Is there a low-cost automated pan/tilt/zoom system?
What you look for is probably a combination of the Bescor / Hague MP360 motorized pan tilt head with the CamRanger controller. CamRanger are selling the combo under their label, you can see some nice video explanations at their web site. If you don't need the extra pizzaz then you can look at just the MP360, or even the lower-end MP101 which is a great product too.

Note that these heads have a tilt limit of 30deg, so, depending on your setting, you may have to throw in a correction plate.