Given is a feed-forward transfer function G(s) of some system, where K is an adjustable parameter. G(s)=\frac{K}{s(s+2)} Assume you apply a unity (negative) feedback loop from the output of this system back the input. a) Find the equivalent transfer function of the closed-loop system Hea(s) b) What is the DC-gain of the closed-loop system? c) What are the values of K that result in a stable closed-loop system? d) For what values of K will the closed-loop system be critically damped / overdamped? e) Determine the damping ratio of the closed-loop system as a function of parameter K. f)Can the closed-loop system be marginally/critically stable for any value of K>0? If so, why? If not, why not? g) Find the steady-state error of the closed-loop system for the unit-step input h) Find the steady-state error of the closed loop system for the unit-ramp input

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10

Fig: 11