Modeling of the piezoelectric-driven stick-slip actuators

Abstract

Previous studies show that the Piezoelectric-Driven Stick-Slip (PDSS) actuator is a promising device in many micropositioning and micromanipulation applications, where positioning with a long range and a high resolution is required. However, research in this area is still in its early stage and many issues remain to be addressed. One key issue is the representation of the dynamic displacement of the end-effector. It is known that such factors as the dynamics of piezoelectric actuator (PEA) and the presliding friction involved can significantly contribute to the displacement dynamics. Although this has been widely accepted, specific quantitative relationship between the aforementioned factors and the displacement dynamics has rarely been defined. The aim of this research is to develop a model to represent the displacement of the end-effecter of the PDSS actuators, in which both the presliding friction and the PEA dynamics are addressed. In order to represent the presliding friction, the models reported in literatures, including Dahl model [Olsson, et al., 1998], Reset Integrator model [Haessig and Friedland 1991], LuGre model [Canudas de Wit et al., 1995] and Elastoplastic model [Dupont et al., 2002] were reviewed and examined; and the LuGre model was chosen to be used because of its efficiency and simple formulation. On the other hand, a linear second order dynamic system model was employed to represent the combination of a PEA and its driven mechanism. On the basis of the pre-sliding friction model and the linearized PEA dynamics model, a model representative of the end-effector displacement of the PDSS actuator model was developed. In order to validate experimentally the developed PDSS model, a displacement measuring and data acquisition experiment system was established and a prototype was developed based on dSPACE and Simulink. On the prototyped actuator, two experiments were designed and conducted to identify the parameters involved in the model. One experiment is for the determination of the parameters of the second order system for the dynamics of the combination of a PEA and its driven mechanism; and other one is for the determination of the parameters of the chosen friction model. The identified parameters were then employed in the developed PDSS model to simulate the displacements and the results were compared with the experimental results that were obtained under the same operating conditions as the simulation. The comparison suggests that the model developed in this study is promising for the end-effector displacement of the PDSS actuator.