Hysteresis and creep modeling and compensation for a piezoelectric actuator using a fractional-order Maxwell resistive capacitor approach

A physics-based fractional-order Maxwell resistive capacitor (FOMRC) model is proposed to characterize nonlinear hysteresis and creep behaviors of a piezoelectric actuator (PEA). The Maxwell resistive capacitor (MRC) model is interpreted physically in the electric domain for PEAs. Based on this interpretation, the MRC model is modified to directly describe the relationship between the input voltage and the output displacement of a PEA. Then a procedure is developed to identify the parameters of the MRC model. This procedure is capable of being carried out using the measured input and output of a PEA only. A fractional-order dynamics is integrated into the MRC model to describe the effect of creep, as well as the detachment of hysteresis loops caused by creep. Moreover, the inverse FOMRC model is constructed to compensate for hysteresis and creep in an open-loop positioning application of PEAs. Simulation and experiments are carried out to validate the proposed model. The PEA compensated by the inverse FOMRC model shows an excellent linear behavior.