Sketch root locus

  • View
    53

  • Download
    1

Embed Size (px)

Text of Sketch root locus

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

13080231

1

Before starting Poles and zerosRoot locus

13080232

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

3

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

1308023

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

13080237

An open loop transfer function:

One pole is on the right hand plane

13080238

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:

130802310

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 :

130802317

130802318

130802319

Figure1 figure2 figure 3

130802320

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

130802321

130802322

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