Remember integral value in PID component when restarting device

**Describe the problem you have/What new integration you would like**

Currently, when using the PID integration and the device is restarted, the integral value is reset to zero. Since the steady state value rarely is zero, this means it will take the process value away from the setpoint until the state stabilises again. For slow heating systems with large time constant, this can take a long time (up to 12h in my case).

**Please describe your use case for this integration and alternatives you've tried:**

My idea was to use a global variable but there is no way to set the integral value. It would be more convenient if this was integrated directly in the component (thus not requiring the used to set up a global).

**Additional context**