TY - JOUR
T1 - Bounding a domain containing all compact invariant sets of the permanent-magnet motor system
AU - Coria, Luis N.
AU - Starkov, Konstantin E.
N1 - Funding Information:
This work was supported by the CONACYT project “ANALISIS DE LOCALIZACION DE CONJUNTOS COMPACTOS INVARIANTES DE SISTEMAS NO LINEALES CON DINAMICA COMPLEJA Y SUS APLICACIONES”, N. 000000000078890, MEXICO.
PY - 2009/11
Y1 - 2009/11
N2 - 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.
AB - 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.
KW - Compact invariant set
KW - Localization
KW - Permanent-magnet motor system
UR - http://www.scopus.com/inward/record.url?scp=67349164294&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2008.09.001
DO - 10.1016/j.cnsns.2008.09.001
M3 - Artículo
SN - 1007-5704
VL - 14
SP - 3879
EP - 3888
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 11
ER -