I don't understand this comment at all. However, I am not claiming that that the integrator limit I use makes a PID equivalent to Phelan's. I am just claiming and demonstrated that a PID doesn't need to overshoot and its response will be faster because a PID has zeros which extend the bandwidth. This contradicts the advantages the pages on your webpage. BTW, the incremental ( velocity ) form of PID doesn't need to overshoot either.
By time constant, I mean the time constant of an
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ The digital world allows one to do things that can't be done in the analog world.