One of the very latest screencasts from LearnChemE discusses the PID family of controllers, what they do, and how they work. The tutorial covers P-only, I-only, PI, D-only and PID. You can also find additional related material in the process control playlist.
If you're not familiar with the LearnChemE series, be sure to peruse the many playlists of chemical engineering topics. Topics range from thermodynamics to engineering computing and more. You can also browse topics based on popular textbooks.