In this paper, a novel scheme is presented to simultaneously compensate the inherent creep and hysteresis nonlinearities of a piezoelectric actuator while positioning the Atomic Force Microscope (AFM) tip. in order to mitigate these nonlinearities, creep and hysteresis phenomenon are first modeled separately by using the classical Prandtl-Ishlinskii (PI) operator. Then, a linear time-invariant (LTI) representation is obtained to identify the creep uncertainty and subsequently an adaptive control scheme is devised for the piezoelectric actuator to track a desired path in the presence of creep. an additional dynamic inversion loop is utilized by using an online approximator to offset the hysteresis effects without the need of identifying the parameters within the hysteresis model. Rigorous performance analysis is conducted using standard Lyapunov stability approach along with simulation results.