To improve the dynamic target tracking performance of optical systems based on piezoelectric fast mirrors， the effect of hysteresis nonlinearity and the corresponding compensation methods are investigated in this study. First， based on the Prandtl–Ishlinskii （P-I） model， a rate dependent hysteresis model in series with the P-I model and the auto regressive empirical model is established. Then， a rate dependent model compound control compensation algorithm based on P-I is proposed. Finally， an experimental platform using a piezoelectric fast mirror is built to identify the hysteresis effect of piezoelectric ceramics， and a feedforward controller is designed based on its inverse model. Simultaneously， the optimization effect of the hysteresis compensation method on the dynamic target tracking system is verified. The experimental results show that the rate dependent model based on P-I is suitable for moving target tracking systems. When the compound control compensation algorithm is applied， the error suppression bandwidth of the dynamic target tracking system is increased by 26 Hz. Thus， the error suppression capability of the dynamic target tracking system is effectively improved.