中文摘要：

超声波电机的输出特性与驱动频率呈非线性关系。同时在驱动频率切换期间，振动的初始状态对转速变化过程也会产生影响。行波超声波电机（traveling-wave ultrasonic motor,TUSM）动态过程与切换频率前后值的选取及频率变化方向有关。将TUSM频率阶跃响应过程近似线性化，利用系统辨识中的非参数建模方法，建立在特定切换频率条件下的二阶线性模型。在TUSM工作范围内，辨识若干组不同切换频率条件下的近似二阶线性模型，将这些模型的参数进行二维或三维拟合，得到了一个关于TUSM传递函数的多输入多输出模型。利用60mm行波超声波电机作为研究实例，实验与仿真结果表明，模型计算值与实测值接近，表明建模方法可行。

英文摘要：

The relations of ultrasonic motor output characteristics and drive frequency are nonlinear. Speed variation is influenced by the initial status of vibrancy during switch time of drive frequency. Dynamic process of traveling-wave ultrasonic motor （TUSM） has related with selection of switch value and frequency change direction. The frequency step response processes of traveling wave ultrasonic motor are approximately linearized. Second order linear model in condition of specific frequency-switch is established according to nonparametric estimation method in the system identification. According to the identification of approximate second-order linear model in a number of groups with different switch frequency, multi-input and multi-output model concerning transfer function of TUSM after 2D or 3D fitting of their parameters. A 60 mm-diameter traveling-wave ultrasonic motor is utilized in this research. Calculating values of this modal are close with experiment and simulation results which validates feasibility of the modal.