A fractional-order Duhem model of rate-dependent hysteresis for piezoelectric actuators

In this paper, a Fractional-Order Duhem Model (FODuhem) is proposed to describe the rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). A fractional-order operator is introduced on the basis of the traditional Duhem model, and the unique nonlocal memory property of the fractional-order operator makes it possible to describe the memory effect inherent in hysteresis. A differential evolutionary algorithm was used to identify the parameters of the FODuhem model. Finally, experimental results clearly show that the FODuhem model can better describe the rate-dependent hysteresis behavior of piezoelectric actuators compared with the conventional Duhem model.