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The system shown in the given figure has a unit step input. In order to make the steady state error 0.1, the value of K required is—
-
- 0.1
- 0.9
- 1.0
- 9.0
- 0.1
Correct Option: D
Given r (t) = u (t) then
| R (s) = | |
| s |
| G(s) = | |
| (s + 1)(0.1s + 1)2 |
H (s) = 1
ess = s → 0Lim sE (s)
| = | ||
| R(s) | 1 + G(s) H(s) |
| E(s) = | |
| 1 + G(s) H(s) |
| = | |
| 1 + K/(s + 1)(0.1 + 1)2 ×1 |
| = | |
| s{(s + 1) (0.1 + 1)2 + K} |
| ess = s → 0Lim | |
| s{(s + 1) (0.1 + 1)2 + K} |
| 0·1 = | |
| (1 × 1 × K) |
or ·
1 + ·1K = 1 ·1 K = 1 – ·1 = ·9
K = 9
