In this paper, a data-driven modeling-free differential-inversion-based iterative control (MFDIIC) method is proposed to compensate for both nonlinear hysteresis and dynamics of hysteresis-like hammerstein systems. Simultaneous hysteresis and dynamics compensation is challenging as hysteresis modeling, in many existing control methods, is rather complicated and prone to errors and uncertainties. The hysteresis and dynamics are coupled in affecting the output tracking, and both hysteresis and dynamics tend to change due to the variations of the system conditions (e.g., the age of smart actuators). The proposed MFDIIC technique aims to compensate for both of these effects with no needs for modeling hysteresis and/or dynamics, and achieve both precision tracking and good robustness against hysteresis/dynamics changes. The convergence of the MFDIIC algorithm is analyzed with random output disturbance/noise considered. It is shown that precision tracking can be achieved with the tracking error close to the noise level in the statistical sense. The proposed MFDIIC method is demonstrated through implementation on high-speed large-range output tracking of two different types of smart actuators with symmetric and asymmetric hysteresis behavior, respectively.