Transfer matrix method for multibody systems for piezoelectric stack actuators

Abstract

In order to achieve a large displacement output from a piezoelectric actuator, we realized the piezoelectric stack actuator (PSA) by mechanically layering/stacking multi-chip piezoelectric wafers in a series and electrically connecting the electrodes in parallel. In this paper, in order to accurately model the hysteresis and the dynamic characteristics of a PSA, the transfer matrix method for multibody systems (MSTMM) was adopted to describe the dynamic characteristics, and the Bouc-Wen hysteresis operator was used to represent the hysteresis. The vibration characteristics of a PSA and a piezo-actuated positioning mechanism (PPM) are derived and analyzed by the MSTMM; then, the dynamic responses of the PSA and the PPM are calculated. The experimental results show that the new method can accurately portray the hysteresis and the dynamic characteristics of a PSA and a PPM. On one hand, if we use this method to model the dynamic response of the PSA and the PPM, the PSA can be considered as a flexible body, as opposed to a mass-spring-damper system, which is in better agreement with the actual condition. On the other hand, the global dynamics equation is not needed for the study of system dynamics, and the dynamics equation has a small-sized matrix and a higher computational speed. Therefore, this method gives a broad range of possibilities for model-based controller design.