A rate-dependent hysteresis nonlinearity mathematical model for piezoelectric actuators is established based on elliptical curves.This modeling process is divided into two parts

which are major loop modeling and minor loop modeling.The major loop is described by constrained conic form elliptical curve.The major loop parameters are identified by the optimal elliptical fitting algorithm.Through the transformation of major loop

the parameters relation between minor loop and major loop is constructed for minor loop modeling.The modeling method based on elliptical curve has high identification precision for both major loop and minor loop of hysteresis curve.The experimental results verify the effectiveness of this method.