On a Linux Mint machine using Cinnamon, the ctrl + space does not work. It appears to do exactly nothing, even though the keymapping is properly configured in PhpStorm.
This problem does not only apply to PhpStorm, but also Eclipse or Netbeans, so I assume this is related to Linux Mint.
I have found the solution, which is:
disabling the shortcut for "IBus", which was set to ctrl-space after upgrading from 14 to 17.
If you search your applications for "ibus" ... you should see "Keyboard Input Methods" pop. Click on that app, and the very first option you can set is the keyboard shortcut for "Next input method". Click this, then "delete" in the popup that shows. Immediate fix for me with PHPStorm not registering any ctrl-space command.