To mitigate the influence of hysteresis and nonlinearity in piezoelectric ceramics on the accuracy of piezoelectric micropositioning platforms, the Hammerstein model is employed to describe the frequency-dependent hysteretic nonlinearity of piezoelectric ceramic actuators. This model comprises an asymmetric Bouc-Wen model and a dynamic linear model to represent static hysteresis nonlinearity and frequency-dependent dynamic properties, respectively. Recognizing that the hysteresis compensator cannot entirely eliminate such issues and there is noise interference in experimental equipment, predictive control based on a Kalman filter is used to enhance the control accuracy of the piezoelectric micropositioning platform. Model predictive control addresses model uncertainties like inverse compensation errors and modeling errors, while the Kalman filter estimates the state of the system. Experimental results indicate that the relative tracking error of the proposed controller is less than 0.68% for sine wave signals and less than 0.70% for triangular wave signals. By incorporating Kalman filter-based predictive control alongside hysteresis compensation, the micropositioning platform effectively achieves high-precision tracking.