Localization of Compact Invariant Sets of Physical and Electromechanical Systems and their Applications

Abstract

Localization of compact invariant sets allows understanding the long-time behavior of a chaotic system. In this paper we apply the solution of the conditional extremum problem to the study of a model of a permanent magnet synchronous motor. The localization set is given by a one-parameter set of ellipsoids, crossed by an elliptical paraboloid and a cylinder. This improves the initial ellipsoidal localization. Numerical simulations are made to show the effectiveness of the method. The results are useful for analyzing the complex behavior of the systems under study. The application of the localization results corresponds to the design of two Thau observers for the PMSM.