Hysteresis poses a significant challenge for control of smart material actuators. If unaccommodated, the hysteresis can result in oscillation, poor tracking performance, and potential instability when the actuators are incorporated in control design. To overcome these problems, a fundamental idea in coping with hysteresis is inverse compensation based on the Preisach model. In this paper, we address systematically the problem of Preisach model inversion and its properties, employing the technique of three-step composition mapping and geometric interpretation of the Preisach model. A Preisach right inverse is achieved via the iterative algorithm proposed, which possesses same properties with the Preisach model. Finally, comparative experiments are performed on a piezoelectric stack actuator (PEA) to test the efficacy of the compensation scheme based on the Preisach right inverse.