Is integration over not constant dt (∆time) a possible thing? Let's say you have a PID loop with differentiating frequency, can the integral part of it still work? (Assuming you know the dt from the last iteration)
Could I just use a variable dt (∆time) in my calculation and the PID principle would still function correctly?
Short answer: yes, as long as you adjust for the real dt you are fine
Longer answer: In reality, we are always using discrete time approximations of continuous time concepts of derivative and integral. So a varying dt just means the accuracy of your approximation is varying over time, but that's ok. Examples of situations where you might run into problems are:
You are on the edge of stability and some of the slower timesteps
are too slow
You dt doesn't change randomly and happens to
interact with important system frequencies