asymptotic magnitude bode plot of fractional order transfer function

how do i plot figure 2 of fractional zero

figure 1 code

(clc;clf;
clear all;close all;
alpha=0.02; 
Wcr=10;
w1=logspace(-1,log10(Wcr),1000);
w2=logspace(log10(Wcr),3,1000); 
Mag1=20*alpha*ones(1,numel(w1)); 
Mag2=@(w2) 20*alpha*log10(w2);
semilogx(w1,Mag1);
hold on;
semilogx(w2,Mag2(w2));
grid on;
xlabel('Frequency');
ylabel('Magnitude dB'))

Answer 1

[Birdman]

The following code should give you what you want:

hold off;
alpha=0.9;Wcr=2;
w1=logspace(-1,log10(Wcr),1000);w2=logspace(log10(Wcr),3,1000); 
Mag1=20*log10(Wcr)*ones(1,numel(w1));Mag2=@(w2) 20*log10(w2);
semilogx(w1,Mag1);hold on;semilogx(w2,Mag2(w2));grid on;xlabel('Frequency');ylabel('dB')


clear
clc
syms w alpha
alpha=0.9;beta=2;
w=logspace(-1,3,1000);
Mag1=@(w) 20*log10(abs(sqrt(((1i.*w).^alpha+beta).^2)));
semilogx(w,Mag1(w));hold on;grid on;xlabel('Frequency');ylabel('dB')

[Irshad Baruah]

why alpha is not multiplied in Mag2 equation of the first portion

[Irshad Baruah]

Mag1=@(w) 20*log10(abs(sqrt(((1i.*w).^alpha+beta).^2))) this equation meaning??

why beta is taken???

[Birdman]

why alpha is not multiplied in Mag2 equation of the first portion?

-Because the first portion represents the ideal plot, so what you need is basically to observe the movement at Wcr.

Mag1=@(w) 20*log10(abs(sqrt(((1i.*w).^alpha+beta).^2))) this equation meaning??

why beta is taken???

-This equation is the representation of the mathematical manipulation for (s+beta)^alpha.

Beta represents the zero value.

[Irshad Baruah]

yes but in the above euation they are changing the 'alpha' value as well as the value of 'a'

[Birdman]

In my script, a is represented by beta. So change alpha and beta and observe the results.

[Irshad Baruah]

but as per the paper i have to show the alpha value in the magnitide equation of the first part of your script

and please justify this equation

Mag1=20*log10(Wcr)*ones(1,numel(w1))

and there is no mention regarding a in the first portion as the equations are

Mag1= 20 log10 |a|;

Mag2=20*alpha*log10(w)

[Irshad Baruah]

i tried to modify but it is not cutting each other as you have shown in your previous code

hold off;
alpha=0.9;
Wcr=2.15;a=2;
w1=logspace(-2,log10(Wcr),1000);
w2=logspace(log10(Wcr),2,1000); 
Mag1= 20*log10(abs(a))*ones(1,numel(w1));
Mag2=@(w2) 20*alpha*log10(w2);
semilogx(w1,Mag1);
hold on;
semilogx(w2,Mag2(w2));
grid on;
xlabel('Frequency');
ylabel('Magnitude dB')

clc;
clear all;
syms w alpha
alpha=0.9;
a=2;
w=logspace(-2,2,1000);
Mag1=@(w) (20*log10(abs(sqrt(((1i.*w).^alpha+a).^2))));
semilogx(w,Mag1(w));
hold on;
grid on;
xlabel('Frequency (rad/sec)');
ylabel('Magnitude (dB)')