This article considers the precision positioning problem associated with high-speed operation of the Atomic Force Microscope (AFM), and presents an inversion-based control approach to achieve precision positioning. Although AFMs have high (nanoscale) spatial resolution, a problem with current AFM systems is that they have low temporal resolution, i.e., AFM imaging is slow. In particular, current AFM imaging cannot be used to provide three-dimensional, time-lapse images of fast processes when imaging relatively-large, soft samples. For instance, current AFM imaging of living cells takes 1-2 minutes (per image frame) - such imaging speeds are too slow to study rapid biological processes that occur in seconds, e.g., to investigate the rapid movement of cells or the fast dehydration and denaturation of collagen. This inability, to rapidly image fast biological processes, motivates our current research to increase the operating speed of the AFM. We apply an inversion-based feedback/feedforward control approach to overcome positioning problems that limit the operating speed of current AFM systems. The efficacy of the method, to achieve high-speed AFM operation, is experimentally evaluated by applying it to image collagen samples.