Tell you what--I've put together a little Matlab script that
plots an ITAE step response along with a Butterworth for
comparison. It's listed below.
How about you coming up with your systems closed loop
transfer function, normalizing it to 1 rad/sec to
allow comparing, and sticking it in the routine below
to see if you can beat ITAE.
I'm thinking that maybe to get a fair evaluation of the
response vs. pole placement issue that using derivative
action to jazz up the response is not allowed. If this
is not right then someone can correct me.
The script is below for a 4th order system, you can
easily change the order as long as you have the
ITAE cofficients handy for your particular order.
%... create prototype 4th order butterworth system
sys_BW=tf(1,[1.0000 2.6131 3.4142 2.6131 1.0000])
%... create prototype 4th order ITAE system
sys_ITAE=tf(1,[1 2.1 3.4 2.7 1]);
%... step response
%... compute ITAE errors