splane5

# splane5 - Sketching the root locus We can see that the root...

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Sketching the root locus We can see that the root locus can be plot- ted by locating the points in the s-plane for which the angles add up to an odd multiple of 180 o . We can now construct rules for sketch- ing a root locus, plotting any point of interest if required. Rule 1: Number of branches: The number of branches of the root locus equals the number of closed loop poles. Why: Each closed loop poles moves as the gain is varied. If we deﬁne a branch as the path that one pole traverses; 1

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Rule 2: Symmetry: The root locus is sym- metrical about the real axis . Why: If complex poles didn’t exist in conjugate pairs, the resulting polynomial would contain complex coeﬃcients, impossible in physically realistic system; Rule 3: Real axis segments: On the real axis, for K> 0 , the root locus exist to the left of an odd number of real axis, ﬁ- nite open-loop poles and/or ﬁnite open- loop zeros. PP j ϖ 43 2 P P 1 Figure: Poles and zeros of a general open loop system with test points, P i , on the real axis.
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splane5 - Sketching the root locus We can see that the root...

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