A new method for analyzing tapping mode atomic force microscopy (AFM) is described. This method uses an automatic resonance-tracking control scheme and a hybrid model to improve the accuracy and speed of topography reconstruction by considering the interactions between the AFM tip and the measured sample. A simplified model captures the complex dynamical behavior and eliminates the need to lock onto the reference distance at every measurement point. The accuracy of this method was verified through numerical simulation of Van der Waals and capillary interaction forces, as well as experimental measurements of a coin's topography.