MATLAB: Difference between polar and nyquist

Question

hello,

I'm trying to obtain a polar plot of a transfer function and I came across two expressions that should give me the same results but they don't and I can't really understand how they work. how do I interpret the two plots?

num = [10];
den = [1 -2];
G = tf(num,den)
%% code number one
[MAG, PHASE] = bode(G);
PHASE = PHASE(1,:);
MAG = MAG(1,:);
polar(PHASE*pi/180, MAG)
%% code number two
nyquist(G)

Answer 1

Your polar call is only plotting half of the evaluated transfer fuctiion.

Try this:

num = [10];
den = [1 -2 1];
G = tf(num,den)
% %% code number one
[MAG, PHASE] = bode(G);
PHASE = PHASE(1,:);
MAG = MAG(1,:);
figure
polar(PHASE*pi/180, MAG)
hold on
polar(-PHASE*pi/180, MAG)
hold off
% %% code number two
figure
nyquist(G)

The nuquist result is more appropriate than the polar result, however the plots are the same if you plot both parts, and include axis equal with the nyquist plot.