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Question 4 (25 marks) and plant a) Consider the feedback system in Figure 04 with controller G,(s) = K 5+ 100 G,(s) Specify K and a of Ge(s) such that the overall closed-loop response to a $+25 unity step reference input has a maximum percentage overshoot (XOS) of 25% and a 1% settling time of 0.1sec. (Hint: use the approximate relationship %OS 1 s X100% ] 0.6 [10 marks] =(1- b) To make the steady-state error to a unit step reference input zero, add an integrator to к the controller of Q4a, i.e. Ge(s) Assuming that a has the value derived in s(s+a) Q4a do the following: (1) Draw the root-locus of the closed-loop system, ask takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (10 marks) (1) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis. (5 marks] Ris) + Els Y(s) Ge(s) G (s) Figure 04: Unity feedback system END OF PAPER