Modeling piezoelectric actuators

The piezoelectric actuator (PEA) is a well-known device for managing extrem ely small displacements in the range from 10 pm (1 pm = 10(-12) m) to 100 m um. When developing a control system for a piezo-actuated positioning mecha nism, the actuator dynamics have to be taken into account. An electromechan ical piezo model, based on physical principles, is presented in this paper. In this model, a first-order differential equation is adopted to describe the hysteresis effect, and a partial differential equation is used to descr ibe the mechanical behavior. Since, in practice, a PEA is most often used a s an actuator for positioning mechanisms, we considered the influence of su ch a mechanism on the overall mechanical behavior of PEA and positioning me chanism together. For a well-designed mechanism, the overall mechanical beh avior practically equals that of a single mass-spring-damper system, of whi ch the undamped eigenfrequency and the relative damping can be designed fav orably. With respect to traditional voltage steering, charge steering has t he advantage that no hysteresis is encountered between electrical input rin d elongation, Electrical steering configurations for both cases of steering are presented. Finally, for the case of charge steering, we derived the to tal model of a piezo-actuated positioning mechanism. This model is dominate d by the mechanical model, which could be designed favorably. Therefore, th is model gives a broad range of possibilities for model-based controller de sign.