A Distributed Parameter Saturated Capacitor Model for Hysteresis in Piezoelectric Actuators

Abstract

Hysteresis is a very important nonlinearity in piezoelectric actuators (PEA). This paper proposes a distributed parameter saturated capacitor (DPSC) approach to model and compensate for hysteresis. The DPSC model is extended from saturated capacitor (SC) hysteresis model. The multiple SCs is replaced by a DPSC, the elastance and saturated charge of which have distributed parameter properties and governed by continuous functions. Thus, compared with the SC model, the DPSC model requires much less parameters. Utilizing a exponential function to describe the elastance, only three parameters are required. Experiments show that it achieves a satisfactory result. The normalized root mean square error of the DPSC model is as less as 0.63%. The hysteresis is compensated for by connecting the DPSC in serial with a PEA. The compensation reduces the hysteresis nonlinearity from 13.8% to 1.69% by 87.8%.