Problem 1: [50 points] Consider the unity negative feedback closed loop system R(s) K G(s) Y(s) where the transfer funct

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Problem 1 50 Points Consider The Unity Negative Feedback Closed Loop System R S K G S Y S Where The Transfer Funct 1 (56.47 KiB) Viewed 58 times

Problem 1: [50 points] Consider the unity negative feedback closed loop system R(s) K G(s) Y(s) where the transfer function G(s) is given by G(s) = (s+3)(s+4) (s+2)(s² +2s+5) The parameter K is a simple gain which can be varied. Sketch the root locus of the system as K varies from 0 to - Perform all the necessary calculations to determine the features of the root locus. Explain all your steps. Also, using the root locus methodology, determine a range for K within (-0, 0] such that the closed loop system is stable. (If the necessary calculations are not provided and explained the sketched root locus and the obtained stability result will not be evaluated even if its correct.)