Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or unstable, and how many roots lie in the left-hand plane of the s-plane diagram. s3 + 2s2 + 6 (1) T(s) = s5 + 6s3 + 5s² + 8s + 20 1 (ii) T(s) = %3D 2s2 + 5s3 + s2 + 2s + 1 (b) For the negative closed loop feedback system with an open loop gain G(s) and a feedback gain H(s) = 1, where (s – a) s(s + b) G(s) = determine the range of values for the gain K when (i) a < 0 and b << 0, and (ii) a > 0 and b > 0.
Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or unstable, and how many roots lie in the left-hand plane of the s-plane diagram. s3 + 2s2 + 6 (1) T(s) = s5 + 6s3 + 5s² + 8s + 20 1 (ii) T(s) = %3D 2s2 + 5s3 + s2 + 2s + 1 (b) For the negative closed loop feedback system with an open loop gain G(s) and a feedback gain H(s) = 1, where (s – a) s(s + b) G(s) = determine the range of values for the gain K when (i) a < 0 and b << 0, and (ii) a > 0 and b > 0.
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![Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or
unstable, and how many roots lie in the left-hand plane of the s-plane diagram.
s3 + 2s2 + 6
(i)
T(s)
s5 + 6s3 + 5s² + 8s + 20
1
(ii)
T(s) =
2s2 + 5s3 + s² + 2s + 1
(b) For the negative closed loop feedback system with an open loop gain G(s) and a
feedback gain H(s) = 1, where
%3D
(s - а)
G(s) = K
s(s + b)
determine the range of values for the gain K when (i) a < 0 and b < 0, and (ii)
a > 0 and b > 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06847163-8975-4eaa-881b-b5abcc2aeaff%2F10ac2f2b-6be5-438b-9551-edb157d40743%2Fve9lkys_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q.5 (a) Using the Routh-Hurwitz crition, determine if the following systems are stable or
unstable, and how many roots lie in the left-hand plane of the s-plane diagram.
s3 + 2s2 + 6
(i)
T(s)
s5 + 6s3 + 5s² + 8s + 20
1
(ii)
T(s) =
2s2 + 5s3 + s² + 2s + 1
(b) For the negative closed loop feedback system with an open loop gain G(s) and a
feedback gain H(s) = 1, where
%3D
(s - а)
G(s) = K
s(s + b)
determine the range of values for the gain K when (i) a < 0 and b < 0, and (ii)
a > 0 and b > 0.
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