Fast steering mirror powered by piezoelectric ceramic has fine dynamic performance, and can meet the demand for high precision positioning in engineering, but its hysteresis effect restricts the further performance development. The mathematical model of hysteresis character based on PLAY operator has the advantages of being simple in structure, convenient for calculation, and high precision of model.However, the realization depends on parameter estimation precision, and it's difficult to obtain the physical quantity with a high precision. An algorithm is proposed to work out the parameters of PI inverse model by using geometric method. Experimental results show that the algorithm has good dynamic performance and high precision of modeling, and the algorithm based feed-forward control of PI inverse model can compensate well for the hysteresis effect of the fast steering mirror powered by piezoelectric ceramic.