A controller $D(s)$ of the form $\left(1+K_D s\right)$ is to be designed for the plant $G(s)=\frac{1000 \sqrt{2}}{s(s+10)^2}$ as shown in the figure. The value of $K_D$ that yields a phase margin of $45^{\circ}$ at the gain cross-over frequency of $10 \mathrm{rad} / \mathrm{sec}$ is _________(round off to one decimal place).

In the given figure, plant $G_p(s)=\frac{2.2}{(1+0.1 s)(1+0.4 s)(1+1.2 s)}$ and compensator $G_c(s)=K\left[\frac{1+T_1 s}{1+T_2 s}\right]$.

The external disturbance input is $D(s)$. It is desired that when the disturbance is a unit step, the steady state error should not exceed 0.1 unit. The minimum value of $K$ is ____________. . (Round off to 2 decimal places)

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

$${G_c}\left( s \right)$$ is a lead compensator if

The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

The phase of the above lead compensator is maximum at