In power electronics, there is a way of power regulation using some method similar to pwm control. What is this called? I thought that this would be a good way to control the heater. And then control this using PID.
You can either control the current or voltage, but since the load is resistive mainly, it would be much easier to use voltage control.
When using AC, you can use zero-crossing detection along with a suitable delay angle (which is modulated/controlled). So, you detect the zero crossing, then delay for a certain time/angle then turn the device on(SCR i think).
I think the transfer function has a lot to do with the power in of the heater and the thermal capacity of your mass, along with the ambient temperature. I'm not really sure how to derive it though
At a previous company I worked at we had temperature chambers as well as belt furnaces. We use SCR which the length the gate is turned on is varied varies the amount of each cycle the voltage is applied. Heater a slow to respond so tuning a PID controller to get good stable temperature is tricky.
The proportional and derivative control will ensure as fast as possible response, while the integral should help with your overshooting. As in any plant, you need an accurate model to really determine the optimal parameters. These are fundamentals of control system design..