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Fernando de Oliveira Souzahttp://lattes.cnpq.br/8069784077217071José Mário AraújoLeonardo Amaral MozelliVictor Costa da Silva CamposCarlos Eduardo Trabuco DóreaTito Luís Maia Santoshttps://lattes.cnpq.br/6166541317897749Danielle Silva Gontijo2023-11-08T19:09:46Z2023-11-08T19:09:46Z2023-08-25http://hdl.handle.net/1843/60647Second-order systems constitute an important class of dynamic systems that are widely em- ployed in engineering to model a variety of physical phenomena. Characterized by their dy- namic behavior, second-order systems require effective control strategies to achieve the de- sired performance. This work presents a design framework for obtaining a robust multivariable Proportional-Integral-Derivative (PID) controller for linear second-order systems. Additionally, a Proportional-Integral-Derivative with Acceleration (PIDA) controller is proposed to address the model regularization problem. Relevant control challenges, such as modeling errors, regu- latory performance optimization, regional pole placement, saturation prevention, input delay, LQR cost function, and observer-based control, are addressed within the framework of control design via Linear Matrix Inequality (LMI). The proposed design strategy is based on rewriting the system model in an appropriate way so that the design of the PID/PIDA controller is equiv- alent to that of a state feedback controller. Firstly, a methodology is proposed for obtaining a PID/PIDA controller, grounded in regional pole placement, H∞ performance, regularization problem, and saturation prevention, all simultaneously addressed. Additionally, a methodology to obtain a robust multivariable Proportional-Integral-Derivative (PID) controller for second- order systems with time-varying input delay is also proposed. Furthermore, a methodologyintroduced to obtain a PD/PID controller using the Linear Quadratic Regulator (LQR) control strategy. Finally, a formulation for observer-based controller design is proposed. This is followed by a methodology based on LMI formulations to obtain an observer-based controller for uncer- tain second-order systems. To demonstrate the efficacy of the proposed control methodologies, simulations with numerical examples and a practical experiment using an inverted pendulum mobile system were conducted. These experiments effectively showcase the advantages of each method.Sistemas de segunda ordem são uma classe importante de sistemas dinâmicos amplamente utilizados na engenharia para modelar uma variedade de fenômenos físicos. Caracterizados por seu comportamento dinâmico, os sistemas de segunda ordem requerem estratégias de controle eficazes para atingir o desempenho desejado. Este trabalho apresenta uma estrutura de projeto para obter um controlador robusto multivariável Proporcional-Integral-Derivativo (PID) para sistemas lineares de segunda ordem, e um controlador Proporcional-Integral-Derivativo mais Aceleração (PIDA), para lidar com o problema de regularização do modelo. Desafios de controle relevantes, como erro de modelagem, otimização de desempenho regulatório, alocação regional de polos, prevenção de saturação, atraso de entrada, função de custo LQR e controle baseado no observador, são tratados dentro da abordagem de projeto via desigualdade matricial linear (LMI). A estratégia de projeto proposta baseia-se em rescrever o modelo do sistema de uma maneira apropriada de forma que o projeto do controlador PID/PIDA seja equivalente a de um controlador por realimentação de estados. Primeiramente, uma metodologia é pro- posta para a obtenção de um controlador PID/PIDA, fundamentada na alocação regional de polos, desempenho H∞ , problema de regularização e prevenção de saturação, tratados simultaneamente. Uma metodologia para obter um controlador multivariável Proporcional-Integral- Derivativo (PID) robusto para sistemas de segunda ordem com atraso de entrada variante no tempo também é proposta. Ademais, é apresentada uma metodologia para obter um controlador PD/PID por meio da estratégia de controle do Regulador Quadrático Linear (LQR).Por fim, uma formulação para o projeto de controladores baseado em observador também é proposta, e em seguida uma metodologia baseada em formulações LMI para obter um controlador baseado em observador para sistemas de segunda ordem incertos. Para ilustrar a eficácia das metodologias de controle propostas são realizadas simulações, com exemplos numéricos, e um experimento prático, utilizando um pêndulo invertido móvel, destacando os benefícios de cada método.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia ElétricaUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICAEngenharia elétricaControle robustoDesigualdades matriciais linearesControladores PIDSecond-order systemsRobust controlLinear matrix inequalitiesUncertain systemsControl techniques for uncertain second order systems : an LMI approachinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGLICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/60647/4/license.txtcda590c95a0b51b4d15f60c9642ca272MD54ORIGINALControl techniques for uncertain second order systems an LMI approach_Danielle Silva Gontijo.pdfControl techniques for uncertain second order systems an LMI approach_Danielle Silva Gontijo.pdfapplication/pdf1940963https://repositorio.ufmg.br/bitstream/1843/60647/3/Control%20techniques%20for%20uncertain%20second%20order%20systems%20an%20LMI%20approach_Danielle%20Silva%20Gontijo.pdf953da4bee6095ce10d6dd9fdbed2b0c6MD531843/606472023-11-08 16:09:47.833oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-11-08T19:09:47Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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