Bifurcation Analysis of the Permanent Magnet Synchronous Motor Model Under White Gaussian Noises

The Gaussian white noise was introduced into the permanent magnet synchronous motor (PMSM) model, to obtain the system Itô stochastic differential equation through the polar transformation and with the stochastic average method. Hence, the probability density function of the system was calculated, and the mechanism of the P-bifurcation of the system was revealed through numerical simulation. In addition, the complex dynamics of the system in the 2-parameter space was discussed. The simulation results show that, there are lots of "fish-shaped" periodic regions in the parameter space. The regions become unstable under effects of system noises. It is worth noting that, under noises of a certain intensity, the system dynamics will switch from periodic motion to convergence, indicating the dual nature of the effects of noises on the PMSM system dynamics.