[blt]

Do you have any insight on why PID controllers are used for this application? PID assumes a system with a continuous control input, but water boilers usually have an on/off switch. Is the input something like a PWM value?

My temperature controlled kettle does a way-more-than-optimal amount of switching when it's near the setpoint. That's consistent with using a PID controller into a PWM input.

Maybe there is a market opportunity for a water boiler that uses control techniques better suited to on/off inputs :)

[repiret]

A resistive electric heater can be PWM'ed to provide variable output. If you want to maintain a narrow temperature band, you can do that better by feeding the water temperature into your PID loop and have it control the PWM duty cycle, rather than to a simple on-off thermostat.