Multivariable Nonlinear Model of Ultrasonic Motor based on Hammerstein Model and Uniform Design

In this paper, a multivariable nonlinear mathematical model of ultrasonic motor for speed control, which includes all the control variables of ultrasonic motor(the peak-to-peak voltage, frequency and phase difference of two-phase driving voltages), has been presented. Ultrasonic motor has many excellent performance features such as high torque at low speed, quiet operation, no electromagnetic interference, and compact size etc. However, speed property of ultrasonic motor has strong nonlinearities, which are serious problems for accurate speed control. This paper presents a mathematical model represented by Hammerstein model, which is composed of a steady-state nonlinearities and linear dynamics part. The steady-state nonlinearities are represented by hyperbolic tangent and exponential functions, and the linear dynamics part is represented by a first order transfer function. In order to identify the coefficients of the steady-state nonlinear function, Uniform Design was use to design experiment, and the polyfit function (a nonlinear least-squares regression method) of Matlab software was used to deal with the experiment results. This model is simple and has good approximation of the nonlinearity of USM. The comparisons between the estimated speed when using the proposed mathematical model and actual speed in different conditions were conducted. Comparisons results indicate good performance of developed model with respect to the experimental data.