The unimorph deformable mirror (DM) is widely applied in adaptive optics, which utilizes the lateral reverse piezoelectric effect of piezoelectric ceramics to drive the mirror to deform. The hysteresis curve of the deformable mirror is a special "butterfly shape" in the high electric field strength, which increases the difficulty of control, and the deformable mirror cannot work normally. The theory of piezoelectric ceramic polarization and the hysteresis loop of ferroelectric materials were analyzed so that the cause of the butterfly curve could be confirmed. The experimental results show that the covariate field of the DM is between -500 and -400 V/mm, and the hysteresis curve is normalized willow shape. Then a static PID closed loop correction system was designed for the characteristics of the hysteresis curve, and the correction experiment was carried out. The results show that the linearity is obviously improved, and the hysteresis rate is reduced to 1.8% by the PID closed loop correction.