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Consider a root locus of the plant P(s) which satisfies P(0) = -1 shown in...
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Consider a root locus of the plant P(s) which satisfies
P(0) = -1 shown in the figures below, with the controller
C(s) being only a tunable loop gain defined as
k_L.
Figure on the left shows the overall root locus plot of P(s), while the one on the right shows the same root locus zoomed in near the Origin.
The red crosses (x) mark the open loop poles, the blue circle (o) marks the open loop zero, and the red asterisks (*) mark the closed loop poles at a particular loop gain value such that they fall on the same gray dashed line indicated in the plot. It is given also that the two complex conjugate closed loop poles are located on the imaginary axis when , while the closed loop pole on the blue-coloured branch (connects to the open loop zero) crosses over into the right half plane when . k_{L} = k_{crossover}
k_{L} = k_{A}
k_{L} = k_{B}. Note that
0 < k_{crossover} < k_{A} < k_{B} < +\infty
Three possible responses from this closed-loop system are given in the plots that follow, each with their respective labels for your easy reference to answer the question. (The plots are not drawn to the same scales.)
| Plot A | Plot B | Plot C |
|---|---|---|
Image failed to load: Response A
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Image failed to load: Response B
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Image failed to load: Response C
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Match the response plots above to each case that best describes the system response when the closed-loop pole of interest has a loop gain that is: