Add a PID mode

[jmcollin78]

As discussed here a PID mode should be interesting to study: https://forum.hacf.fr/t/smart-thermostat-le-chauffage-controle-par-pid/7633/2

[kadaan]

This would be awesome. I wonder if it would be possible to refactor the PID control from https://github.com/ScratMan/HASmartThermostat into it's own component that could be used by both projects?

[jmcollin78]

The important part is here:

PID output value is the weighted sum of the control terms:
error = set_point - current_temperature
di = temperature change between last two samples
dt = time elapsed between last two samples
P = Kp * error
I = last_I + (Ki * error * dt)
D = -(Kd * di) / dt
output = P + I + D
Output is then limited to 0% to 100% range to control the PWM.

[jmcollin78]

@kadaan I will try to contact the author and see if it is possible to set something in commons.
But I have many work to do before this and TPI works pretty well.

[jmcollin78]

This is not needed. The TPI works well.

EDIT: and full PID are difficult to tune. Then we need an auto-tune.