I used a PD controller for a specific application where we were trying to maintain a specific temperature in the future, and cared more about the trajectory of the temperature over time to reach the goal. We didn’t much care for the integration of that temperature since that wasn’t important in this particular case. An integration factor would actually wind up the rate of temperature change too much!
Integral windup is the term for this issue, there's a few ways to deal with the windup if you need to keep the integral component (e.g. for tracking a moving set point, or to overcome a stable error).
https://en.wikipedia.org/wiki/Integral_windup
