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.
The general purpose of this paper is to develop new aspects of bifurcation structures in a 3D parametric space. Identification of generic bifurcation structures in former studies was based on the arrangement of bifurcation curves in the parameter plane. So by analogy to such studies, we define the bifurcation surface in 3D parameter space as the main feature of the said generic structures. The implementation of this idea is made on the permanent magnet synchronous machine (PMSM) whose speed is regulated with a field-oriented control (FOC). Sufficient conditions are given for the existence of three main bifurcations: limit point (LP), Hopf (H) and Bogdanov–Takens (BT). Starting from bifurcation curves traced in a parameter plane and changing a third parameter, a qualitative bifurcation surface is constructed in a 3D parametric space. This led to underline the increasing complexity of the bifurcation structures when dealing with more than two parameters. This study put into evidence not only the complex behavior of PMSM, but stands as a starting point for a new formalism on the bifurcation structures in a 3D parametric space.
This paper includes two main parts: the first part investigates the coexistence and the bifurcation of equilibrium points in the dynamics of permanent magnet sychronous motor (PMSM). Some critical points are detected for a set of system parameters and initial condition, namely Hopf and saddle Node bifurcations. The second part deals with the synchronization of chaos by using a PI regulator. The role of Largest Lyapunov exponents and their computation are among the main issues discussed in this part.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.