To address the challenges of hysteresis nonlinearity and low-damping resonant vibrations in piezoelectric micro-positioning platforms, a Hammerstein mathematical model is developed to describe the system. Bouc-Wen inverse hysteresis model is employed for feedforward compensation, effectively reducing the hysteresis nonlinearity. To mitigate the effects of low-damping resonant vibrations, a pole placement controller is designed based on state feedback, increasing the system bandwidth by 39.07 Hz. Additionally, to minimize the steady-state error introduced by the pole placement strategy, a proportional controller is tuned using frequency-domain analysis to optimize the proportional gain. Experimental validation on the micro-positioning platform shows that for a 50 Hz sinusoidal reference signal with a maximum stroke of 42.14 µm, the maximum steady-state tracking error is only 1.855 µm, achieving a tracking accuracy of 95.598%.