Modelagem e controle de sistemas fuzzy Takagi-Sugeno
Carregando...
Data
2003-11-20
Autores
Machado, Erica Regina Marani Daruichi [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho aborda o problema de modelagem e controle de uma classe de sistemas não lineares atraves dos modelos fuzzy Takagi-Sugeno (TS). Primeiramente são apresentados dois metodos de modelagem existentes na literatura. O primeiro e um metodo de modelagem exata e o segundo, baseado em modelos locais otimos, e utilizado em todos os desenvolvimentos desta tese. A seguir e proposto um novo metodo para se obter os modelos locais, baseado em Desigualdades Matriciais Lineares (LMIs-Linear Matrix Inequalities), utilizando os modelos locais otimos com novos graus de liberdade e que permitem uma melhor aproximação local do sistema. Novas funções de pertinência, que servem para combinar os modelos locais, são obtidas a partir da solu ção de um problema de otimização (um dos metodos para obter a solução e baseado em LMIs), que tem como objetivo minimizar a norma Euclidiana do erro entre o modelo Takagi-Sugeno e a planta. Um algoritmo para determinar quantos e quais modelos locais devem ser utilizados na aproximação, considerando o m aximo erro de modelagem permitido, e desenvolvido. Este algoritmo tem como parâmetro o erro de modelagem. Um exemplo ilustrativo deste algoritmo e apresentado. Utilizando a modelagem proposta foram desenvolvidos dois novos metodos de projetos de reguladores fuzzy, baseados em LMIs, que consideram o erro de modelagem. No primeiro projeto e utilizado um conjunto de pontos na região de operação considerando somente as componentes do vetor de estado que fazem parte das não-linearidades do sistema e os erros de aproximação das funções nestes pontos. No segundo projeto e utilizada a maxima norma Euclidiana do erro obtido no ponto onde a aproximação e mais de ciente. Estes metodos permitem a construção de modelos fuzzy Takagi-Sugeno, em termos do numero de modelos locais, quando comparados com os metodos descritos na literatura. As tecnicas de projeto propostas tambem permitem a...
This work considers the problem of modeling and designing of a class of nonlinear systems represented by Takagi-Sugeno (TS) fuzzy models. Initially, two methods of modeling described in the literature are presented. The rst one, is a method of exact modeling and the second one, based on optimal local models, is utilized in all development in this thesis. A new method, based on LMIs (Linear Matrix Inequalities), to obtain better local models using new degrees of freedom is proposed. New membership functions, that combine the local models, are obtained starting from an optimization problem (one method is based on LMIs), that has as the end to minimize the Euclidian norm of the error between the Takagi-Sugeno fuzzy models and the plant model. An algorithm to nd the number of local models, their operation points and matrices, considering the maximum modeling erros allowed, is presented. This algorithm has as parameter the modeling error and it is illustrated by an example. Taking into account the proposed modeling methods, two new methods of fuzzy regulator designs based on LMIs were proposed, considering the modeling errors. In the rst design a set of points in the region of operation is used considering only the components of the state vector that compound the non-linearities of the system and the modeling error in these points. The second design method used the largest value of the Euclidian norm of the modeling error. These methods allow the construction of reduced TS fuzzy models, in terms of the number of local models, when compared with the methods described in the literature. The speci cation of the decay rate, constraints on control input and output are also described by LMIs. The design and simulations of the new control laws for an inverted pendulum illustrate the studied methods. A comparison between the new design methods and the method of exact modeling showed that the proposed methods allowed simpler controllers and, in ...
This work considers the problem of modeling and designing of a class of nonlinear systems represented by Takagi-Sugeno (TS) fuzzy models. Initially, two methods of modeling described in the literature are presented. The rst one, is a method of exact modeling and the second one, based on optimal local models, is utilized in all development in this thesis. A new method, based on LMIs (Linear Matrix Inequalities), to obtain better local models using new degrees of freedom is proposed. New membership functions, that combine the local models, are obtained starting from an optimization problem (one method is based on LMIs), that has as the end to minimize the Euclidian norm of the error between the Takagi-Sugeno fuzzy models and the plant model. An algorithm to nd the number of local models, their operation points and matrices, considering the maximum modeling erros allowed, is presented. This algorithm has as parameter the modeling error and it is illustrated by an example. Taking into account the proposed modeling methods, two new methods of fuzzy regulator designs based on LMIs were proposed, considering the modeling errors. In the rst design a set of points in the region of operation is used considering only the components of the state vector that compound the non-linearities of the system and the modeling error in these points. The second design method used the largest value of the Euclidian norm of the modeling error. These methods allow the construction of reduced TS fuzzy models, in terms of the number of local models, when compared with the methods described in the literature. The speci cation of the decay rate, constraints on control input and output are also described by LMIs. The design and simulations of the new control laws for an inverted pendulum illustrate the studied methods. A comparison between the new design methods and the method of exact modeling showed that the proposed methods allowed simpler controllers and, in ...
Descrição
Palavras-chave
Sistemas difusos, Modelos e construção de modelos, Controle automatico, Sistemas fuzzy Takagi-Sugeno
Como citar
MACHADO, Erica Regina Marani Daruichi. Modelagem e controle de sistemas fuzzy Takagi-Sugeno. 2003. xvii, 190 p. Tese (doutorado) - Universidade Estadual Paulista, Faculdade de Engenharia de Ilha Solteira, 2003.