Question: Consider a third-order process with G m = G v = 2 and G p = G d = 2 / (s + 2) 3

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.

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a The characteristic equation for above is shown as s 3 6s 2 12s 8 8K c 0 Substituting s ... View full answer

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