A Distributed Parameter Maxwell-Slip Model for the Hysteresis in Piezoelectric Actuators

Abstract

In this paper, the Maxwell-slip model is extended to a distributed parameter Maxwell-slip (DPMS) model, and a DPMS model parameter identification process is proposed for the hysteresis in piezoelectric actuators (PEAs). This model is governed by a saturation deformation function (SDF) and a stiffness function (SF); it requires only a few parameters and can capture nonconvex hysteresis. It has a clear interpretation in the mechanical domain and provides insight into the mechanism of hysteresis generation; hence, it can predict the performance in the unidentified range. With a linear SDF, exponential, power-law, and polynomial SFs are studied for a PEA-based nanopositioning system. The normalized root-mean-square (NRMS) errors for these SFs are 0.60%, 0.43%, and 0.47%, respectively. With parameters identified from the middle hysteresis loop, the NRMS error is 0.68%. For the nonconvex hysteresis, the NRMS error is 2.78%. With compensation by DPMS models with the above three SFs, the hysteresis decreases by 86.95%, 87.13%, and 97.13%, respectively. The rate dependence of the frequency response is eliminated, and the $-$ 3-dB bandwidth increases from 320 to 890 Hz.