PID Tutorial

As most know the subject of PID varies dependent on application. A motion application and a temperature application can vary greatly in the values used even though the algorithm is the similar.

I have many links to many sites pertaining to PID. I know the act of using PID involves an advanced knowledge/skills and familiarity to understand and work with.

What I am looking for is a "fair" turtorial covering the basics, not something reciting math formulas but does state them and explains theM.

Again I ask the impossible but to anyone willing to tackle this endeavor I will be highly appreciative

You posted one of my favorite links for explaining PIDs.

U of M Control Tutorial

What part don't you understand? This link does skip a step when it goes from open loop to close loop with only proportional gains. It assumes one knows how the PID gains are combined with the open loop system to get a transfer function. This page makes no sense if one does not know what the s is all about.