Problem 3 (15 points) Given the Nyquist plots and loop transfer functions given

Question

Problem 3 (15 points) Given the Nyquist plots and loop transfer functions given below, use the Nyquist stability criterion to determine whether the corresponding closed-loop system is BIBO stable Assume the unity negative feedback (i.e the standard feedback we studied in class). Ex plain your answers, and if the closed-loop system is not stable, state the number of unstable closed-loop poles. (8 1)( 2) (a) (5 points) L(s) (s 3)( 4) Nyquist Diagram 0.8 0.6 0.4 0.2 E 0.2 0.4 0.6 0.8 0.8 0.6 -0.4 -0.2 1.8 1.6 1.4 1.2 Real Axis

Explanation / Answer

For unstable closed loop poles , equating denominator to zero .

a)   (s + 3) = 0        ,    (s + 4) = 0

=> s = -3   , s = -4

b) (s - 3) = 0        ,    (s - 4) = 0

=> s = 3   , s = 4

c)   (s + 3) = 0        ,    (s + 4) = 0

=> s = -3   , s = -4

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