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Signals and systems electrical engineering miscellaneous

  1. The closed-loop transfer function of a control system is given by
    C(s)
    =
    2(s - 1)
    R(s)(s + 2)(s + 1)

    For a unit step input the output is
    1. – 3e– 2t + 4e – t – 1
    2. – 3e– 2t – 4e– t + 1
    3. zero
    4. infinity
Correct Option: A

C(s)
=
2(s - 1)
; R(s) =
1
R(s)(s + 2)(s + 1)s

∴ C(s) =
2(s - 1)
(s + 1)(s + 2)

Expanding in partial fractions
=
k1
+
k2
+
k3
ss + 1s + 3

∴ k1 =
- 2
= - 1
2

k2 =
2(s - 1)
|s=-1 =
2(- 2)
= 4
s(s + 2)- 1(1)

k3 =
2(s - 1)
|s=-2 =
2(- 3)
= - 3
s(s + 2)- 2( - 2)

Hence C(s) =
1
+
4
-
3
ss + 1s + 2

and output, c(t) = [– 1 + 4e– t – 3e– 2t] u(t).



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