I am trying to understand the concept of realizability for an improper transfer function, and I am struggling to understand some concepts. I know that if I have an improper transfer function, for example:
I can make an approximation to make it realizable by adding a pole at high frequnecies using a low pass fiter of the type:
and so the transfer function:
is realizable. What I don't undesrstand, is that I have seen that if I do this, at high frequencies I obtain noise attenuation, for example look at this video : video.
But, if I plot the Bode plot of this transfer function I see that it behaves as a lead compensator, which could have the problem of amplifying noise at high frequencies. Here is my Bode plot:
s = tf('s'); P = s+1; filter = 1/(1+0.001*s); P_approx = P*filter; bode(P_approx),grid;
which is exacly the plot of a lead compensator.
So, suppose I am considering a control scheme with a feedforward term
Can somebody please explain me why does a pole at high frequencies attenuates noise?