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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 ????????????