Yes, I know. In past projects I have put a clamp on the effect of the integral affect on the calculation, but I wanted to leave it as simple as possible.
Yes, it would be. I've gotten that same feedback from some other people.
Interestingly, I have always tuned PID systems with the classic P followed by I followed by D. When you said I may have it reversed, I thought, "no I don't, what is he talking about?" I googled, and, in fact, found a couple examples where it is P followed by D as you suggest.
That's should be an intersting study to see which method is better suited for mobile robotics. When I get some time, I should experiment.
The problem is that neither method will be exact unless your robot is on a smooth and predictable surface. It will encounter variable surface resistance and load which will almost certainly affect response characteristics of the system.
Why are you suggesting a book?
The purpose of the essay was to describe PID for hobbyists who might not be interested in the math. It isn't that I don't know the math, but describing PID in conceptual terms as well as simple algebra (added later)
In my code, which has drifted from the text over the months, I like the idea of adding differential filtering, that's pretty easy. I was considering an "auto-tuning" version, but that would alter the code quite a bit and complicate it further.