I'm looking for a good introduction to Discrete Time Control Theory which includes model based control.  Is there a book or online resource that would be good for learning this?

This article is a good introduction to digital control systems:

https://www.ifac-control.org/publications/list-of-professional-briefs/pb_wittenmark_etal_final.pdf/view

"Digital Control of Dynamic Systems" by Gene F. Franklin, and others is also a classic textbook on the topic.

For PID system, a very good explanation from Tim Wescott:

https://www.dsprelated.com/showarticle/943/pid-without-a-phd