On the Impossibility of Building a Thau Observer for a Nonlinear Model of an Induction Motor

Given the simplicity of Thau observer, it could be attractive to try to build this kind of observer for an induction motor. However, in this paper, (metaheuristic) arguments are provided to explain why such purpose cannot be accomplished. In order to establish the impossibility of developing a Thau observer for the nonlinear model of an induction motor, first, it must be established that Thau inequality cannot be satisfied. Therefore, Lipschitz constant for nonlinear model of the motor was determined. Next, given the absence of a systematic procedure of design and due to the great diversity of possible values for observer parameters, Thau relation should be maximized. Nevertheless, as this last task is difficult and in order to avoid the drawbacks of classical methods, in this work, differential evolution algorithm was used. In spite of having maximized successfully Thau relation, Thau inequality could not be satisfied. As a last attempt, the motor model was scaled. Lipschitz constant for this model was minimized and Thau relation was again maximized. Notwithstanding, Thau inequality could not be satisfied for scaled model. Based on exhaustive bibliographic searches, it can be assured that this is the first time that this kind of problem is considered in the technical literature.