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The open-loop transfer function of a unity feedback control system is
G(s) H(s) = 30 s(s + 1)(s + T)
where T is a variable parameter. The closed-loop system will be stable for all values of
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- T > 0
- 0 < T < 3
- T > 5
- 3 < T < 4
Correct Option: C
| G(s) H(s) = | ||
| s(s + 1)(s + T) |
The characteristics equation becomes
s (s + 1) (s + T) + 30 = 0
⇒ s3 + s2 (1 + T) + sT + 30 = 0
Constructing Routh Tables
(1 + T) > 0 or T > – 1
| ∴ | > 0 | |
| 1 + T |
| ⇒ | > 0 | |
| (1 + T) |
⇒ T > – 6, or T > 5
Therefore T > 5
