# What are the disadvantages of PDDD controller

I have a system that has the following transfer function:

$G(s) = \frac{1}{s^2(s^2+4+1)}$

As can be seen it is a 4th order system. This is the bode plot of the system:

I need to use a lead compensator in order to generate sufficient phase margin. If I use a tame PDD controller I am limiting my crossover frequency around the position of the green arrow, as the double derivative action can theoretically only provide 180 phase lead. However if I use a tame PDDD action I can place my crossover frequency in the vicinity of the orange arrow. This also means that I can make my system infinitely fast, if there is no limit on control action...

My question is: is it realistic to use a triple tame derivative action? I can't find a similar controller anywhere on the internet!