Modeling of V-Shape Linear Ultrasonic Motor Based on Hammerstein Model

Abstract

A two-variable nonlinear mathematical model of V-shape linear ultrasonic motor (LUSM) has been presented. The relations of LUSM speed characteristics and its control variables are nonlinear, which are serious problems for accurate speed control. This paper presents a mathematical model based on Hammerstein model, which is composed of a steady-state nonlinear part and a linear dynamics part. The steady-state nonlinear part is represented by a hyperbolic tangent function, 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 used to design experiment, the nlinfit and polyfit function of Matlab software was used to deal with the experiment results. The comparisons between the estimated speed with 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.