Determine the value of parameters " \(a\) " and " \(b\)," so that the control system, shown in Fig. 5.2 , has the fastest response without any damping oscillation to a unit step function.

1) \(\left\{\begin{array}{l}a^{2}-4 b0\end{array}ight.\)
2) \(\left\{\begin{array}{l}a^{2}-4 b=28 \\ a>0\end{array}ight.\)
3) \(\left\{\begin{array}{l}a^{2}-4 b0 \\ b>-7\end{array}ight.\)
4) \(\left\{\begin{array}{l}a^{2}-4 b=28 \\ a>0 \\ b>-7\end{array}ight.\)

Figure 5.2

R(s)- 7 s+as+b C(s)