As in most applications of nanotechnology, speed and precision are important requirements for getting good topographical maps of material surfaces using Scanning Tunneling Microscopes (STM) and Atomic Force Microscopes (AFM). Many STMs and AFMs use piezoelectric tubes for scanning and positioning with nanometer resolution. In this work a piezoelectric tube of the type typically used in STMs and AFMs is considered. Scanning using this piezoelectric tube is hampered by the presence of a low-frequency resonance mode that is easily excited to produce unwanted vibrations. The presence of this low-frequency resonance mode restricts the scanning speed of the piezoelectric tube. Concept of a Positive Velocity and Position Feedback (PVPF) controller is introduced and a controller is designed to damp this undesired resonance mode. To achieve good precision, inputs are then shaped for the closed loop system to track a raster pattern. Experimental results reveal a significant damping of the resonance mode of interest, and consequently, a good tracking performance.