Nonlinear Dynamics And Chaos Control Of The Permanent-magnet Synchronous Motor

The Permanent magnet synchronous motor is the only motor which has been proved to display chaos by models. People of all ages use it because of its small size, light weight, high power factor, fast response, high efficiency and output torque. It is widely used in daily life and production. However, the permanent magnet synchronous motor will appear chaotic behavior under certain parameters and operating conditions, and these nonlinear behaviors are the important factors which cause instability during working time. This article focuses on exploring nonlinear dynamic behavior of PMSM in some parameters, and trying to control their movement in the chaotic motion, making the trajectory go to our desired target so as to eliminate the chaos and improve the efficiency of permanent magnet synchronous motor. The main work of this paper is as follows:1、Using dqo coordinates to establish a permanent magnet synchronous motor ontology model, and simplified ontology model of PMSM by using two methods. One method is the affine transformation, the other one is time-scale transformation. At the same time, we discussed equilibrium point to make it into a non-dimensional mathematical model which is easy to analyze and make the analysis of the stability of differential equations.2、Two dynamics mathematical models of permanent magnet synchronous motor under the condition of outage or continuous electricity were established with the situation of uniform air gap and non-uniform air gap. By simulation, we obtained bifurcation diagrams, Lyapunov exponent spectrum, the time response plots, phase diagrams and Poincare section diagram for each system model by the use of numerical calculation.3、Using bifurcation diagrams, Lyapunov exponent spectrum, the time response plots, phase diagrams and Poincare section diagram to carefully analyze each mathematical model, we found when parameters of permanent magnet synchronous motor system continuously change, the system had the nonlinear dynamics characteristics through doubling bifurcation leading to chaos.4、Analyzed the dynamic behavior of various parameters to obtain periodic motion system, quasi-periodic and chaotic motion movement. We give the optimal working range of different models for each parameter.5、Using negative feedback method and external periodic signal method to control chaotic behavior of permanent magnet synchronous motor. Moreover using fourth-order variable step method of Runge-Kutta to simulate and we obtained the bifurcation diagram and Lyapunov exponent diagram when parameter r is controlled before and after in the condition of uniform air gap under power outages, and achieved the intended purpose.