For micro-positioning systems using piezoelectric actuators for precision grinding process control, sinusoidal command signals will be used and will give additional problems in comparison with the commonly used step signals due to the hysteresis effects, which require a good modeling approach. In order to avoid the discontinuity problem in obtaining the values of the piezoelectric constant, a new approach of direct mapping with polynomial fit is proposed. Theoretical and experimental studies are conducted and comparative studies are made. Compared with the single polynomial approach, the proposed method of direct mapping with polynomial fit is able to reduce the modeling error to 12.5%, which is 6.5% lower, and the problems in obtaining the values of the piezoelectric constant are avoided. The proposed approach is shown advantageous. Further studies are necessary to significantly reduce the modeling error.