Design and modeling of a piezo-actuated positioning mechanism

We are involved in the design and control of a 1-dimensional positioning mechanism for a range of 50 mu m and an accuracy of 30 pm. Only piezo electric actuators can be used to manage such small displacements. However, these actuators show hysteretic behavior and lengthening saturation. The extremely small displacements are measured by means of capacitive sensors. In order to design a controller a model of the positioning mechanism and the actuators is developed. Contrary to the existing literature known to us, in our model the hysteresis is described by a differential equation. The mechanical characteristics of the design, and therefore also of the model, are chosen such that they are practically realizable and advantageous for controller design. The final nonlinear fifth order state space model is believed to be suitable for a nonlinear control technique like feedback linearization.