GATE EC 2014 Set 4 — Question 58
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
The characteristic equation of a unity negative feedback system is . The open loop transfer function has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.
The constant damping ratio line, for , intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of at point A is ________.
Correct answer
0.32 to 0.41
Solution
The open loop transfer function is . The characteristic equation is , which gives .Point A lies on the root locus where the damping ratio and the radial distance from the origin is . In the s-plane, the location of point A is given by:
where .Thus, .To find the value of at point A, we apply the magnitude condition :Calculating the magnitudes:
.
where .Thus, .To find the value of at point A, we apply the magnitude condition :Calculating the magnitudes:
1.
2.
3.
Substituting these values:.
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