In this study, the Coleman-hysteresis model is utilised in the piezoelectric actuator (PZTA) dynamic model and a non-linear robust control strategy is then developed to actively control the displacement of the PZTA effective tip. The proposed control technique is designed based on the partial knowledge of the hysteresis model while the mass of the PZTA is assumed to be uncertain. The piezoelectric charge measurement is utilised in the controller design to reduce the effects of the hysteresis. Lyapunov-based stability analysis techniques are utilised to ensure that a desired displacement trajectory is accurately tracked. Representative numerical results are presented and discussed to demonstrate the tracking performance of several desired displacement trajectories with different frequencies and amplitudes. Finally, comparisons with a standard PID controller and a sliding mode controller were performed to examine the effectiveness of the proposed control design.