watched these guys:
https://www.youtube.com/watch?v=SefKQb9y_B4https://www.youtube.com/watch?v=16Clfh5eBzg&t=944sand read a bit and came up with this:
Derivative works on the rate of change of error in order to approach the setpoint slower, over and undershoot the setpoint fewer times and to overshoot and undershoot the setpoint to a smaller degree.
so, keeping with the same example, the LED is looking to achieve a setpoint of 75% DC. If the Proportional gain is adjusted properly the setpoint will be reached with an acceptable reaction time and will hunt a minimal of times. The derivative gain can be adjusted to reach setpoint with fewer hunts and less over and undershoot amount. The downside of this tends to be a slowing of the reaction time near approaching the setpoint.
Integral gain works to cover the rest by closing the remaining error gap by adding smaller amounts of DC until the setpoint is reached.
I now understand that as the setpoint changes, the PID functions are used together and separately, depending on how easily the setpoint is to reach. I always thought these had an operative order, P, I, then D and were always computed and reacting in that order, that is not necessarily true. I also thought they were all being computed every time the setpoint changed, that is not necessarily true either.
I'm trying to understand how their root words of derivative (to derive, or to copy/obtain from something else) and integral (integer, a whole number) pertain to the functional operation they perform, as I am expected to fully understand the concept for my employment as of late, unrelated to automotive application.
I'm still getting a grasp on the fundamental mathematics of how these work and interact but I think I have it.