Localización de conjuntos compactos invariantes de sistemas físicos y electromecánicos y sus aplicaciones
Localization of Compact Invariant Sets of Physical and Electromechanical Systems and their Applications1
Luis Néstor Coria de los Rios y Konstantin E. Starkov
Centro de Investigación y Desarrollo de Tecnología Digital, Instituto Politécnico Nacional Ave. del Parque 1310, Mesa de Otay, Tijuana,B.C, México luis.coria@gmail.com, konst@citedi.mx
]]>Artículo recibido el 26/01/2011;
aceptado el 10/08/2011.
Resumen
Con la localización de conjuntos compactos invariantes se pretende entender la dinámica a largo plazo de un sistema caótico. En esta investigación se aplica el método de localización por medio de condiciones de extrema y el teorema iterativo para estudiar la dinámica de un modelo de un motor síncrono de imán permanente (PMSM). De esta forma, se determina una localización dada por un elipsoide que es cortada por un paraboloide elíptico y un cilindro. Para los resultados obtenidos se realizan simulaciones numéricas en las que se observan las superficies de localización respecto al atractor caótico del sistema en estudio. Los resultados son contribuciones útiles en el análisis de la dinámica compleja de los sistemas estudiados. La aplicación de resultados de localización corresponde al diseño de dos observadores de Thau para el PMSM.
Palabras clave: Caos, conjuntos compactos invariantes, sistema electromecánico, motor síncrono de imán permanente.
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.
]]> Keywords: Chaos, compact invariant set, electromechanical system, permanent magnet synchronous motor.
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Agradecimientos
El trabajo de tesis doctoral fue realizado en el marco del proyecto SEP-CONACYT 78890 y el proyecto DGEST TIJ-IET-2009-217.
Referencias
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]]> Nota
Resumen extendido de tesis doctoral. Graduado: Luis N. Coria. Director: Konstantin E. Starkov. Fecha de graduación: 18/03/2010
Extended abstract of PhD thesis. Graduated: Luis N. Coria. Advisor: Konstantin E. Starkov. Graduation date: 18/03/2010.
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