A novel modified Preisach model is proposed to identify and simulate the hysteresis phenomena observed in a piezoelectric stack actuator. Further, an open-loop controller is incorporated to eliminate hysteresis influence. The proposed approach with a continuous, analytical distribution function performs very well when considering the low amount of parameters. In contrast to the classical and discrete Preisach model, this approach can also handle a non-constant frequency dependence by employing a time-derivative correction technique. Parameter estimation and model verification were subsequently carried out, demonstrating high accuracy of the derived model, keeping the deviation in the low percentage range (about 2-3%). Finally, our model performance is demonstrated by an open loop compensation algorithm based on the inversion of the improved Preisach model.