In order to improve the control accuracy of large-aperture piezoelectric fast steering mirror(FSM) in precision image stabilization system in space telescope, the compound control strategy combining hysteresis feed forward compensation with the optimal PID control algorithm was adopted. According to the problems that the reversibility of Prandtl-Ishlinskii (PI) model based on Play operator was limited by the constraint condition and the estimation error accumulation of model parameters in the inverse process, the PI inverse model based on the generalized Stop operator was proposed to compensate the PZT hysteresis. The optimal PID closed loop controller was added in the control system for the problems of the inverse hysteresis model uncertainty and the poor anti-interference ability of direct feed forward control. The adaptive differential evolution(ADE) was used to optimize the hysteresis inverse model and PID controller parameters and the chaos search mechanism was introduced to improve the performance of ADE. The experimental results show that, compared with the traditional analytic method to obtain the inverse model, the hysteresis inverse model based on the Stop operator can better describe the inverse hysteresis curve, and the fitting precision increases by 78.04% when fitting the hysteresis curve with 1 Hz frequency; the tracking accuracy of compound control algorithm increases by 38.56%,22.92% and 13.5% respectively compared with the direct feedforward control, in the real-time tracking for target swinging displacements of large-aperture piezoelectric fast steering mirror with 1 Hz,10 Hz and 20 Hz frequencies.