Dynamics and Stability of Permanent-Magnet Synchronous Motor

The aim of this article is to explore the dynamic characteristics and stability of the permanent-magnet synchronous motor (PMSM). PMSM equilibrium local stability condition and Hopf bifurcation condition, pitchfork bifurcation condition, and fold bifurcation condition have been derived by using the Routh-Hurwitz criterion and the bifurcation theory, respectively. Bifurcation curves of the equilibrium with single and double parameters are obtained by continuation method. Numerical simulations not only confirm the theoretical analysis results but also show one kind of codimension-two-bifurcation points of the equilibrium. PMSM, with or without external load, can exhibit rich dynamic behaviors in different parameters regions. It is shown that if unstable equilibrium appears in the parameters regions, the PMSM may not be able to work stably. To ensure the PMSMs work stably, the inherent parameters should be designed in the region which has only one stable equilibrium.