The open loop transfer function of a unity feedback control system is given as $$G\left( s \right) = {{as + 1} \over {{s^2}}}.$$. The value of $$‘a’$$ to give a phase margin of $${45^0}$$ is equal to

The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ gain at a frequency of $$\omega = 0.5a$$ are respectively

The function corresponding to the Bode plot of Figure, is

A unity feedback system with the open loop transfer function $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}$$ has gain margin of ... $$dB.$$