The open-loop transfer function of the control system, shown in Fig. 11.1 , is as follows:

Design a proportional controller, in the form of \(G_{c}(s)=k_{p}\), so that the damping ratio of the closed-loop system is 0.7.

1) \(G_{c}(s)=11.25\)
2) \(G_{c}(s)=22.5\)
3) \(G_{c}(s)=5.62\)
4) \(G_{c}(s)=45\)

Figure 11.1 

G(s) 2 (s+3)(s+6)