Calculate the poles and zeros of the systems with the following transfer functions. Comment on the stability of each and the expected response characteristics. 1 s + 1 s2 + 5s + 6' s+3 i) G(s) = ii) G(s) = s2 + 8s + 20 s2 + 4s + 3 s3 +5s² + 6s iii) G(s) = iv) G(s) = (s² + s – 6)(s² + 2s + 10)` (s² + 5s + 4)(s2 – 6s + 25)

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Do iv)
Calculate the poles and zeros of the systems with the following transfer functions. Comment on the
stability of each and the expected response characteristics.
1
s + 1
s+ 3
i) G(s) =
ii) G(s)
s² + 5s + 6'
s2 + 8s + 20
s2 + 4s + 3
g3 + 5s² + 6s
iii) G(s) =
iv) G(s) =
(s² + s – 6)(s² + 2s + 10)’
(s² + 5s + 4)(s² – 6s + 25)
-
Figure Q5 shows a block diagram for a feedback control system. Determine the values of the closed
loop poles and hence the stability of the system with the following combinations of controller and plant
transfer functions.
1
1
i) k(s) = K(s+ 1), K = 1, g(s) =
ii) k(s) = K(s+ 1), K = 3, g(s) =
s² + s – 2’
s² + s – 2
1
1
iii) k(s) = Ks, K = 2, g(s) =
iv) k(s) = Ks, K = 5, g(s) =
s2 – 3s + 2'
s2 – 3s + 2
R(s)
C(s)
k(s)
g(s)
Transcribed Image Text:Calculate the poles and zeros of the systems with the following transfer functions. Comment on the stability of each and the expected response characteristics. 1 s + 1 s+ 3 i) G(s) = ii) G(s) s² + 5s + 6' s2 + 8s + 20 s2 + 4s + 3 g3 + 5s² + 6s iii) G(s) = iv) G(s) = (s² + s – 6)(s² + 2s + 10)’ (s² + 5s + 4)(s² – 6s + 25) - Figure Q5 shows a block diagram for a feedback control system. Determine the values of the closed loop poles and hence the stability of the system with the following combinations of controller and plant transfer functions. 1 1 i) k(s) = K(s+ 1), K = 1, g(s) = ii) k(s) = K(s+ 1), K = 3, g(s) = s² + s – 2’ s² + s – 2 1 1 iii) k(s) = Ks, K = 2, g(s) = iv) k(s) = Ks, K = 5, g(s) = s2 – 3s + 2' s2 – 3s + 2 R(s) C(s) k(s) g(s)
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