I'm not really sure what you mean. The system uses a real time clock and the commanded position is based on the time of day, so in effect it is doing 1 rotation every 24 hours.
Right now it uses an equation to work out the suns position, but I think a better way to do it is have the machine running in celestial coordinates and use a kinematic transformation to drive the motors. That way other targets could be easily added ie the moon at night.
As for resolution this is defined by the gearing used. The gear on the azimuth (horizontal) axis is much bigger as the beam shines through a hole in its center. current design gives resolutions of :
Elevation mirror 0.23 deg/step
Azimuth axis 0.04 deg/step