Bounding a domain containing all compact invariant sets of the permanent-magnet motor system |
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| Authors: | Luis N Coria Konstantin E Starkov |
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| Institution: | 1. Instituto Politécnico Nacional–CITEDI, Av. del Parque 1310, Mesa de Otay, Tijuana, B.C., Mexico;2. Sección de Estudios de Posgrado e Investigación, ESIME-Z, Instituto Politécnico Nacional, Mexico, D.F. 07738, Mexico;1. Instituto Politécnico Nacional – CITEDI, Ave. del Parque 1310, Mesa de Otay, Tijuana B.C. 22510, Mexico;2. Department of Computer Science, Division of Applied Physics, CICESE, Carretera Ensenada-Tijuana 3918, Zona Playitas, Ensenada B.C. 22860, Mexico;1. Department of Computer Science, Division of Applied Physics, CICESE, Carretera Ensenada-Tijuana No. 3918, Ensenada, BC 22860, Mexico;2. Instituto Politécnico Nacional, CITEDI, Ave. del Parque No. 1310, Mesa de Otay, Tijuana, BC 22510, Mexico;1. Université de Lyon, INSA-Lyon, INL, CNRS-UMR5270, Villeurbanne F-69621, France;2. Digital Technology Research and Development Center, National Polytechnic Institute (CITEDI-IPN), Tijuana, Mexico;1. Doctorado en Ciencias de la Ingeniería, Departamento de Ingeniería Eléctrica y Electrónica, Instituto Tecnológico de Tijuana, Blvd. Industrial y Av. ITR Tijuana S/N, Mesa Otay C.P. 22500, Tijuana BC, Mexico;2. Departamento de Ingeniería Electrónica, Universidad Politécnica de Valencia, Spain |
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| Abstract: | In this paper we characterize a locus of compact invariant sets of the system describing dynamics of the permanent-magnet synchronous motor (PMSM). We establish that all compact invariant sets of this system are contained in the intersection of one-parameter set of ellipsoids and compute its parameters. In addition, localizations by using a parabolic cylinder, an elliptic paraboloid and a hyperbolic cylinder are obtained. Simple polytopic bounds are derived with help of these localizations. Most of localizations mentioned above remain valid for more specific motor systems; namely, for the interior magnet PMSM and for the surface magnet PMSM. Yet another localization set for the interior magnet PMSM is described. Examples of localization of chaotic attractors existing for some values of parameters of PMSMs are presented as well. |
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