what is the MATLAB code for Sketch the polar plot of the frequency response for the following loop transfer functions: i. Gc(s)G(s

1. Sketch the polar plot of the frequency response for the following loop transfer functions: using MATLAB

i. Gc(s)G(s) = 1 / ((1 + 0.25s)(1 + 3s))

ii. Gc(s)G(s) = 5(s2 + 1.4s + 1) / (s – 1)2

iii. Gc(s)G(s) = (s – 8) / (s2 + 6s + 8)

iv. Gc(s)G(s) = 20(s + 8) / (s(s +2)(s + 2))

1. Sketch the Bode diagram representation of the frequency response for the transfer functions give in problem (i).

[Dyuman Joshi]

@Jerome, Why have you posted your question as an answer, twice?

And as this is clearly a homework assignment, show what you have tried yet.

[Jerome]

I'm trying to figure out the code for the polar and bode plot for this homework assignment, Can you help me out?

Answer 1

[Sam Chak]

Hi @Jerome

I believe that it is fair to ask for guidance on where you can find more information to solve problems by yourself. You asked for the command in MATLAB to sketch the polar plot of the frequency response. If I interpreted correctly, it should be the standard nyquist() command.

https://www.mathworks.com/help/ident/ref/dynamicsystem.nyquist.html

If you like more plot customization options, then use nyquistplot() command:

https://www.mathworks.com/help/ident/ref/dynamicsystem.nyquistplot.html

%% The System
G   = tf(3, [1 2 3])

G =
 
        3
  -------------
  s^2 + 2 s + 3
 
Continuous-time transfer function.

%% Nyquist Plot
nyquist(G), grid on

Answer 2

[yara]

function polar_plot_H()
  
    num = [2];              
    den = [1, 5, 17, 13, 0]; 

    sys = tf(num, den);
    
    w = logspace(-1, 2, 1000); 
    

    [mag, phase] = bode(sys, w);

    mag = squeeze(mag);
    phase = squeeze(phase);
 
    figure;
    polarplot(phase * pi / 180, mag, 'LineWidth', 2);
  
    title('Polar Plot of H(s) = 2/(s^4 + 5s^3 + 17s^2 + 13s)');
    xlabel('Phase (radians)');
    ylabel('Magnitude');
end