Consider the unity feedback of P(s) where k is a scalar gain. (please check the attached file)
Determine k such that the closed-loop system is under-damped with a damping factor of 0.5.
Finding thevalue of K that is gain using MATLAB
k ( s +2 )
T.F= s ( s+1 ) ( s +3 )
From the equation the numerator gives zero at point -2 while,
The denominator gives the poles at origin, -1 and…