Why it seems like that PID Loop cannot control it.
The factor mentioned will effect the output current which can be controlled through feedback loop using PID.
Also input need not be linear. Conditions are not linear thats why feed back loops are employed.

Suggetion:
Thyrisor firing angle control is widely used for speed control of DC motor. There output is speed. You can go through litera of DC motor control.
WHat is output current range. ? Instead of Thyristor you can go for MOSFET or IGBT. They can give you better control as there switching freq can be in range of 10 khz and you can apply correction in vert short duration of 100-500 usec whereas in case of thysitor it will be only after interval of 10 msec.