedback and dynamic output feedback types, as well as for the synthesis of static and dynamic anti-windup compensators. Regarding synthesis objectives two possibilities were considered, that the system is free or not of disturbances. In the first case, the stabilizing control law is computed considering the maximization of the set of admissible initial conditions D. In the case the set D is given, this stabilizing control law should guarantee asymptotic stability of the closed-loop system. In the second case, considering the problems of tolerance and disturbance attenuation, the control laws are proposed in order to minimize the L2 gain between to disturbance and the regulated output of system, or in order to maximize the bound on the admissible disturbances for which the trajectories are bounded. Local and global conditions for stabilization are obtained from the theory of Lyapunov and the modeling of the saturation by means of deadzone nonlinearities and the consequent application of a modified sector condition. For continuous systems, in order to obtain delay dependent conditions, these tools are combined with descriptor approach. In the case of discrete-time systems, these two tools are combined with the utilization of Finsler's Lemma. The use of these leads to the conditions in the form of Linear Matrix Inequalities (LMI's) or almost linear, allowing the formulation of convex optimization problems.

Orientador: Fábio Roberto Chavarette / Resumo: São diversos os equipamentos de engenharia que apresentam vibrações mecânicas, e estas podem ser observadas em forma de acelerações, deslocamentos e velocidade. Os primeiros estudos envolvendo vibrações foram direcionados aos fenômenos naturais e modelagem matemática de sistemas vibrantes, então, começou a aplicação desses estudos em equipamentos de engenharia. Vibrações mecânicas, na maioria dos sistemas dinâmicos, são consideradas como algo indesejado e podem ser danosos. Porém, existem situações que são utilizadas para melhorar o funcionamento e desempenho de máquinas. São diversas as causas de vibrações em sistemas de engenharia, neste trabalho, destaca-se as vibrações causadas por impacto. Quando componentes destes sistemas impactam entre si, causando ruídos de curta duração, são caracterizados como sistemas tipo vibro - impacto. Podem ser citados diversos equipamentos com essas características, como rolos compactadores de solo, martelos de impacto, perfuratrizes de solo, etc. Neste trabalho, demonstra-se o comportamento dinâmico de um sistema vibro – impactante. Para análise deste sistema, foram desenvolvidos códigos computacionais, através do software Octave. No diagrama de estabilidade de Lyapunov, verificou-se que, pontualmente o sistema se apresenta de forma estável. A partir da variação da frequência de excitação, foi observado através dos históricos no tempo, espectros de frequência, mapas de Poincaré e planos de fase, um comportamento periódico e estável, com sit... (Resumo completo, clicar acesso eletrônico abaixo) / Mestre

Este trabalho dedica-se ao projeto e desenvolvimento de um veículo aéreo não tripulado. Tais veículos podem ser utilizados em diversas aplicações como monitoramento, vigilância, transporte, resgate, entre outros. Dentre os diversos tipos de veículos aéreos, este trabalho irá focar no modelo do quadrirotor, composto por quatro hélices contra-rotoras que estabilizam e movimentam o veículo. Para alcançar o objetivo de controlar este tipo de veículo, várias propostas e metodologias podem ser aplicadas, todas buscando contemplar o controle de todas ou parte das variáveis de estado presentes nesta planta. Neste texto serão descritas: as equações cinemáticas e dinâmicas que regem este sistema; o projeto e composição mecânica da aeronave; definição de sensores e atuadores juntamente com seus métodos de utilização; implementação de controlador linear por alocação direta de polos e Regulador Linear Quadrático juntamente com observador de estados de ordem plena e filtro de Kalman, para recuperação de estados não mensurados e filtragem de ruídos. Serão apresentados resultados em simulações para cada método de controle selecionado visando optar pelo melhor controlador para a aplicação da aeronave. O método selecionado será implementado para controlar a aeronave com os sensores e atuadores selecionados. Esta implementação será realizada a partir da técnica HIL Hardware in The Loop juntamente com o software MATLAB/Simulink visando validar o controlador em conjunto com a planta real, bem como o modelo dinâmico construído. / This work is dedicated to the project and development of an unmanned aerial vehicle. Such vehicles can be employed in various applications such as monitoring, surveillance, transportation, rescue and others. Among the types of aerial vehicles, this work is focused on the quadrotor, composed by four counter-rotating propellers which stabilize and displace the vehicle. In order to fulfill the objective of controlling this vehicle, many methodologies and propositions can be applied, seeking the control of all or a snippet of the state variables present in the system. There will be described in this work: the cinematic and dynamic equations that govern this system; the mechanical project and construction of the aircraft; sensors and actuators definition, along with its usage methods; linear control implementation of the pole placement and Linear Quadratic Regulator techniques along full order state observer and Kalman filtering in order to recover and filter non-measured states. Performance results in simulations will be presented on each control implementation to validate the best controller for the application and this implementation will be applied on the projected aircraft using the sensors and actuators selected. This implementation will be given through the HIL - Hardware in the Loop method using MATLAB/Simulink software to validate the control technique applied and the constructed dynamic model.