a phase angle controller is not a current controller but a voltage control, so the control will be not as good as with a real feedback system.
But there is no reason a phase angle controller cannot have current feedback and function as a current control.
Trying to Attached a Drawing of the original system used.
The problem it seems was they used the length of the wire (very Critical) to adjust the heat / current. The process of changing the wire could take all day to get right.
I'm now looking at a phase angle controller that is set with a simple POT adjustment Or even a 4-20ma signal...
This is exactly what the SSRMAN-1P does, as I mentioned earlier. see
link. Very simple, cheap, and robust. I cannot see your schematic but I understand the control is on the secondary. Any reason it cannot be on the primary? How much power are we talking about?
If you used this in conjunction with a simple PID controller with current feedback, the length of wire would not matter.
This is also optimal, as with no current feedback/control, the temp of the wire will drop as product is cut by it (heat is drawn away from wire, into product). Using a voltage-only control, or cutting the wire to exact length , it will not compensate for this heat loss. If you cut the wire and get it exact length needed and everything is perfect while static (not cutting) then as soon as you introduce product the temp drops, increasing drag on the wire, increasing stress on the wire, decreasing life span. If you cut it the perfect length to remain hot while cutting, then as soon as you are done cutting and product is removed, wire temp will increase to the point it may burn out the wire. this is the only drawback that my design suffered but it was workable. If I were to do it again, I would use current feedback and some control.