The open-loop transfer function of the control system, which is shown in Fig. 11.2 , is as follows:

Figure 11.2

Design a proportional-integrate (PI) controller, in the form of \(G_{c}(s)=k_{p}+\frac{k_{l}}{s}\), so that the damping ratio of the closedloop system is 0.7 .

1) \(G_{c}(s)=9+\frac{27}{s}\)
2) \(G_{c}(s)=9+\frac{9}{s}\)
3) \(G_{c}(s)=1+\frac{27}{s}\)
4) \(G_{c}(s)=27+\frac{9}{s}\)

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