Table of Contents
Smart Materials Research
Volume 2012, Article ID 164062, 15 pages
Research Article

Modeling Hysteresis with Inertial-Dependent Prandtl-Ishlinskii Model in Wide-Band Frequency-Operated Piezoelectric Actuator

Division of Mechatronics & Design, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

Received 12 November 2011; Accepted 3 January 2012

Academic Editor: Tao Li

Copyright © 2012 Vahid Hassani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


One of the major problems occurring in many technical applications is the presence of the hysteretic behavior in sensors and actuators, which causes a nonlinear relationship between input and output variables in such devices. Since the nonlinear phenomenon of hysteresis degrades the performance of the piezoelectric materials and piezoelectric drive mechanisms, for example, in positioning control framework, it has to be characterized in order to mitigate the effect of the nonlinearity in the devices. This paper is aimed to characterize and model the hysteresis in typical piezoelectric actuators under load-free and preloaded circumstances incorporating the inertial effect of the system. For this purpose, the piezoelectric actuator is modeled as a mass-spring-damper system, which is expressed in terms of a stop operator as one of the essential yet efficient hysteresis operators in the Prandtl-Ishlinskii (PI) model. The reason of utilizing the stop operator in this study is for the sake of control purposes, as the stop operator plays as the inverse of the play operator in the PI model and can be used in a feed-forward controller scheme to suppress the effect of hysteresis in general control framework. The results reveal that this model exhibits better correspondence to the measurement output compared to that of the classical PI model.