Example

The system stated in the figure operates with $K=164\mathrm{.}6,$ a damping ratio of $0\mathrm{.}174$ and a natural frequency of $3\mathrm{.}98ra\frac{d}{s}.$ The addition of the ideal integral compensator reduces the steady$-$state error to zero for a step input without appreciably affecting the transient response. The compensating network is chosen with a pole at the origin to increase the system type and a zero at $0\mathrm{.}1,$ close to the compensator pole, so that the angular contribution of the compensator is approximately zero.

$($a$)$ Find K

One block representation