Questions

Dear Dr.Skogestad

My name is Ouiserg,Kim and I'm a graduate student in mechanical
eng,Seoul National Univ.Korea.
I have studied on magnetic bearing,especially magnetic levitated stage.
I use your book as the best reference in MIMO control.It's excellent.
Seveal types of H infinity loop shaping control could be implemented
with your book.
Thanks.
There are three main questions.
The maglev stage is controlled by Hinf loop shaping with normalized
coprime factorization.
The stage has little gain at low frequencies so that I added a integral
actions.
Therefore, the stage shows nice steady state error cancellation but the
stage has a bad time responses( long rise time, low stiffness of
magnetic bearing etc). It needed an additinal design process on time
domain.

First question,
I tried to change the controller scheme with 2 dof control for good time
response but I don't know exactly how I should divide the controller
with K1 and K2 shown in Figure 9.22 on your book. I need more
explanation detaily.

Next one,
I guess the low stiffness of the magnetic bearing using Hinf with ncf is
due to integral windup.
Because the controller shows quite large gains to the stage but the
stage would go mad from the beginning of the control action is turned
on. The controlled output are saturated already as soon as the control
starts.
So I have no choice to use a little bit low gains. If the anti-windup
can be implemented, the stage will get a high stiffness with high gains.
I read a lots of literature and papers on the anti-windup and understand
theorically(not perfectly).
But,I can't find out how to implemet with matlab or on the actual
system.
I would like to get some examples.

The last one,
while I was designing a loop shaping with ncf, 'align' step was comming
out.So I run the align command at that step. wow. It aligned whole
singular value plots perfectly as the same one. I was suprised with the
powerful algorithm and made a controller. The controller was converted
at last with c2d command for implementation to the dsp control board. I
was surprised once more because the output were mixed up. What happened?

I also checked the system is well-conditioned. The sign of the control
ouput were converted each other.
Is there any step to check out first before I run "align.m" ?

Thank you for reading.

Best Regads,

Ouiserg,Kim