How often does an autopilot update the position of the ailerons (or any other control surface) during cruise? Per second, per minute, or something else?
So often that to any observer (visual or tactile) it appears continuous.
I say this as someone who has 2500 hours operating a transport category airplane. The flight director provides continuous guidance that the autopilot continuously follows. When holding the control column with autopilot on (below 10k feet you hold the controls even with autopilot engaged) you would interpret it as continuous input (the autopilot moves the controls just as if the other pilot were flying).
According to the paper Reconfigurable autopilot design for a high performance aircraft using model predictive control, each control surface is updated at a different rate depending on the needs of the overall system. What they used in their experiments (and is most likely not the same in every aircraft because they will test to see what is required) is as follows:
The bandwidth column shows you how often the control surface is updated, and ranges from 3.9 times per second (on the slow moving leading edge of the wing) to 13.8 times per second (on the aileron because of the fast response of the airplane to roll control inputs).
This is a fixed value selected during the system design, and does not change based on the phase of flight (so it would be the same whether in cruise or in the landing configuration).
This is not only an Autopilot-specific question but also a design-specific question, which will be different based on the OEM (Original Equipment Manufacturer) and the Aircraft Specification.
Usually in modern aircraft, the Autopilot sends commands to Flight Control System which then sends commands to Actuators and this progression of commands happens at different rates. This update rate could be, for example, 100 Hz (10 ms), 80 Hz (12.5 ms) or may be even slower or faster, depending on the flight control system of the aircraft.
So, the command is not sent per second or minute, but rather 100's of commands per second, because commands to move the control surface are the most critical commands on an aircraft.
Well I remember doing a night flight from Japan to Uk over russia in a JAl 747 and a perfect view of the wing, and night start et all..
And one thing I noticed was that the inner airelon moved once every four seconds as in a change, next, next, next no predictable will be up or down or whatever way.. just a maybe 10cm movement or less, continuously.. was a joy to watch and some PID controller.. http://en.wikipedia.org/wiki/PID_controller
It depends on the manufacturer and model.
Although it's possible to create an autopilot that updates real-time/continuously, not all autopilots are actually designed to do so. Some autopilots (particularly older ones) updated once a minute, sometimes even slower. There are several logical reasons to do this - one is to conserve power, the other is to lower cost - slower computers used to be significantly cheaper than ones that were fast enough to compute real time. It's also simply unnecessary to continuously update the control surfaces. So say you drift a couple hundred feet off course because the wind changed, the autopilot will correct within the next minute, and you'll end up continuing on merrily and you (as a pilot or passenger) would not have noticed. The only time you need continuous updates to the control surfaces and engine speed, is during landing, and if I'm not mistaken, there's isn't a fully autonomously landing autopilot on the market (for civilian planes anyhow).
In fact, an autopilot that continuously updates the control surfaces may end up creating a jerky flight because it's constantly auto-correcting for wind gusts and changes in wind direction.