I looked at the root locus with the PID and I don't believe this will be enough to adequately stabilize this system. Just for kicks I tried utilizing looptune to stabilize the system and was successful in finding a 4th order TF that would do it. Since I know nothing of your system other than the SS matrices it may or may not make any sense.
If you replace the PID with a Transfer fcn block this should stabilize the system:
num = [-1.19566835199456 0.150677296783384 -4.87470249290078 -5.9378741332245 -3.64167152790914e-05];
den = [1 32.4776016633891 994.732763803663 6558.83645377611 0.0401083722778298];
The resulting controller doesn't do a particularly good job but your system may not be easy to stabilize anyway.
What is the 2nd input and why don't you use it?