The open-loop transfer function of a control system that includes a negative unity feedback is as follows:

Determine the proportional controller gain \(\left(k_{P}ight)\) for a proportional-integral-derivative (PID) controller in ZieglerNichols's method.

1) \(\frac{T_{1}+T_{2}}{T_{1} T_{2}}\)
2) \(\frac{5\left(T_{1}+T_{2}ight)}{3 T_{1} T_{2}}\)
3) \(\frac{3 T_{1} T_{2}}{5\left(T_{1}+T_{2}ight)}\)
4) \(\frac{3\left(T_{1}+T_{2}ight)}{5 T_{1} T_{2}}\)

k G(s)= s(1+Ts)(1 + T28)