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In this brief, the compensation for both the nonlinear hysteresis and the vibrational dynamics effects of piezo actuators is studied. Piezo actuators are the enabling device in many applications such as atomic force microscopy (AFM) to provide nano- to atomic-levels precision positioning. During high-speed, large-range positioning, however, large positioning errors can be generated due to the combined hysteresis and dynamics effects of piezo actuators, making it challenging to achieve precision positioning. The main contribution of this brief is the use of an inversion-based iterative control (IIC) technique to compensate for both the hysteresis and vibrational dynamics effects of piezo actuators. The convergence of the IIC algorithm is investigated by capturing the input-output behavior of piezo actuators with a cascade model consisting of a rate-independent hysteresis at the input followed by the dynamics part of the system. The size of the hysteresis and the vibrational dynamics variations that can be compensated for (by using the IIC method) is quantified. The IIC approach is illustrated through experiments on a piezotube actuator used for positioning on an AFM system. Experimental results show that high-speed, large-range precision positioning can be achieved by using the proposed IIC technique. Furthermore, the proposed IIC algorithm is also applied to experimentally validate the cascade model and the rate-independence of the hysteresis effect of the piezo actuator.