[tarotuser]

> Beyond that, though, the controller will modulate the boiler to maintain the set point -- heating systems term this "TPI", I assume it's not a PID controller because it lacks the derivative component.

The term for this control theory operation is called "Bang bang". The basic logic is "Turn on if under set point, and turn off if at or above set point". Ovens and cheaper HVAC heating controllers use this extensively.

You do see a bit of hysteresis, since it's goal is not to be under the point, but overshoots are definitely a thing. And since it's a simple instantaneous decision (unlike PID), it's also pretty simple to make very cheaply.

https://en.m.wikipedia.org/wiki/Bang%E2%80%93bang_control

[andrewaylett]

That's the non-smart behaviour -- TPI stands for "Temperature Proportional and Integral" and is the basic behaviour to try to automatically modulate the heating output to maintain the set point without overshooting. While PID is "Proportional Integral Derivative" which is a step smarter again.

The Honeywell system I have seems to have gained extra derivative-based functionality recently too, which is nice :).