Determine the closed-loop transfer function of the system shc Q3a. The plant transfer functions are: (a) 1 g1(s) =41 4 g2(s) = s+2 and the feedback transfer functions are: h1(s) = 0.25s 1 h2(s) s+1 R(s) CC 81(s) 82(s) h(s) h2(s) Figure Q3a

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Q3
(а)
Determine the closed-loop transfer function of the system shown in Figure
Q3a. The plant transfer functions are:
g1(s) =
s)%3D
g2 +1
4
g2(s) =
s+2
and the feedback transfer functions are:
h1(s) = 0.25s
h2(s) =
s+1
R(s)
C(s)
g1(s)
> 82(s)
h(s) +
h2(s)
Figure Q3a
(b)
(i)
Using the Routh-Hurwitz criterion, find the range of values of parameter
*a' for which the system shown in Figure Q3b is stable.
Is the system stable for a = 30? If not, how many positive (unstable)
poles does it have?
(ii)
R(s)
E(s)
C(s)
s+4
6+s+ 2s
Figure Q3b
Transcribed Image Text:Q3 (а) Determine the closed-loop transfer function of the system shown in Figure Q3a. The plant transfer functions are: g1(s) = s)%3D g2 +1 4 g2(s) = s+2 and the feedback transfer functions are: h1(s) = 0.25s h2(s) = s+1 R(s) C(s) g1(s) > 82(s) h(s) + h2(s) Figure Q3a (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter *a' for which the system shown in Figure Q3b is stable. Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) s+4 6+s+ 2s Figure Q3b
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