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Let the open loop transfer function of a positive feedback closed loop system be K(sāˆ’3)/(s^2+3s+2), where K is a non-negative real valued parameter. Consider the corresponding locus of closed loop poles. Which one of the following statements is TRUE? a)The region (-āˆž, -2) lies on the root locus b)The region (-āˆž, -1) lies on the root locus c) The region (-2, -1) lies on the root locus d) The region (-1, 3) lies on the root locus

I drew the root locus of the transfer function but there are two region on real axis (-infinity,-2) and (-1,3) . But only one option is correct. What option should I choose?

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    \$\begingroup\$ You say, positive feedback. Most softwares and textbooks draw root locus for negative feedback. Are you sure the drawn locus is correct? \$\endgroup\$ – AJN Oct 27 '20 at 15:35
  • \$\begingroup\$ Yes... It's positive feedback \$\endgroup\$ – Camila's voice Oct 27 '20 at 15:44
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What you have drawn seems to be for negative feedback.

This is the result for positive feedback.

RootLocusPlot[k (s - 3)/(s^2 + 3 s + 2), {k, 0, 10}, FeedbackType -> "Positive"]

enter image description here

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