-
Given G(s) = 1 - Is s(s + 2)
The system with the transfer function is operated in a close-loop with unity feedback. The closed loop system is—
-
- stable
- unstable
- marginally stable
- conditionally stable
- stable
Correct Option: A
Given
| G(s) = | |
| s(s + 2) |
H (s) = 1
| T.F. = | = | ||
| R(s) | 1 + G(s) H(s) |
| = | ||
| R(s) | 1 + (1 - s)/s(s + 2)× 1 |
| = | ||
| R(s) | s2 + 2s + 1 - s |
| = | ||
| R(s) | s2 + s + 1 |
the C.E. equation = s2 + s + 1
R.H.C.
s2 1 1
s1 1 0
s0 1
since all the element in the first column are positive hence the system is stable. Alternative (A) is the correct answer.
NOTE : In such type of questions on seeing first time it seems to be unstable system, as we realize that one zero in the R.H.S., so the system will be unstable, but actually not.
