I am studying control system and I have encountered the topic of the inversion of the dynamics. So I have seen that the ideal situation would be
but there are some problem with doing that and one of these is the fact that if P(s) is proper, its inversion would be improper. Now, I have also seen that to try to overcome this problem we could place poles at high frequencies in order to make the inverse proper.
One thing I really cannot understand is why do we do this? So why do we need to place the pole at high frequencies and not a low frequencies?
I don't understand why necessarely at high frequencies.
Can somebody help me? Thank's in advance.
[EDIT] My idea is that if we insert a pole we are creating a low pass filter and so it is better to insert it at high frequencies beacuse at low frequency there is our signal of interest, while at high frequrncy there is noise. So if we insert the pole a low frequency we touch also the signal we care about, while if we insert at high frequency we leave it untouched and the filter cuts only noise.
Is it correct?
Thanks in advance