State estimation of dynamical systems with nonlinearities by using proportional-integral observer

Abstract

In this paper the application of a PI observer technique to dynamical systems with nonlinearities is proposed. The PI observer has two feedback loops, a proportional loop and an integral loop of the estimation error. In this way the PI observer combines the structures of the practical orientated nonlinearity observer developed by the third author and the classical Luenberger observer. The structure and the estimation performance of the PI observer are discussed and analysed. The results show that the PI observer can estimate the states not only of linear systems, but also, more significantly, of systems with any arbitrary external input which appear as unknown input, nonlinearity or unmodelled dynamics. It is shown that the PI observer works with weak assumptions, which can be fulfilled by many classes of systems to be observed. Owing to the weak assumptions it can improve many observer-based technical solutions as diagnosis or control based on observers. In the paper the conditions are given and proved. The design method is declared and carried out with illustrative examples of a linear system and of a nonlinear system of a link manipulator with flexible joints. The results are good and they show the efficiency of the PI observer. In the case of nonlinear systems the advantages of ‘robustness’ and the model independency of the proposed observer scheme can be shown clearly.