In the control system, shown in Fig. 5.5 , determine the value of " \(k_{1}\) " and " \(k_{2}\)," so that the settling time ( \(2 \%\) criterion) and the peak time of the closed-loop system are \(\frac{4}{3}\) seconds and \(\frac{\pi}{4}\) seconds, respectively.

1) \(k_{1}=25, k_{2}=0.02\)
2) \(k_{1}=25, k_{2}=0.04\)
3) \(k_{1} \approx 16, k_{2}=0.02\)
4) \(k_{1} \approx 16, k_{2} \approx \frac{1}{16}\)

Figure 5.5

R(s) k s+5 k2 Y(s) S