B$-5-7.$ Consider the system shown in Figure $5-74($a$).$ The damping ratio of this system is $0\mathrm{.}158$ and the undamped natural frequency is $3\mathrm{.}16ra\frac{d}{sec}.$ To improve the relative stability, we employ tachometer feedback. Figure $5-74($b$)$ shows such a tachometer$-$feedback system.

Determine the value of $K_h$ so that the damping ratio of the system is $0\mathrm{.}5.$ Draw unit$-$step response curves of both the original and tachometer$-$feedback systems. Also draw the error$-$versus$-$time curves for the unit$-$ramp response of both systems.

rigure $5-14$

$($a$)$ Control system; $($b$)$ control system with tachometer feedback.