5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given that the transfer functions of the individual blocks are: G,(s) = G,(8) = -, H,(8) = 5s, H,(s) = K . ² + 3s + 2 Using block diagram simplification techniques show that the transfer function of the system is: C(s) R(s) s'+8s + 2s + K H2 R(s) C(s) G1 G2 H1 Figure Q.5(a)

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SECTION B
5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given
that the transfer functions of the individual blocks are:
G,(s) =
G,(s) = , H,(s) = 5s, H,(s) = K .
s + 3s + 2
Using block diagram simplification techniques show that the transfer function of the
system is:
C(s)
R(s) s'+8s² + 2s + K
H2
R(s)
C(s)
G1
G2
H1
Figure Q.5(a)
b) Using Routh's Stability Criteria, determine the range of values of K to ensure that the
system shown in Figure Q.5(a) is stable.
c) A system has a characteristic equation which can be factorised to give:
(s+ 4)(s² - 4s +13) =0
Comment on the stability and characteristic response of this system.
Transcribed Image Text:SECTION B 5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given that the transfer functions of the individual blocks are: G,(s) = G,(s) = , H,(s) = 5s, H,(s) = K . s + 3s + 2 Using block diagram simplification techniques show that the transfer function of the system is: C(s) R(s) s'+8s² + 2s + K H2 R(s) C(s) G1 G2 H1 Figure Q.5(a) b) Using Routh's Stability Criteria, determine the range of values of K to ensure that the system shown in Figure Q.5(a) is stable. c) A system has a characteristic equation which can be factorised to give: (s+ 4)(s² - 4s +13) =0 Comment on the stability and characteristic response of this system.
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