STATE OBSERVATION OF NONLINEAR AND UNCERTAIN SYSTEMS: APPLICATION TO INDUCTION MOTORS

Abstract

This paper deals with a study of performances and characteristics of four advanced state observers: the high gain observer (exponential observer), the multimodel observer, the sliding mode observer and the linear parameter variation observer (LPV observer). The main characteristic of the first observer lies in its calibration. Thus, the gain of the exponential observer does not use any kind of transformation and it is obtained from an algebraic Lyapunov equation. In addition, this observer requires the choice of a single parameter to calculate its gain. For the multimodel observer, it is based on the fusion of linear observers which are built around different operating points and the use of the validity notion. The most distinguished feature of the sliding mode observer is the ability to result in robust control. Indeed, its correction term is based on discontinuous functions. The last observation approach is the LPV observer. In this approach, we consider that the process is defined by a linear system with polytopic representation and linear parameter variation. Thus, the observer, designed in the same structure, is based on the notion of quadratic detectability and the use of LMI 1 tools to calculate its observation gain. The performances of these observers are highlighted through the estimation of state variables of an induction machine and specially the rotor flux with the stator current and voltage measurements. Numerical simulation study has confirmed the availability and the interesting results of the nonlinear and robust state observer approaches.