Problem $7$

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.

$($b$)$

Figure $5-74($a$)$ Control system; $($b$)$ control system with tachometer feedback.