Feature request: integrate the error over the elapsed interval (trapezoidal rule) to avoid integral jumps after long stable periods

[Loic691]

Context
The PID is recalculated on state_changed events from the target sensor. Many sensors (e.g. Zigbee2MQTT devices such as the Aqara air monitor) only produce a state change when the value changes, so with a stable temperature the gap between two calculations can be long (55 min in my case).

Current behaviour (pid_controller/init.py)

python
self._dt = self._input_time - self._last_input_time
self._integral += self._Ki * self._error * self._dt

The new error is applied to the whole elapsed interval, although during that interval the measured temperature was the previous one.

Real example (v2026.10.2, ki = 0.007)

Temperature stable at 19.96 °C (setpoint 20) for ~55 min.
An oven raises the room to 20.57 °C, so the next sensor update arrives with error = −0.57.
Integral update: 0.007 × (−0.57) × 3292 s ≈ −13.1. Observed: 7.9 → −5.3.
With the previous error applied to that interval, the change would have been about +0.9, followed by normal integration of the overshoot.

Result: the integral loses hours of accumulated heating demand, and the heater restarts late once the extra heat source is gone. It is especially visible with high-inertia systems (electric underfloor heating).

Proposal
Integrate using the trapezoidal rule (or the previous error):

python
self._integral += self._Ki * 0.5 * (self._error + self._last_error) * self._dt

with _last_error stored at the end of each calculation (and reset when the integral is cleared or the setpoint changes). This is a small change, and it makes the integral independent of how often the sensor reports.

[ScratMan]

Done in release 2026.11.0, thanks for suggestion