Portable Electronic Systems are increasingly being sought by the company, either for leisure or for work. And this happens due to ease these devices bring to everyday life, and by their mobility, easy access to wireless networks, size, weight, functionality, among other. However, for their operation, portable electronic systems require a power source, the battery. Thus, this study seeks to find in the Theory of Identification Systems, a mathematical model to make the prediction of the lifetime of a battery. For this we conducted a literature review on batteries, on the state of the art of mathematical modeling to predict the lifetime of batteries and the Theory of System Identification. Later, was chosen a structure model of the Theory of System Identification, Auto Regressive model. Met the parameters of the model that fits the experimental data set obtained from a test platform, built for this purpose. The computational model was implemented using the software tool MATLAB and then held validation. The study with the Auto Regressive model showed good results.

Abstract    The growing demand for MEMS requires each device to be tested, ensuring the quality of all devices that go to market. However the tests are expensive, increasing the final price. Mathematical modeling is an alternative to verify the quality of MEMS quickly and efficiently. The objective is to find a satisfactory model in with the order selected under the Partial Autocorrelation Function (PACF) criteria. The technique consists of five steps of system identification. The first step is to collect the data obtained from an experimental platform. Then the model order is selected based on the PACF. Then the model parameters are estimated by the least squares method. Then, the model is validated by calculating the percentage error. Quantitatively, the model has an error below 2%. The behavioral performance provides satisfactory results, proving that it is possible to define the order of an appropriate model under the presented criteria.Keywords    Dynamic System, Gray box modeling, MEMS Sensors, System identification, Time seriesResumo    A crescente demanda de MEMS exige que cada dispositivo seja testado, garantindo a qualidade de todos os dipositivos que vão para o mercado. Porém os testes são caros, aumentando o seu preço final. A modelagem matemática surge como uma alternativa para verificar a qualidade dos MEMS de forma rápida e eficiente. O objetivo do estudo é encontrar um modelo satisfatório com ordem selecionada sob o critério da Função de Autocorrelação Parcial (PACF). A técnica consiste das cinco etapas da identificação de sistemas. A primeira etapa é coletar os dados obtidos de uma plataforma experimental. Então a ordem do modelo é selecionada baseada na PACF. Em seguida os parâmetros do modelo são estimados pelo método dos mínimos quadrados. Depois o modelo é validado calculando o erro percentual e o erro percentual médio absoluto. Quantitativamente, o modelo apresenta erro inferior a 2%. O desempenho comportamental apresenta resultados satisfatórios, comprovando que é possível definir a ordem de um modelo adequado sob os critérios apresentados.Palavras-chave    Identificação de sistemas, Modelagem caixa cinza, Sensores MEMS,Séries temporais, Sistema Dinâmico