Solução geral da equação algébrica de Riccati Discreta utilizando estimador não quadrático e decomposição matricial aplicado no modelo em espaço de estado de um gerador eólico

• Ano de defesa: 2016
• Autor(a) principal: Queiroz, Jonathan Araujo
• Orientador(a): BARROS FILHO, Allan Kardec Duailibe
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA DE ELETRICIDADE/CCET
• Departamento: DEPARTAMENTO DE ENGENHARIA DA ELETRICIDADE/CCET
• País: Brasil
• Palavras-chave em Português: Equação Algébrica de Riccati Discreta; Estimador não Quadrático; Decomposicão Matricial; Estabilidade Numérica; Velocidade de Convergência Gerador Eólico
• Palavras-chave em Inglês: Discrete Algebraic Riccati Equation; Non-squares Approximators; Matrix decomposition; Numerical Stability; Convergence Speed; Wind Generator
• Área do conhecimento CNPq: Sistemas Elétricos de Potência
• Link de acesso: http://tedebc.ufma.br:8080/jspui/handle/tede/1691

The discrete Riccati algebraic equation has played an increasingly important role in optimal control theory and adaptive ltering. For this reason, various techniques have been developed to solve the DARE, for example the approach based on self vectors or approaches related to invariant subspaces [1], which require mathematical rigor and precision. However, these approaches present a number of problems, among them the fact that they can not be implemented in real-time due to its high computational cost to estimate the solution of DARE in many systems, especially systems with higher order three. In order to overcomes this problem, we propose to solve the DARE using as an estimator based on the sum of potential error pairs. The estimator is similar to the Recursive Least Squares (RLS), but with a better performance in terms of convergence speed and estimation accuracy without a signi- cant increase in computational complexity. The estimator is called Recursive Least Non-Squares (RLNS). One other aspect in unraveling the general DARE is to ensure that DARE is numerically well conditioned. To perform the numerical conditioning of DARE, a matrix decomposition technique known as Moore-Penrose inverse or generalized inverse is used. The proposed method is evaluated in a multivariate system 6th order corresponding to the wind generator. The method is evaluated under the numerical stability point of view and speed of convergence.