-
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
-
- – 3e– 2t + 4e – t – 1
- – 3e– 2t – 4e– t + 1
- zero
- infinity
Correct Option: A
= | ; R(s) = | |||
R(s) | (s + 2)(s + 1) | s |
∴ C(s) = | ||
(s + 1)(s + 2) |
Expanding in partial fractions
= | + | + | |||
s | s + 1 | s + 3 |
∴ k1 = | = - 1 | |
2 |
k2 = | |s=-1 = | = 4 | ||
s(s + 2) | - 1(1) |
k3 = | |s=-2 = | = - 3 | ||
s(s + 2) | - 2( - 2) |
Hence C(s) = | + | - | |||
s | s + 1 | s + 2 |
and output, c(t) = [– 1 + 4e– t – 3e– 2t] u(t).