Nyquist diagram, Limit cycle - Diagrama de Nyquist, Ciclo límite

Good morning, from the following data, how would you go about drawing the Nyquist graph that is observed? Thank you very much.

Buenos días, a partir de los siguientes datos ¿cómo se haría para sacar la gráfica de Nyquist que se observa? Muchas gracias.

Answer 1

[Balavignesh]

Hi Jesus,

As per my understanding, you would like to find the Nyquist plot of the Transfer function

G1(s) = 4/((s^0.7)*(s+1)^2).

You might have tried using the 'nyquist' function to get the Nyquist plot but encountered some errors on your end. It looks like the transfer function '1/s^0.7' is not directly compatible with the 'nyquist' function in MATLAB because the exponent of 0.7 is not a valid transfer function power.

I suggest you take a numerical approach to approximate the 'nyquist' plot for the transfer function by defining a frequency range for evaluation.

Here is an example showing how you can do it:

close all;

% Frequency Range for evaluation
w = logspace(-3,3,1000);

% Complex Frequency 
s = 1i*w; 

% Transfer Function
G = 4./((s.^0.7).*(s+1).^2); 

% Plotting the Nyquist plot numerically
figure;
plot(real(G) , imag(G));
xlim([-1 0]);
ylim([-0.15 0.1]);
title('Approximated Nyquist Plot');
xlabel('Real Axis');
ylabel('Imaginary Axis');
grid on

Please refer to the following documentation links to know more about

• 'Plot' function: https://www.mathworks.com/help/matlab/ref/plot.html
• 'Nyquist' function: https://www.mathworks.com/help/control/ref/dynamicsystem.nyquist.html