How to colour regions in a graph: poles and zeros

Hi guys! Hoping for some help if anyone here has expertise plotting a graph using complex conjugates and zeros

We've been given the task to find a region where a specific set of values are valid on the real and complex axis. I've calculated the borders(?) and was wondering if anyone would know how I could add this to my current matlab code, as Im checking what fits in the borders :)

The borders are:

-2.665 + 0i to 0±2.7996i

at an angle of 46.37 degrees from -2.665 in both directions

sorry if the wording is a little confusing.

this is the code I'd like to plot on this shading.

hold on

for kp=[2, 4, 8, 16, 32, 64]

disp(kp)

G = tf([kp 64], [1 10 16 0]);

CLTF = feedback(kp*G,1)

pzmap(CLTF)

end

If anyone could help this would be mad appreciated

Answer 1

[TED MOSBY]

Hi,

You can achieve this by using the fill function in MATLAB to create the shaded region before you plot your pole-zero map. It looks like the region you've described is a triangle with vertices at (-2.665, 0), (0, 2.7996), and (0, -2.7996).

Here is how you can do that:

figure;
hold on;
x_vertices = [-2.665, 0, 0];
y_vertices = [0, 2.7996, -2.7996];

fill(x_vertices, y_vertices, 'y', 'FaceAlpha', 0.2, 'EdgeColor', 'k', 'LineStyle', '--');
for kp = [2, 4, 8, 16, 32, 64]
   G = tf([kp 64], [1 10 16 0]);
   CLTF = feedback(kp*G, 1);
   p = pole(CLTF);
end
grid on;
xlabel('Real Axis (\sigma)');
ylabel('Imaginary Axis (j\omega)');

ax = gca; 
ax.XAxisLocation = 'origin'; 
ax.YAxisLocation = 'origin';
axis equal; 
hold off;

Here is more information on "fill" : https://www.mathworks.com/help/matlab/ref/fill.html

Hope it helps!