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There is a need, in the wide ranging scientific community, to perform fast scans using scanning tunneling microscopes (STMs) and atomic force microscopes (AFMs) with nanoscale precision. In this paper, a piezoelectric tube of the type typically used in STMs and AFMs is considered. The resonant mode that hampers the fast scanning is identified and damped using a feedback control technique known as integral resonant control (IRC). The piezoelectric tube is then actuated to perform fast and accurate scans. IRC is a new feedback control technique suitable for damping highly resonant structures. Here, the IRC control technique is suitably modified to damp the resonance of a piezoelectric tube and achieve fast tracking of a wideband set point.