# Sketch root locus

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Lecture : 23 Sketch root locus

Lecture : 23Sketch root locus

Presented By :Mirza asif haiderId:1308023

Department of Electronics and Telecommunication Engineering. Chittagong University of Engineering and Technology

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Before starting Poles and zerosRoot locus

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Poles & zerosPOLES:In a Transfer Function: >Which Value Causes The Function to become Infinity ZEROS:In a Transfer Function:>Which Value Causes The Function to become zero

the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively13080233Consider the transfer function:

H(s)=

S+2

S + .252=0We have a Zero at s> -2Poles at : -i/2 and +i/2

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ROOT locus

13080234(Here K is an unknown parameter)

Root locus13080235Now We have Two Questions

DesignEffects of VariationsWhat value ok K should one Choose to meet the Systems Performance RequirementsWhat is the Effect of a variation of K on the System ?For random value of k:XXXXXXXXX

..Repeating the process : k

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XXXXXXXXS is a real valueS corresponds a exponential increase or decay decayincreaseS- planeIma(w)Real()Root locuszerosSystem =--------polesstability

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An open loop transfer function:

One pole is on the right hand plane

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Ploting by matlabHow poles and zeros effect the root locus comes from understanding this rules by how to draw them by hand

13080239Example:A Classic Way to setup a root locus problem is like this:

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Q(s)Here G(s)=--------P(s)

There are 10 rules of sketching or drawing a Root locus :

Start From This Form , 1+K G(s) = 0 Q( s) or, 1 + K -------------- P (s)

130802311Sketching Root Locus :RULE No. 1There are n lines where n is the degree of Q or P , which one is greater Q(s)Here G(s)=--------P(s)

So there will be 3 lines

130802312As K increases from 0 to the roots move from the poles of G(S) to the zeros of G(s)

Sketching Root Locus :RULE No. 2

130802313Sketching Root Locus :RULE No. 2 Extension

130802314Sketching Root Locus :RULE No. 3

130802315Sketching Root Locus :RULE No. 4

130802316Sketching Root Locus :

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Figure1 figure2 figure 3

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n = number of poles, m = number of zeros, n-m = lines goes to infinity

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130802323 ANY QUESTION ????????????

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