Dynamic electromechanical drift model for PZT

Lead zirconate titanate (PZT) offers high resolution down to the sub-nanometer range, high stiffness, and fast response times. Unfortunately, PZT suffers from creep or drifting in open loop control, namely an undesirable drift in displacement and increase in error with time, therefore there is a strong need for a model to compensate for drift in PZT actuators for high precision and accuracy tracking and control applications. In this paper the drift of a PZT stack actuator is experimentally investigated. The authors present an explanation of the findings and develop a drift operator that is incorporated into a comprehensive dynamic electromechanical model for PZT. The presented model compensates for drift and hysteresis inherent to PZT and describes both the electrical and mechanical properties of PZT, along with the electromechanical coupling between the two domains, to achieve absolute positioning for minutes in duration. The model is experimentally tested over extended periods of time for a variety of static and dynamic input conditions, namely with step inputs, square wave inputs, an on/off switch-like waveform, and sinusoidal input excitations, to yield a maximum average error of 68.2 nm. The model has the potential of expanding the bandwidth of PZT applications to very low frequencies for use in switches and load cells and can achieve higher accuracies in both open loop positioning and closed loop tracking systems.