I'm curious about what does really integration and differentiation mean in electronic stuff like PID controller. In the frequency stabilization of diode laser, the cavity length is changing by applying a sinusoidal voltage to the piezo attached to it. By turning the piezo integrator of the PID controller, I'm able to lock the frequency to a fixed frequency. The example may not necessary point to PI controller. Differentiation means differentiation of a curve? This also mean the same thing in PID controller? Let's say a laser give an absorption wave profile of an atom, differentation means to differentiate the graph shown on the oscilloscope??? Thank you.