I am trying to plot the frequency response control effort of a control scheme in Matlab, and in particular I want to do this for different values of tau, which is a constant used to add a pole at high frequency.

The plot that i get is:

enter image description here

in particular, this is the control sensitivity function of a 2 dof control scheme:

enter image description here

and the code for obtaining the plot above is:

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

%2 DOF

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);

Q1 = (C+CF_1)/(1+P*C);
Q2 = (C+CF_2)/(1+P*C);
Q3 = (C+CF_3)/(1+P*C);

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

my doubt is given by the fact that the control sensitivity function starts at zero for all the three cases. Shouldn't it start at an high value and then decrease?

In this case it does the opposite, so it starts at zero and grows until a value and stays constant there.

How do I read this plot? Or it is complitely wrong?

If I plot the step response I obtain:

enter image description here

from it I zoomed to show better all the coloured lines.

Can somebody help me clarify my doubts? Thanks in advance.


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