To stop fields from export, you need to set:
$col["export"] = false;

I didn't explain well.
Normally the hidden fields ($grid["hidden"]=true) are unchecked in the "show/hidden dialog" and aren't exported.
But if you don't enter in the "show/hidden dialog" and click on the ok button these fields are, instead, exported.
It's possible to change this behaviour?
Thanks in advance

Yes, to initially stop these fields from export (before dialog selection) you need to set:
$col["export"] = false;

Excuse me Abu.
One more time I didn't explain properly.
In the "show/hidden dialog" the hidden fields ($grid["hidden"]=true) are unchecked but are exported anyway. For not exporting these columns you need to open the "show/hidden dialog" and click on the ok button.
If you set $col["export"] = false; you will never export.
Vice versa, for exporting the hidden columns, if necessary, I would like to open the "show/hidden dialog", check these columns and click on the ok button.
In the screenshoot sequence below you can view:
1. a code fragment of the fields hidden declaration
2. the grid
3. the show-hidden dialog
4. the PDF export
5. the show-hidden dialog in witch I clicked ok button
6. the final PDF export

I would like to obtain this final export without enter in the show-hide dialog

https://www.dropbox.com/s/azkvtx5wcayq6jw/1.code_fragment_with_hidden_fields.png?dl=0

https://www.dropbox.com/s/yz65970we28vjcp/2.grid_with_hidden_fields_%28hidden_of_course%29.png?dl=0

https://www.dropbox.com/s/wbnnzkbcgy1e5do/3.show-hidden_dialog.png?dl=0

https://www.dropbox.com/s/ybw2o1jlm211faa/4.export_%28with_hidden_fields%29.png?dl=0

https://www.dropbox.com/s/pok2cvoyr8rchr6/5.show-hidden_dialog_with_click_on_ok.png?dl=0

https://www.dropbox.com/s/r01c4ws5f0u1v4r/6.export_%28without_hidden_fields%29.png?dl=0

It's possible?
Thanks in advance

Not yet.
i'll be updating you.

Some news?
Thanks in advance

Are you using state persistence feature?
I am unable to generate this issue here. Can you email me code + test db of this grid for review?