This paper proposes a model-based adaptive control methodology for piezoelectric actuation systems to follow specified motion trajectories. This is motivated by a search for an effective control strategy to deal with the problem of parametric uncertainties such as disturbance and hysteresis effects. The proposed adaptive law is formulated by combining a parameter compensator and a conventional PD feedback control for a system to drive its position tracking error converging to zero. The fundamental concept lies in the properties of a quasinatural potential function, which allows a saturated position error function in the control formulation. Implementation of the control law requires only the knowledge of initial estimate of the system parameters. Control experiments conducted using the proposed control law on a piezoelectric actuator (PEA) system has demonstrated promising tracking ability in following a specified motion trajectory. Being capable of motion tracking under unknown system parameters and uncertainties due to disturbance and hysteresis, the adaptive control law is very attractive in the field of micro/nano manipulation in which high performance PEA control applications could be realised.