Given the following combinations of disturbance and transfer function models:

(1) ∇???????? = (1 − 0.7????)????????

(1 − 0.4????)Y???? = 5.0????????−1+

(2) ∇???????? = (1 − 0.5????)????????

(1 − 1.2???? + 0.4????2)Y???? = (20 − 8.5)????????−1+

(3) ∇2???????? = (1 − 0.9???? + 0.5????2)????????

(1 − 0.7????)Y???? = 3.0????????−1+

(4) ∇???????? = (1 − 0.7????)????????

(1 − 0.4????)Y???? = 5.0????????−2+

(a) Design the minimum mean square error feedback control schemes associated with each combination of disturbance and transfer function model.

(b) For case (4), derive an expression for the error ???????? and for its variance in terms of

????2

????.

(c) For case (4), design a nomogram suitable for carrying out the control action manually by a process operator.