PID is just a means of error signal conditioning. A classic PI controller uses a proportional gain stage and an integral stage to produce smooth regulation.
A controller that has only P- proportional gain will control the temperature around the set point but will over and undershoot in inverse proportion to the error gain.
Adding the I- integral stage gives the circuit a means to adjust based on trends. i.e. as the error signal increases, the proportional stage will adjust the heater turn on and off timing to smooth out the bumps from a strictly proportional system. This works very well but has a limitation in responding to sudden changes in the error signal as the proportional gain is fixed.
Adding D - derivative gain allows the controller to act like it has a dual gain proportional stage.
All of these derive their control functions from setting the gains to match the performance of whatever it is you are controlling.
In the case of an electric generator the system timing for control is going to be in the millisecond range. In the case of a smoker this gain timing will be in minutes.
I don't know about other controllers on the market but my Black Cat controllers have an auto tune function which measures the timing of your system and sets the PID gains appropriately. You can also set the parameters individually if you wish.
Even with a PID controller, a smoker with high PID gains will tend to overshoot before settling into regulation.
I have designed and built PID and PI control loops for a number of purposes.
JC
