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splane6

# splane6 - Rening the root locus sketch We have covered the...

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Refining the root locus sketch We have covered the rules for a rapid sketch of the root locus. For full use of the sketch we need to calculate the points of interest of the sketch, point on the real axis where the root locus enters or leaves the complex plane–real- axis breakaway and break-in points –and the axis crossings, and angles of departure and arrival. Real axis breakaway and break-in points Looking at the locus sketch below we can see a breakaway point point at - σ 1 and a break-in point at - σ 2 . 1

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Root Locus Real Axis Imag Axis -2 -1 0 1 2 3 4 5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 5 σ 2 σ 1 -1 -2 At the breakaway or break-in point the branches form an angle of 180 o /n with the real axis, where n is the number of branches, i.e. num- ber of closed poles arriving at or departing from that point. For the example above there are two such poles leading to an angle of 90 o . 2
As the two closed loop poles, at - 1 and - 2 when K = 0, moves towards each other, the gain increases from a value of zero.

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splane6 - Rening the root locus sketch We have covered the...

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