I will try to explain it the way I understand it.
You keep running the test with the same processor with the same data and wonder why the results are the same. Try running it in a Logix processor
First the scan times between the ML1400 and a Logix processor are completely different, the Logix processors are about 1000 time faster.
With the ML1400 the PID control updates when the rung is true and the update time times out
Just realised you might not have the full picture because the discussion began in a different thread. The last sentence in your quoted text above is correct if the PID is set up for a timed update. But this one is not - it's set for an STI update. This means that the output updates each and every time it's scanned, and you must put the PID in an STI routine of the same period as your specified loop update time. Otherwise, your tuning values are at the mercy of your scan time.
In the other thread I basically said that I've got a PID loop that is set up incorrectly (should be in an STI routine but is actually being scanned continuously), and I a now migrating it to a CLX where it will be set up correctly (i.e. in a periodic task). Since it has been tuned up with an incorrect loop update time, the tuning values will not directly translate, even once it is in a periodic task, because the loop update time will now be correct where previously it was not. So I want to work out how to re-calculate what the equivalent tuning values would be, if the loop update time were correct.