How to perform mathematical conditions

I have to reproduce this plot:

The function is :

As you see in the plot, on the Y-axis we have this condition : [0,-pi]

So my attempt:

function alfa= fas(O,Q)
a=O/Q; b=1-O.^2;
alfa = atan(-(a)./(b));
end

clc
clear all
O=0:0.01:3.1;
for Q = [2 5 10]
    
y=fas(O,Q);
plot(O,y)
hold on
grid on
xlabel('/Omega')
ylabel('phase')
end

How can I get a plot just like the first one ?

I dont know how to perform the condition on Y-axis which is [0,-pi]

Answer 1

[KSSV]

Use atan2 instead of atan.

function alfa= fas(O,Q)
a=O/Q; b=1-O.^2;
alfa = atan2(-a, b);
end

[Pouyan Msgn]

Thanks! but if you look at Y-axis it is in the range of [0,-3] while it must be between [0,-1]....

[KSSV]

Normalize y.

[Rik]

The plot you posted in your question is a bit confusing. Are the y-axis units pi in that plot? In that case you can simply divide the phase by pi to rescale your y-axis.

[Pouyan Msgn]

Thank you! It was the first time I saw atan2! Cant we draw it with if condition? I mean program it without using atan2?

[Rik]

Where do you see an 'if condition'? And why do you want to avoid atan2?

[Pouyan Msgn]

It was little hard for me to understand the logic of atan2... but thank you anyway