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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

1. POLES AND ZEROS2. ROOT LOCUS

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 respectively

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Consider the transfer function:

H(s)=

S+2

S + .252=0

We have a Zero at s—> -2Poles at : -i/2 and +i/2

ROOT LOCUS

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(Here K is an unknown parameter)

ROOT LOCUS

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Now We have Two Questions…

Design Effects of Variations

What value ok K should one Choose to meet the Systems Performance Requirements

What is the Effect of a variation of K on the System ?

For random value of k:

𝑆3+4𝑆2+0𝑆+1=0

X

X

X

X

X

X

X

X

X .

.Repeating the process : k ∞

X

X

X

X X X X X

S is a real valueS corresponds a exponential increase or decay

decay

increase

S- plane

Ima(w)

Real(∂)

Root locus

zerosSystem =--------

polesstabilit

y

An open loop transfer function:

One pole is on the right hand plane

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Ploting by matlab

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

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Example:

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)

Sketching Root Locus :

RULE No. 1

There 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

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As 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

Sketching Root Locus :

RULE No. 2 Extension

Sketching Root Locus :

RULE No. 3

Sketching Root Locus :

RULE No. 4

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Sketching Root Locus :

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Figure1 figure2 figure 3

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

ANY QUESTION ????????????