2. (10 points) Sketch, by hand, the root locus for the following system to inclu

Question

2. (10 points) Sketch, by hand, the root locus for the following system to include finding the real axis intercept and the asymptote angles. K(s +3) s(s + 2Xs + 4)(s + 6)(s +8)(s+1%+12) E(s) C(s) Using your sketch of the root locus, explain how you would find the following gains (you do not have to actually find the gain...yet): (a) The range of K that yields a stable closed loop system. (b) The gain K that would yield a critically damped response. (c) The gain K that yields an underdamped response with a % overshoot of43.2%. (d) The gain K that yields an undamped response. (c) The gain K the yields an overdamped response with a settling time of 8 sec.

Explanation / Answer

A) range of k is -3 to 42

B)

Critically damped response Damping constant <1

Hence k =6

C)

% overshoot = 43.2

K = 9

D)

Undamped response means K =1

K=3

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