Stochastic Response Of A Permanent-magnet Synchronous Motor System Under Stochastic Noise Excitation

Permanent magnet synchronous motor(PMSM)has been widely used in many fields due to its advantages of high precision,high power density and small volume.Its mathematical model,as a typical nonlinear power system model,has been favored by scholars.In the actual environment,PMSM is inevitably affected by temperature,damping,external magnetic field and other factors,which can be regarded as stochastic noise.Because noise excitation may damage the system’s internal mechanism,which affect the smooth operation of the motor,so in order to better improve the robustness of PMSM,In this paper,stochastic dynamics theory is used to establish a permanent magnet motor system with random excitation dissipation by introducing noise term,so as to restore the actual working conditions as far as possible,respectively discusses the gaussian white noise and color noise and non-gaussian noise under the incentive of stochastic stability of the permanent magnet systems,and stochastic bifurcation,The main research contents are as follows:1.The model of permanent magnet synchronous motor(PMSM)excited by gaussian white noise is studied.The central manifold theorem is used to simplify the model,and stochastic differential equation is obtained by means of the stochastic average method through the transformation of polar coordinates.Based on maximum Lyapunov index exponent and singular boundary theory to discuss the global and local stability conditions,analysis of the state by the probability density function is the system stochastic P-bifurcation,get along with the noise intensity change of probability density plot.Finally the analytical solution of the stationary probability density is in good agreement with the simulated solution shows the effectiveness of the results of the analysis by the Monte Carlo simulation verification.2.A permanent magnet synchronous motor(PMSM)model was established under the excitation of Gaussian color noise.The noise was whitened by the approximate principle of uniform color noise,and the PMSM model under the excitation of white noise was obtained.The dimensions of the model were also reduced according to the central manifold theorem,and the stochastic ?Ito differential equation of the system was solved by the Stochastic average method.The stochastic stability and stochastic bifurcation of the system are analyzed,and the stochastic stability conditions and Pbifurcation critical conditions of the system are obtained.The critical position of Pbifurcation is verified by numerical simulation with appropriate parameters,and the conclusion is corresponding to the Gaussian white noise excitation model.3.A permanent magnet synchronous motor(PMSM)model under non-Gaussian noise excitation is studied.The model is simplified according to the central popular theorem,and the stationary probability function of the system is obtained according to the path integral method and the uniform color noise approximation principle.The stationary probability density changes of the system under the influence of additive noise,multiplicative noise,correlation time and deviation parameters are analyzed.In addition,the dynamic behavior of PMSM system under the influence of two parameters is further investigated,and the bifurcation structure of PMSM system under the influence of non-Gaussian noise is simulated by numerical simulation.