Domain wall model for hysteresis in piezoelectric materials

This paper addresses the modeling of hysteresis and nonlinear constitutive relations in piezoelectric materials at moderate to high drive levels. Hysteresis and nonlinearities are due to the domain structure inherent to the materials and both aspects must be addressed to attain the full potential of the materials as sensors and actuators in high performance applications. The model employed here is based on previously developed theory for hysteresis in general ferroelectric materials. This theory is based on the quantification of the reversible and irreversible motion of domain walls pinned at inclusions in the material. This yields an ordinary differential equation (ODE) model having five parameters. The relationship of the parameters to physical attributes of the materials is detailed and algorithms for determining estimates of the parameters using measured values of the coercive field, differential susceptibility and saturation properties of the materials are detailed. The accuracy of the model and its capability for the prediction of measured polarization at various drive levels is illustrated through a comparison with experimental data from PZT5A, PZT5H and PZT4 compounds. Finally, the ODE model formulation is amenable to inversion which facilitates the construction of an inverse compensator for linear control design.