Consider a closed loop system as shown.

$$ G_p(s)=\frac{14.4}{s(1+0.1 s)} $$

is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}$. (Round off to 2 decimal places).

The Bode magnitude plot for the transfer function $\frac{V_0(s)}{V_i(s)}$ of the circuit is as shown. The value of $R$ is $\Omega$. (Round off to 2 decimal places)

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)

$$ \text { The state space representation of a first-order system is given as } $$

$$ \begin{aligned} & \dot{x}=-x+u \\ & y=x \end{aligned} $$

Where, $x$ is the state variable, $u$ is the control input and $y$ is the controlled output. Let $u=-k x$ be the control law, where $K$ is the controller gain. To place a closed loop pole at -2 , the value of $k$ is $\_\_\_\_$