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This paper describes the occurrence of certain dynamic responses of the permanent magnet synchronous motor submitted to a FOC control under a parameter variation. In addition to the transition between limit cycles and equilibrium points due to the Hopf bifurcation, the multistability property is put into evidence by the identification of several attractors for the same motor and control parameter sets and for different sets of initial conditions. An illustration of the domains or basins of attractions of different attractors is given in a three dimensional phase space. Analytical expressions of equilibrium point coordinates are determined from the differential system equations; their stability can be known from the characteristic polynomial solutions.

A qualitative characterization of the PMSM behavior, based on certain characteristic bifurcation structures is discussed. The equilibrium points of the PMSM were derived from the mathematical model and the stability of the origin equilibrium stability conditions were given. Foliation of the parametric plane and its role to understand the bifurcation mechanisms was illustrated. A particular structure including bifurcations of codimension one and two was identified.