Radar servo velocity error coefficient

For a type-1 system with a ramp input of slope $\omega$ (constant angular velocity), the steady-state error is $e_{ss} = \frac{\omega}{K_v}$. So the required $K_v = \frac{\omega}{e_{ss,\max}}$.

Angular velocity of the line of sight

The antenna must turn at the angular rate of the aeroplane as seen from the radar:

$$\begin{aligned} v &= 600\ \text{km/h} = \frac{600\times1000}{3600} = 166.67\ \text{m/s} \\ \omega &= \frac{v}{r} = \frac{166.67}{2000} = 0.08333\ \text{rad/s} \\ &= 0.08333\times\frac{180}{\pi} = 4.775^\circ/\text{s} \end{aligned}$$

So the input to the servo is a ramp $\theta_r(t) = 4.775\,t$ degrees.

Velocity error coefficient

For $G(s)=\frac{K_v}{s(1+sT)}$ (type 1):

$$\lim_{s\to0}sG(s) = K_v$$ $$e_{ss} = \frac{\omega}{K_v} \le 0.1^\circ \quad\Rightarrow\quad K_v \ge \frac{4.775}{0.1} = 47.75\ \text{s}^{-1}$$

Answer: Required velocity error coefficient $K_v \ge 47.75\ \text{s}^{-1}$ (about $48\ \text{s}^{-1}$).