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Lecture notes - School Of Electrical & Electronic Engineering - USM

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Root Locus<br />

Bode Plot<br />

Example on Root Locus<br />

Rules of sketching ROOT LOCI<br />

overview<br />

general rules of Root Loci sketching<br />

The intersection of the root loci with the unit circle |z| = 1<br />

can be found by using the extended R-H or Jury’s stability<br />

test.<br />

The magnitude criterion enables us to determine the value<br />

of the gain K at any specific root location on the locus. The<br />

gain K can be found as follows:<br />

K =<br />

(z + p 1 )(z + p 2 ) . . . (z + p n )<br />

∣ (z + z 1 )(z + z 2 ) . . . (z + z m ) ∣ (8)<br />

Given the value of the gain, the closed loop pole for that<br />

gain can also be found by using the same formula.<br />

nasiruddin@eng.usm.my EEE 354 : STABILITY ANALYSIS TECHNIQUES

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