I am trying to prove with Matlab that if I have an improper system and I place poles at higher and higher frequencies the performances of the system improves. In particular I am considering the following two degree of freedom scheme:

enter image description here

and my code is the following:

s = tf('s');
P = 1/[(1+s)*(1+0.05*s)^2];
C = (s+1)/s;

tau_1 = 0.1;
CF_1 = [(1+s)*(1+0.05*s)^2]/((1+tau_1*s)^3);

tau_2 = 0.01;
CF_2 = [(1+s)*(1+0.05*s)^2]/((1+tau_2*s)^3);

tau_3 = 0.001;
CF_3 = [(1+s)*(1+0.05*s)^2]/((1+tau_3*s)^3);

T1 = (C+CF_1)*P/(1+P*C);
T2 = (C+CF_2)*P/(1+P*C);
T3 = (C+CF_3)*P/(1+P*C);

legend('tau = 0.1','tau = 0.01','tau = 0.001')

so what I expected is that the performances with respect to the reference tracking increse as tau gets smaller, but if I do the Bode plot, what I get is:

enter image description here

from which I don't really see much of an improvement. Moreover if I change some values:

enter image description here

which is somenthing that to me does not makes sense because I should have that with $\tau =1$ I should have better performances than with $\tau =10$, this because with $\tau =1$ the pole is at higher frequencies that with $\tau =10$.

Can somebody please help me solving this problem?

Thanks in advance.

[EDIT] If I plot the step responses I see the same problem:

enter image description here

  • \$\begingroup\$ Don't you need to show something more like step responses? \$\endgroup\$ – Scott Seidman Nov 19 '19 at 17:49
  • \$\begingroup\$ What would you expect to see for various \$\tau\$ values, other than a range of bandwidths? \$\endgroup\$ – Chu Nov 19 '19 at 23:04
  • \$\begingroup\$ Thanks for the answers. Shoudn't I see a lower peak of reasonance, which means an increasing of performances? Beacuse otherwise how can I see the increase of performances?Probably I am missing this point. \$\endgroup\$ – J.D. Nov 20 '19 at 7:34
  • \$\begingroup\$ Also I was expecting less overshoot in the step response for decreasing values of tau, but it does not happens because tau=1 has more overshoot than tau= 10 \$\endgroup\$ – J.D. Nov 20 '19 at 8:00

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