I have to disappoint you. Most closed loop controls - at least with factory ecu's - do NOT use a proper PID control. In some cases that would even lead to unwanted results.
With a full proper PID control the fueling could be kept on exactly lambda 1.000 almost all of the time. Unfortunately, that is unwanted because the catalyst will loose one of it's functions, which is only performed when the mixture is slightly rich.

Also look at the way the turbo boost is controlled when the intake air gets hot on Weber-Marelli ecu's. The pwm signal is modified, not the desired boost level.

I still would like to know more about the feed forward control and how to predict and smooth fuel/ignition.