The design and implementation of an antenna beam-waveguide (BWG) mirror position control system at the DSS-13 34-m antenna is presented. While it has several potential applications, a positioner on the last flat-plate BWG mirror (M6) at DSS 13 is installed to demonstrate the conical scan (conscan) angle-tracking technique at the Ka-band (32-GHz) operating frequency. Radio frequency (RF) beam-scanning predictions for the M6 mirror, computed from a diffraction analysis, are presented. From these predictions, position control system requirements are then derived. The final mechanical positioner and servo system designs, as implemented at DSS 13, are illustrated with detailed design descriptions given in the appendices. Preliminary measurements of antenna Ka-band beam scan versus M6 mirror tilt made at DSS 13 in December 1993 are presented. After reduction, the initial measurements are shown to be in agreement with the RF predicts. Plans for preliminary conscan experimentation at DSS 13 are summarized.