Consider a third-order process with G m = G v = 2 and G p = G

Question:

Consider a third-order process with G_m = G_v = 2 and G_p = G_d = 2 / (s + 2)³.

(a) Find the roots of the characteristic equation for a proportional controller G_c = K_c for K_c = 1, 8, and 27. Classify each case as stable, unstable, or marginally stable. Derive a formula for the offset for a disturbance change as a function of K_c.
(b) Show that there is no offset for a PI controller using the Final Value Theorem for a disturbance change.