I am aware that the function of these systems is to artificially modify (augment) the apparent stability and control characteristics of an airplane in the event that it fails to meet the requirements in some way (which is mostly the case).
My question is this : on large commercial airliners, are pilots aware that for a particular flight maneuver, even though the controls they are inputting brings about the desired/anticipated aircraft response, their perceived control surface deflection may not be entirely accurate?
For example, the aircraft is flying straight and level and now the pilot wants to pitch up 5 degrees. He would pull back on the yoke/stick until his pitch attitude was 5 degrees. The associated control surface deflection required to bring about this aircraft response would be the elevator deflecting upwards for the entire period that the yoke/stick is being pulled. To my understanding, in reality, the elevator would constantly be deflecting upwards and downwards (as being commanded by the augmentation system) to prevent the aircraft from going into an unwanted dynamic state of motion (in this case, a phugoid). Is the pilot aware that the elevator is not fixed in position and is actually moving to make corrections? And can a pilot turn such an autopilot control system off?
If I have grossly misunderstood the entire concept, I am sincerely sorry.