Rules for root locus construction

The eharaeteristie equation for a elosed-loop system (5.24) may also be written as 

Sinee equation (5.54) is a veetor quantity, it ean be represented in terms of angle and magnitude as 

Equation (5.55) may be interpreted as For a point s to he on the loeus, the sum of all angles for veetors between open-loop poles (positive angles) and zeros (negative angles) to point. vi must equal 180°.  

If a point. vi lies on a loeus, then the value of the open-loop gain eonstant K at that point may be evaluated by using the magnitude eriterion. 

If there are no open-loop zeros in the transfer funetion, then the denominator of equation (5.62) is unity. 

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