A stable closed loop control system with PI controller is shown below,

The suitable values of controller parameters are

K_{p} > 0 a n d K_{I} > \frac{K_{p}}{3} - 3

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K_{I} > 0 a n d K_{p} > (\frac{K_{I}}{3} - 2)

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K_{I} > \frac{K_{p}}{3} - 2 (o r) K_{p} > 0

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K_{I} > 0, K_{p} > 0

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Solution

The correct option is B $K_{I} > 0 a n d K_{p} > (\frac{K_{I}}{3} - 2)$
The characteristic equation is

$1 + G (s) H (s) = 0$
$1 + (K_{P} + \frac{K_{I}}{s}) (\frac{1}{(s + 1) (s + 2)}) = 0$

(or) $s^{3} + 3 s^{2} + (2 + K_{p}) s + K_{I} = 0$

Forming Routh Array:

For stable system, $K_{I} > 0$
and $K_{p} > \frac{K_{I}}{3} - 2$

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