[throwaway9870]

If you know characteristics of the system, like thermal mass, inertia etc., then coupling feed-forward control along with the PID can help. The idea is that if you know the thermal mass (and you do for a coffee maker's internal elements), then you have a reasonable estimate of how many watts are needed to change the temp of those parts. So, don't make the PID put those watts in, instead just add them separately based on your simple physics model. The PID runs in parallel and corrects all the short-comings of your model.

[wildekek]

Thanks, I never really understood feed-forward well, but modeling the thermal mass makes a lot of sense for keeping the terms in check. (As I understood it in Betaflight, it overrides the PID controller and mixes setpoints directly into the output.)

[carlmr]

I found it funny that if you did robotics this is the first thing they teach you, and in control systems they went onto other more "fancy" controllers, but never explained how to make PID work well for a range of systems.