Determine the closed-loop transfer function of the system shown in Figure Qla. The plant transfer functions are: (a) g1(s) = g2(s) = s+ 2 and the feedback transfer functions are: h1(s) = 0.25s 1 h2(s) = +1 R(s) C(s) 81(s) 82(s) h(s) h2(s) Figure Qla (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter 'a' for which the system shown in Figure Qlb is stable. I Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) a s+4 52 +s+9

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Determine the closed-loop transfer function of the system shown in Figure
Qla. The plant transfer functions are:
(a)
g1(s) =
92(s) =
s+ 2
and the feedback transfer functions are:
h1(s) = 0.25s
1
h2(s) =
+1
R(s)
C(s)
81(s)
82(s)
hi(s)
h2(s)
Figure Qla
(b)
(i)
Using the Routh-Hurwitz criterion, find the range of values of
parameter 'a' for which the system shown in Figure Q1b is stable. I
Is the system stable for a = 30? If not, how many positive (unstable)
poles does it have?
(ii)
R(s)
E(s)
C(s)
a
s+4
g2 +s+9
Transcribed Image Text:Determine the closed-loop transfer function of the system shown in Figure Qla. The plant transfer functions are: (a) g1(s) = 92(s) = s+ 2 and the feedback transfer functions are: h1(s) = 0.25s 1 h2(s) = +1 R(s) C(s) 81(s) 82(s) hi(s) h2(s) Figure Qla (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter 'a' for which the system shown in Figure Q1b is stable. I Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) a s+4 g2 +s+9
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