一类永磁同步电动机混沌模型与霍夫分叉

THE CHAOTIC MODEL AND HOPF BIFURCATION OF A TYPE OF PERMANENT-MAGNET SYNCHRONOUS MOTOR

从基本d - q轴永磁同步电动机模型出发 ,应用时间尺度变换和线性仿射变换 ,建立了一个适用于永磁同步电动机混沌运动分析的模型。在研究永磁同步电动机同步速附近运动条件下 ,得到一个三阶的非线性自治方程。利用该方程 ,根据李雅普诺夫稳定性分析理论 ,针对不同外部输入电压状况对其出现霍夫分叉的条件及稳定性进行了分析。研究表明 ,当均匀气隙永磁同步电动机参数确定情况下 ,在一定输入电压范围内 ,它将在同步速附近产生不稳定的霍夫分叉运动 ,并进入混沌状态和产生奇怪吸引子 ,计算机仿真展现了这一过程。

According to the basic d-q axes model of permanent magnet synchronous motor (PMSM), and applying a time scaling transformation and a linear affine transformation to it, the paper develops a model for analysis of chaos phenomena of PMSM. Study on operating nearly at synchronous speed of PMSM,the chaos model will be simplified a three order non linear autonomous equations. Depending on the equations and applying Lyapunov stability analytic theory to them, the conditions for Hopf bifurcation and operating stability of PMSM are analyzed under different input voltages .The results present that the even gas gap PMSM will operates in instability Hopf bifurcation , enters chaos and produces the strange attractors at a certain input voltage limitations when other parameters of PMSM are constants . The simulations are good agreement with them.