Problem 3 [(a)-4pts, (b)-6pts, (c)-2pts, (d)-6pts] In the closed-loop control system in the figure below, the fixed plant or process is given to be: 1 G(s)= (s+2)(s+10) To examine the effect of feedback performance in the system, a unit step input is applied to the system with gain K. (a) Determine the sensitivity: ST(s) in its simplest form, where T(s) = (b) For a gain K = 12, find the system response c(t), and sketch its graph, clearly labeled. (c) For a gain K = 12, what the settling time Ts of the feedback system? (d) For a gain K = 12, determine the value of the steady state error e (c) of the system response. R(s) K G(s) -> C(s) - Solution:

Fig: 1