Consider the two feedback control strategies shown in Fig. 12.6 (with G = G_vG_pG_m) and the following transfer functions:

(a) Design an IMC controller,G^ˆ—_c, using a filter, f = 1/(Ï„_cs + 1).
(b) Suppose that the IMC controller will be implemented as a controller G_c in the classical feedback control configuration of Fig.12.6(a). Derive an expression for G_c and report it in a standard form (e.g., P, PI, or PID).

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2(1 – s) G,(s) = G,(8) = 2-9, G„(s) = 1 G,(s) = 2,