The stochastic stability and bifurcation analysis of permanent magnet synchronous motor excited by Gaussian white noise

Extensive engineering applications have confirmed the necessity of introducing stochastic disturbance into the permanent magnet synchronous motor (PMSM) system. Therefore the stochastic stability and bifurcation of the system under Gaussian white noise are investigated in this study. The stochastic average method transforms the system equation into Ito stochastic differential equation. Further, the stability of the model under white noise excitation is analysed based on the theoretical calculation process. Notably, the mechanism of P-bifurcation of the system is revealed by simulating the evolution process of probability density function with the change in noise intensity. Moreover, the complex dynamics of the system in two-parameter space are explored using multiple numerical tools, in which extensive fish-shaped periodic regions appear. It is particularly interesting that the noise inevitably erodes the boundaries of these fish-shaped periodic regions. Besides, it is noteworthy that a new phenomenon is found from the numerical simulation results that noise intensity can induce convergence behaviour in the periodic oscillation region, which also shows the two-sidedness of noise effect on the system.