Consider a general closed-loop unity feedback control system shown in Figure 5.34, where \(K\) is the controller gain and \(G(s)\) is the plant Transfer Function model. Using simple rules, sketch the root loci for the two systems with the following plant Transfer Function models:

\[\begin{aligned}G & =\frac{1}{s(s+2)(s+3)} \\G(s) & =\frac{s+4}{s(s+2)(s+3)(s+5)}\end{aligned}\]

R(s) + Y(s) K G(s) Figure 5.34 Closed-loop unity feedback block diagram.