How to generate a golden ratio graph in simulink

I want to generate a golden ratio graph using xy graph block. Can someone help me?

[Sam Chak]

Can you at least show the golden ratio equation in MATLAB code format for the plotting purposes?

[Ragavendra Joshi]

I don't have code for the golden ratio, but I do have one for a spiral trajectory. Can you help me to implement this trajectory in Simulink?

% Spiral trajectory parameters
a = 1;      % Scale factor
b = 0.2;    % Angular frequency
h = 0.1;    % Height above the ground

% Time vector
t = 0:0.01:10;

x = a * exp(b*t) .* cos(t);
y = a * exp(b*t) .* sin(t);
theta = atan2(y,x) + h*t;

traj = timeseries([x', y', theta', t'], t');

plot(x,y);
xlabel('X position');
ylabel('Y position');
title('Spiral Trajectory');

Answer 1

[Sam Chak]

Hi @Ragavendra Joshi

18 Apr 2023 (Update): Here are the basic blocks in Simulink that you can use to create the Golden Ratio Spiral plot. The simulation time is , the same as shown in the MATLAB code. Max Step size is set to 0.001.

16 Apr 2023: If you are looking to show something like this, then modify the code to plot for a longer arclength.

t = linspace(0, 2*pi, 1000);

% define the Golden Ratio constant
phi = (1 + sqrt(5)) / 2;

% define parametric equations 
x = cos(t);
y = sin(t);
x_phi = cos(t) .* exp(phi*t/(2*pi));
y_phi = sin(t) .* exp(phi*t/(2*pi));

% plotting
figure;
plot(x, y, 'Color', '#A7B7F7', 'linewidth', 2);
hold on;
plot(x_phi, y_phi, 'Color', '#3952B2', 'linewidth', 2);
legend('Circle', 'Golden Spiral');
title('Parametric equation of the Golden Ratio');

% other settings
grid on
axis equal;
box off;

[Ragavendra Joshi]

Could you please guide me on how to plot this in Simulink?

[Sam Chak]

@Ragavendra Joshi, I'm a bit confused. Weren't you the one who guided me with your original code to plot the spiral arc?

I inserted this golden ratio, and modified the parametric equations.

If the plot is as expected or the math is wrong, feel free to modify the code.

% define the Golden Ratio constant
phi = (1 + sqrt(5)) / 2;

[Ragavendra Joshi]

Your code is perfect, but I want to view the spiral arc in simulink’s scope or xy graph block. I tried using matlab function block but I am not getting the spiral arc. Can you please help me to get this exact same spiral in simulink?

[Sam Chak]

@Ragavendra Joshi, I have updated the Answer with the Simulink blocks. You can follow the guide and construct the model. The Block names are shown.

[Ragavendra Joshi]

Thank you very much!

[Sam Chak]

You are welcome, @Ragavendra Joshi.

[Ragavendra Joshi]

Hey, @Sam Chak it's me again!

I have this leminiscate code and I am trying to get this in simulink xy graph block. Everytime I try, there is an error. Can you please help me with this?

t = linspace(0, 2*pi, 1000); % generate 1000 equally spaced points between 0 and 2*pi
a = 1; 
x = a*sqrt(2)*cos(t) ./ (sin(t).^2 + 1); % calculate the x-coordinates
y = a*sqrt(2)*cos(t).*sin(t) ./ (sin(t).^2 + 1); % calculate the y-coordinates
lemniscate = [x' y']; 
plot(lemniscate(:,1), lemniscate(:,2)); 
axis equal; 
title('Lemniscate Plot'); 
xlabel('x'); 
ylabel('y'); 

[Sam Chak]

Please show your Simulink block diagram like I did in my Answer. Insert by clicking the "Image" button under the INSERT tab.

[Ragavendra Joshi]

[Ragavendra Joshi]

[Ragavendra Joshi]

How can I make it smooth? Can you please help me?

[Sam Chak]

Oh I see. You can '_smoothen_' the plot by running the sim at a smaller step size. Go to the config menu and set the max step size to 0.01 or 1e-3.

[Ragavendra Joshi]

Thanks a lot!