Dynamics and Tuning of Systems with Large Delay

It is shown that for a general class of resonant systems, the cross-over frequency exhibits a discontinuous dependence on the process delay. This implies that Ziegler-Nichols type tuning techniques, which make explicit use of the cross-over frequency, will not be robust to errors/perturbations in the delay. For nonresonant systems with a cross-over frequency that depends on the delay continuously, we propose a new tuning rule for PI controllers that is superior to the classical Ziegler-Nichols and Cohen-Coon methods and show that it rapidly approaches the optimal ISE at large delay.