Measure the governing parameters i.e. settling time, natural frequency, damping ratio from the graphical representation of a transfer function In MATLAB

Find rise time, Settling time, Percentage Overshoot, poles and zeros for the given transfer functions:

Calculation:

w_n²=9

w_n=3

s² +2ζw_n+w²= s² +6s+9

s² +2ζ (3) +(3)²= s² +6s+9

s² +6ζ +9= s² +6s+9

ζ=1

 

Source code: 

clc

clear all

close all

%%BAEM-F18-025

Num=[12];

Dem=[1 6 9];

G3=tf(Num,Dem)

figure(1)

step(G3);

zeta=1;

wn=3;

Settling_Time=4/(zeta.*wn)

Rise_Time=(1-0.4167.*(zeta)+2.917.*(zeta^2)/wn)

under=sqrt(1-zeta^2);

iner=(pi.*zeta/under);

Percentage_Overshoot=exp(-iner).*100

Pole=pole(G3)

Zero=zero(G3)

figure(2)

pzmap(G3)

OUTPUT:

Graph: