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The open-loop transfer function with unity feedback are given below for different systems
1. G(s) = 2 s + 2 2. G(s) = 2 s(s + 2) 3. G(s) = 2 s2(s + 2) 4. G(s) = 2(s + 1) s(s + 2)
Among these systems, the unstable system is—
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- 1
- 2
- 3
- 4
- 1
Correct Option: C
In order to check the stability of the system, apply R.H.C.
Given
H(s) = 1
For 1st system
| G(s) = | |
| (s + 2) |
| C.E. = 1 + G(s) H(s) = 1 + | 1 = s + 4 = 0 stable | |
| s + 2 |
For 2nd system
| G(s) = 1 | |
| s(s + 2) |
C.E. = 1 + G(s) H(s) = 0
| = 1 + | . 1 = s2 + 2s + 2 = 0 | |
| s(s + 2) |
s2 1 2
s1 2 0
s0 3
Hence system is stable.
for 3rd system
| G(s) = | |
| s2(s + 2) |
C.E. = 1 + G(s) H(s) = 0
| 1 + | . 1 = s3 + 2s2 + 2 = 0 | |
| s(s + 2) |
From this expression we see that there is one missing form (i.e., s).
Hence the system is unstable.
