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Please answer all 3 questions correctly as they all revolve around question 1.

Print Name Seat No ECE431 Test 2 November 14, 2016 Closed book exam. No books, notes, or other reference material permitted. No computers, cellphones, or similar devices permitted. Calculators are permitted Problem 1 The closed-loop transfer function of a certain linear system is KF(s) H(s) HK() with s2 +8s 52 (s + 4)2 +36 s(s3 +6s2 28s 40) s(s2)(s2)2 +16 Find the range (if any) of the forward gain K for which the closed-loop system is stable. Problem 2 Sketch the locus of poles of the system of Problem 1, showing important parameters, including segments (if any) on the real axis * crossings (if any) of the imaginary axis asymptotes as K-+ oo Problem 3 Sketch the Nyquist diagram for F(s) of the system of Problem 1, showing important properties, including » behavior as w0 behavior as u -, oo crossings (if any) of the real axis » crossings (if any) of the imaginary axis region of stability

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