Question: Suppose that for a unity feedback system, the forward transfer function is given by G(s) = (8 +12)/(276s + 112s2 + 1988 +84 +560): a.

Suppose that for a unity feedback system, the

Suppose that for a unity feedback system, the forward transfer function is given by G(s) = (8 +12)/(276s + 112s2 + 1988 +84 +560): a. Using vector representation of complex numbers, evaluate the closed-loop transfer function at the point s = -5+ 2i. For simplicity, let K = 1. The result must be in polar form. [3 pts] b. Show a sketch of the root locus. [3 pts] c. What are the break-in and/or breakaway points? [5 pts] d. What are the real-axis intercepts and angles of the asymptotes? [5 pts] e. What is the range of values for K so that the closed-loop system is stable? [5 pts] f. What should be the value of gain K, if a damping ratio of = 0.2 is desired? [6 pts] g. If a pole was added on the origin so that the damping ratio is still 5 = 0.2, what would be the new pole locations and the gain K? [8 pts] Suppose that for a unity feedback system, the forward transfer function is given by G(s) = (8 +12)/(276s + 112s2 + 1988 +84 +560): a. Using vector representation of complex numbers, evaluate the closed-loop transfer function at the point s = -5+ 2i. For simplicity, let K = 1. The result must be in polar form. [3 pts] b. Show a sketch of the root locus. [3 pts] c. What are the break-in and/or breakaway points? [5 pts] d. What are the real-axis intercepts and angles of the asymptotes? [5 pts] e. What is the range of values for K so that the closed-loop system is stable? [5 pts] f. What should be the value of gain K, if a damping ratio of = 0.2 is desired? [6 pts] g. If a pole was added on the origin so that the damping ratio is still 5 = 0.2, what would be the new pole locations and the gain K? [8 pts]

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