混合式步进电机磁网络模型的数学特征及数值算法

本文提出并证明了步进电机磁网络模型节点方程的系数矩阵具有对称正定性质,并用共轭斜量算法取代了以前的拟牛顿迭代法。共轭斜量法的优点是收敛域为全体实数,在角度步长和磁势步长放开的同时方法的收敛速度不受损失,从而使混合式步进电机的计算机辅助分析设计的计算时间大为缩短,为优化设计辅平了道路。另外,本文提出的结论和计算方法,对没有受控源且连通的、不含负电阻的线性和非线性电阻网络都是适用的。

THE MATHEMATICAL FEATURES AND THE ALGORITHM OF THE MAGNETIC NETWORK MODEL FOR HYBRID STEPPING MOTOR

This paper presents and proves that the coefficient matrix of the nodeequations for the stepping motor's magnetic network has symmetric andpositive definite property,and the former quasi-newton method for this nonlinear equations is replaced by the conjugate gradient method(CGM).Theadvantage of CGM is that the convergence domain exists in all real numberfield and the angle step as well as magnetic-force step may become largerwithout the loss of the convergence speed,so the computer time of the analytic design for the hybrid stepping motor is obviously shortened,the way to theoptimum design for hybrid stepping motor is easily accessed. Furthermore,the conclusion and the algorithm of this paper can alsoapplied for the mesh and resistent network which dose not contain controlledsources and negative resistance.