Avaliação numérica e experimental dos métodos ERA e ERA/OKID para a identificação de sistemas mecânicos

Abstract

This work presents two algorithms of identification of state-space linear systems, as follows: ERA (Eigensystem Realization Algorithm), developed by Juang and Pappa (1985), and ERA/ OKID (Observer/ Kalman Filter Identification), by Phan et al. (1992). Both were conceived at the environment of Aerospace Engineering, where it was indispensable the appearance of a trustworthy tool to identify the complex structures and the inherent systems. The first one requires that the system is subjected to an impulse input and that the output (Markov Parameters) is organized in a known matrix as Hankel matrix. This matrix is then decomposed in singular values, which permits, with the help of the concepts of controllability and observability, a convenient mathematical manipulation that gives the desired realization, that is the system in state-space. The second one was conceived for underdamping systems. Therefore, it results, mathematically, in a state observer, so that, a virtual damping at the signal is added. This resource allows a data compression and, consequently, lower computational effort. Thus, OKID provides, from any sort of input, Markov parameters of the observer and the system, and the last one will feed ERA. The motivation of the work is to help the Control Engineering in the identification, in state-space, of complex systems, whose analytical modelling is difficult due to several reasons. Furthermore, it helps its simulations. In order to make it possible, the work presents the Theory of Systems Realization, ERA and ERA/ OKID algorithms, and from these concepts, a numerical assessment of a mechanical system with two degrees of freedom using ERA, and an experimental assessment of an acoustic pipe using ERA/ OKID. The dissertation concluded that, for the studied cases, the presented tecniques are efficient, and as a result, they become powerful tools of identification and points out some future perspectives in the realized research.