To test the effectiveness of the PID loop, I've only given a nonzero value to the K_p constant and varied it over a series of runs to verify the response by the controller.
The following is a plot of the baseline compared to the P-active simulations for different proportionality gain constants. I've yet to determine whether all the trends in behavior are physical.
Each different case has an evident droop (steady-state error), and seem to be destabilizing as K_p increases. However, most cases reach steady-state quicker than the baseline.
It should be noted that the ring heater is not correcting any effects from the beam, as it is turned off. The ring heater is correcting itself; or rather, its own initial heat pulse of 5 W * delta_t (600s) = 3000 J before the controller becomes active.