Niclas,
The plot is what is called a phase plot where you plot two dynamically changing variables against each other.
I am not sure what you mean here by nonlinear. Perhaps I'll try to explain better what I wanted to know.
If I may try to guess what has been done: in the 'fixed PF' series:
- you chose the setpoint at 103-ish measured water temp. and went down with the set-point down to 95 deg stepping every 2-3 minutes
- then you set it to 103 again and measured the water temp. and after a bit to 104 and again about 104. (red line)
Then you started taking the PF after the setpoint has been reached with the setpoint varying only slightly and the small variation of water temp. we are seeing is due to monor differences in you simulated tamping procedure. (green line)
If my guess is correct than the non-linear effect you mention is called hystheresis and is due to additional dynamics in the system, which is outside the control loop, as we are only controlling what is easy to control - just the boiler. Ideally we should be controlling water temperature when it hits the coffee, but this is difficult. The alternative is to wait between the shots until the temperatures equilibrate and trust Silvia's relatively large thermal inertia for temp. stability during the shot.
What you did can help to find some characteristics of this non-controlled dynamics.
Control-wise I think what you (and others) have done is the best achievable without major revolution within the hardware, or multiple sensor (boiler and group temperature, observation of brewing switch etc.) control system with two heaters: boiler and group. I doubt it is a sensible thing to do. And as everybody is happy with the coffee quality improvement - well, what else do we need?
I'll draw what I think the system is and post in in a bit for discussion.
W.
The non-linear result from where I removed the porta filter shows that when removing the filter, the exposed "filter holder" drops in temperature faster. The intervals between each test was about 2-3 minutes. Keep in mind that Silvias "normal" brewing system is not a linear system! (e.g. if you have two measuments then you could forecast a third point). I guess your plot would have been "more linear" if a temperature controlled brew head and a controlled incoming water temperature was involved. The PID as I see it only gives you a reference point (a repeatable one!).