PI observer stability and application in an induction motor control system

The paper discusses the problem of stability of a proportional-integral Luenberger observer, designated for the state variables reconstruction of a linear, time-invariant dynamical system. It is proven, that there exists such a class of observed systems, for which the observer is always unstable, independently of its gains. Stability can be provided in every possible case after application of proposed modifications to the structure of the observer. It is proven, that stability of the modified observer depends only on its gains. It is shown, that an induction motor is the exemplary observed system, for which application of the unmodified observer is impossible due to its lack of stability, while the modified observer provides proper operation of the control system. Finally, some experimental results are presented, obtained in the multiscalar control system of the induction motor, equipped with the modified proportional-integral observer.