Question: (a) Consider the following unity-feedback system shown in the below figure, where 1 G(s) = = (s+1)(s+4)(s+10) 10 8 0.6 0.8 40 Imaginary Axis

Consider the following unity-feedback system shown in the below figure, where G(s) = R(s) 0 (a) Imaginary

(a) Consider the following unity-feedback system shown in the below figure, where 1 G(s) = = (s+1)(s+4)(s+10) 10 8 0.6 0.8 40 Imaginary Axis (seconds) 24 6 * 23 + 1 s3+15s+54s+40 0.4 0.2 R(s) K G(s) + Y(s) Point K P A 17.04 -2.25 B 39.55 -2.19+1.64i 10 8 4 A2 C 77.82 -1.96+2.61i D 150.1 -1.61+3.68i E 310.1-1.04+5.10i F 770 + 7.35i 0.8 0.6 0.4 0.2 -10 -12 -10 -8 -6 -4 -2 0 Real Axis (seconds) Find the range of gain K, which makes the system stable. (i) from the graph and table (ii) using Routh-Hurwitz criteria.

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