利用伺服电机参数,在建立电路和机械能量方程的基础上,应用拉格朗日一麦克斯韦方程,通过Park变换,将三相定子参考系的拉格朗日一麦克斯韦方程变换到两相转子参考系。推导了便于实施控制的永磁同步伺服电机两相转子参考系的机电耦合动力学方程。该机电耦联动力学建模方法不需测量电动机的磁路尺寸,只要测量电动机dq0坐标系绕组电感和永磁体磁链的幅值就可直接列出微分方程,推导简洁高效,便于应用。通过对伺服电机机电耦合动力学的仿真,验证了伺服电机的机电耦合动力学建模正确;电机的速度和电流控制器设计合理。
Based on the established electrical and mechanical energy equations consisting of servomotor parameters, Lagrange- Maxwell equations of three-phase stator reference coordinates were transformed to the equations of two-phase rotor reference coordinates by Park transform. Electromechanical coupling dynamics equations of permanent magnet synchronous servomotor in two-phase reference coordinates were obtained. In this dynamical modeling method of electromechanical coupling system, the dynamical differential equations can be established by only measuring amplitude of the flux induced by the permanent magnets and the winding inductance in dqO reference of the motor, the size of magnetic circuit needs not to be measured. The method is terse, efficient, and is easy to be used. Electromechanical coupling dynamics system of servomotor was simulated. Simulation results show that the deduced electromechanical coupling dynamics equations for servomotor are correct, and current control schemes are reasonable.