Anca Maria Nagy

Model structure simplification of a biological reactor

This article proposes an analytical method for decomposing a dynamic nonlinear system into a multiple model form in order to reduce its complexity and to study more easily identification, stability analysis and controller design problems. The majority of existing methods are order reduction based techniques, which come with an information loss of the initial system, whereas the method proposed here avoids this particular loss. The multiple model constitutes an efficient tool to represent nonlinear systems. These are decomposed into several linear time invariant systems (LTI) which are weighted and aggregated that allows to benefit from important analysis tools. This method is applied to a simplified activated sludge reactor model.

State estimation of the three-tank system using a multiple model

This paper addresses the exact transformation of nonlinear systems into a multiple model form with unmeasurable premise variables. The multiple model structure serves to treat the observability and the state estimation problem of nonlinear systems. Using a method with no information loss, a nonlinear system is transformed into a multiple model, depending on the choice of premise variables. It is a key point, since it allows to choose, between different multiple model forms, the one that has suitable structure and properties, in order to design an observer. The convergence conditions of the state estimation error are expressed in LMI formulation using the Lyapunov method. These proposals are investigated and applied to the three-tank system.