A unity feedback system has

$1$

$15,()()()=++$

G s s s s

with a phase$-$lead compensator

G s K s

s c$()()=+$

$+$

$2$

$15.$

Determine K so that the complex roots have

$=12.$ Consider the prefilter

G s $.$ p

s p $($a$)$ Determine the percent overshoot and rise time

for G s p$()=1$ and for p $=1.($b$)$ Select an appropriate

value for p that will give an overshoot of P O$..1\%,$

and compare the results.