Consider the control strategy structures shown in Fig. D1.5 (a) and (b). Given nominal value of \(K=1\), show that both have same transfer function \(C(s) / X(s)\). Evaluate \(\left|S_{K}^{T} \right|\) for both at \(\omega=5 \mathrm{rad} / \mathrm{sec}\) and comment on result. Does information about sensitivity provide any clue to the selection of a particular control strategy?

x(t)- x(1) +41 25 (x + 1) s+5 25 + (a) (b) Controlled system K s (s + 1) G(s)= Controlled system G(s) = K s(s+1) 4s c(t) c(t)