Question: Problem 3 (30 points) A feedback system is shown in the figure below. R(s) + 10 Y(s) (s+2)(s+5) K S+K 1) Derive the root

Problem 3 (30 points) A feedback system is shown in the figure below. R(s) + 10 Y(s) (s+2)(s+5) K S+K 1) Derive the root locus equation in forms A(s) + K B(s) and 1 + KL(s). (5 points) 2) Without MATLAB, use the rules to sketch the root locus as K varies from 0 to . (10 points) 3) Find a value of K such that (OS%) Mp < 5% and ts,2% < 2.5[s]. (5 points) 4) Verify your root locus plot with MATLAB (rlocus()) and produce the step response to verify the value of K selected (step()). (10 points)

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