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The condition of a stability for a unity feedback control system whose open loop transfer function is given by
G(s) = e–sT s(s + 2)
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- T < 2
- T = 2
- T > 2
- 0
- T < 2
Correct Option: A
Given
| G(s) = | . H(s) = 1 | |
| s(s + 2) |
We know that,
| = | ||
| R(s) | 1 + G(s)H(S) |
or
| = | ||
| R(s) | s22s - e-sT |
The C.E. s2 + 2s + e–sT = 0
or
s2 + 2s + (1 – st + st2/2! – ……) = 0
or
s2 + 2s + 1 – st = 0
or
s2 + s (2 – t) + 1 = 0
for stability 2 – T > 0
or
T < 2
