Question: Q 2 . Consider the unity negative feedback system with the open - loop transfer function given as G ( s ) = [ 2

Q2. Consider the unity negative feedback system with the open-loop transfer function given as
G(s)=[2(s+K)]/[(s^2+3s+K)(s+1)]
a. Sketch the root locus for K0 with all the detalls like break-away/in points and imaginary axis crossings.
b. Based on the root locus, what can you say about the behavior of the frequency of oscillations observed in the step-response of the closed-loop system, i.e., does it increase/decrease/remain constant? Explain you answer.
c. Based on your root locus, find the minimum settling-time (2%) the closed-loop system can have. Hint: For this system, the minimum settling-time is reached when all three closed-loop poles have the same real part.
Q 2 . Consider the unity negative feedback system

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