Different Bode Plots from Same Function

Hello there,

I am quite confused as to why there are two bode plots being produced for this function. In the code, estimated_ntf4 has an extra pole and zero in the numerator and denominator while estimated_ntf3 does not, but they are essentially the same function. These two lines produce drastically different Bode Plots despite being the same function. Is this an issue with the bode plot function with Matlab?

diff = tf([1 -1], [1 0], 1);
diff.Variable = 'z^-1';

lf.num = tf([.28125 .6875 .03125 0], [1 0 0 0 0], 1);
lf.den = tf([1 -2 1], [1 0 0],1);

lf.num.Variable = 'z^-1';
lf.den.Variable = 'z^-1';

lf.tf = (lf.num)/(lf.den);

estimated_ntf3 = (diff)^2/(diff+lf.num); % Produces CORRECT bode plot
estimated_ntf4 = (diff*lf.den)/(lf.den+diff*lf.num); % Produces WRONG bode plot

figure; bode(estimated_ntf3)

figure; bode(estimated_ntf4)

Answer 1

[Sam Chak]

Hi @Prithvi Nathan

It seems that they are not exactly the same from the mathematical perspective.

format long g

estimated_ntf3 = (diff)^2/(diff+lf.num) % Produces CORRECT bode plot

estimated_ntf3 =
 
               1 - 2 z^-1 + z^-2
  --------------------------------------------
  1 - 0.7188 z^-1 + 0.6875 z^-2 + 0.03125 z^-3
 
Sample time: 1 seconds
Discrete-time transfer function.

estimated_ntf4 = (diff*lf.den)/(lf.den+diff*lf.num) % Produces WRONG bode plot

estimated_ntf4 =
 
                 1 - 3 z^-1 + 3 z^-2 - z^-3
  --------------------------------------------------------
  1 - 1.719 z^-1 + 1.406 z^-2 - 0.6562 z^-3 - 0.03125 z^-4
 
Sample time: 1 seconds
Discrete-time transfer function.

z3 = zero(estimated_ntf3)

z3 = 3×1

0 1 1

p3 = pole(estimated_ntf3)

p3 = 
          0.381059741972577 +     0.758515788742094i
          0.381059741972577 -     0.758515788742094i
        -0.0433694839451542 +                     0i

z4 = zero(estimated_ntf4)

z4 = 
                          0 +                     0i
           1.00000657194364 +                     0i
          0.999996714028179 +  5.69145454681503e-06i
          0.999996714028179 -  5.69145454681503e-06i

p4 = pole(estimated_ntf4)

p4 = 
          0.999999999999999 +                     0i
          0.381059741972577 +     0.758515788742095i
          0.381059741972577 -     0.758515788742095i
        -0.0433694839451543 +                     0i

[Paul]

I wonder what this code is trying to do.