To understand this recall that high frequencynopise amplification is caused mainly by the "D" part of the PID controller. Consider the transfer function due to the
D part (lets call it D(s)):
D(s)= Ks.
We see that as gets large, so does |D|. To
offset this effect, what we need is a means to limit high frequency gain, i.e.,
to bound the value of |D|. Let us consider a modified version of D(s) as
D(s)=Ks/(s+N),
with N being large. The interpretation is that we have "added" a
high frequency pole to the transfer function. So how does this help?
At low
frequencies (small s), we see that |(s+N)| ~= |N| (because N is chosen large).
Therefore, |D|~=|K/N|*|s|. Thus at low frequencies, the transfer function behaves
just like the plain differentiatior (Ks) - our old transfer function.
At high
frequencies (s large), we see that s swamps out N, and hence |(s+N)| ~= |s|.
The high frequency gain is therefore limited by |K| (D(s) ~= K).
Thus by including a high frequency pole, we have limited the amplification of
high frequency noise.