2- (10 points) Consider the following feedback system, C(s) R(s) 1 + K $312 s2 +44 s + 48 a) Design a Lag compensator that will yield a steady-state error of 0.48 without appreciable changing of the dominant pole location that yields a 10%OS. Place the compensator's pole at -0.01. b) Plot the root locus of the uncompensated system and find the dominant's poles, gain and settling time c) Plot the root locus of the compensated system and find the dominant's poles, gain and settling time d) Plot the step response of the uncompensated and the compensated systems on the same plot. e) Compare the transient and steady-state performance of the uncompensated and compensated systems f) Describe any problems with your design