Physics · Control Systems
In root-locus construction, the potential real-axis breakaway or break-in points sb are obtained from the condition dK/ds = 0. When multiple values of sb are found, which of the following statements provides the necessary and sufficient algebraic test to confirm that a specific sb lies on the actual root locus?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The gain value K at s = sb, obtained from the magnitude criterion, must be real and positive.✓
- 2The second derivative, d2K/ds2 at s = sb, must be positive for a breakaway point and negative for a break-in point.
- 3The real part of sb must be less than the centroid.
- 4The total number of open-loop poles and zeros to the right of sb must be odd.
Correct answer
The gain value K at s = sb, obtained from the magnitude criterion, must be real and positive.
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