Modeling of Piezoelectric Tube Actuators

A new dynamic model is presented for piezoelectric tube actuators commonly used in high-precision instruments. The model captures coupling between motions in all three axes such as bending motion due to a supposedly pure extension of the actuator. Both hysteresis and creep phenomena are included in the overall actuator model permitting modeling nonlinear sensitivity in the voltage to displacement response. Experimental data on hysteresis and creep are presented to support the modeling. Experiments and model predictions show that due to coupling a voltage Vz corresponding to vertical displacement will produce lateral displacement that acts as a disturbance to the main lateral response. The resonance frequency for the lateral dynamics is inherently lower than that of the longitudinal dynamics. Therefore, Vz is expected to contain frequencies that may excite the lateral resonance. Accordingly, this out of bandwidth disturbance will not be well compensated for either in open or closed loop control of the actuator. In order to preserve performance in open loop actuator control and stability and performance in closed loop control, a large reduction in the bandwidth of vertical motion would be required to avoid exciting the first bending mode.