The parallel form of the PID controller has the transfer function given by Eq. 8-14. Many commercial analog controllers can be described by the series form given by Eq. 8-15.
(a) For the simplest case, α → 0, find the relations between the settings for the parallel form (K†c, τ†1, τ†D) and the settings for the series form (Kc, τ1, τD).
(b) Does the series torte make each controller setting (Kc, τ1, or τD) larger or smaller than would be expected for the parallel form?
(c) What are the magnitudes of these interaction effects for Kc = τ1 = 10 min, τD = 2 mm?
(d) What can you say about die effect of nonzero on these relations? (Discuss only first-order effects.)