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Consider a closed loop system shown in figure (a) below. The root locus for it is shown in figure (b). The closed-loop transfer function for the system is—
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K 1 + (0·5s + 1) (10s + 1)
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K (s + 2) (s + 0·1)
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K 1 + K (0·5s + 1) (10s + 1)
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K K + (0·5s + 1) (10s + 1)
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Correct Option: D
From root locus, the poles of G(s) lie at s = – 0·1 and s = – 2.
Hence we can have G(s) of the form KG(s) F
| = | |
| (0·5s + 1) (10s + 1) |
Hence the closed-loop transfer function
| = | |
| R(s) |
| = | |
| 1 + KG(s) H(s) |
Since, H(s) = 1, we have
| = | ||
| R(s) | 1 + KG(s) |
| = | |
| 1 + K/(0·5s + 1) (10s + 1) |
| = | |
| (0·5s + 1) (10s + 1) + K |
Hence (D) is the correct choice.
