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In the unity feedback system shown below, the value of derivative feedback constant a, which will increase the damping ratio of the system to 0.7 is—
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- 0.152
- 0.245
- 0.353
- 0.558
- 0.152
Correct Option: B
On solving block 2
| = | ||
| R′(s) | 1+8/s(s+2).as |
| = | ||
| R′(s) | s2 + s (8a + 2) |
Now, again simplifying block 1
| = | ||
| R′(s) | 8/s2 + s (8a + 2).1 + 1 |
| = | |
| s2 + (8a + 2)s + 8 |
C.E. is s2 + (2 + 8a) s + 8 = 0
on comparing with the standard equation
s2 + 2 ξ ωns + ωn2 = 0
ωn2 = 8 ⇒ ωn = 2√2
2 ξ ωn = 2 + 8a
or
| ξ = | ⇒ 0·7 = | ||
| 2.ωn | 2.2√2 |
on solving we get a = 0.245
