Consider a dynamic system whose plant transfer function and proportional controller are given (respectively) by

\[\begin{aligned}G(s) & =\frac{1}{20 s} \\D(s) & =K=20\end{aligned}\]

The plant is in a unity feedback arrangement with the proportional controller \(K\) as depicted in Figure 5.28.

(a) If the plant is delayed by one second, draw the new block diagram.

(b) Find the exact Transfer Function model of the delayed system.

(c) Using the first-order Pade approximation, find the approximate Transfer Function model of the system.

(d) Hence, determine whether the delayed system is stable.

Y(s) R(s) + K G(s) Figure 5.28 Closed-loop unity feedback block diagram.