MM43
...my reasoning doesn't support the theory, simply because each actuator is either in pilot input or auto mode, and positional feedback from the control surfaces should avoid the hysteresis problem alluded to.
MM43, I will borrow from the subject of PIO since that situation is the closest approximation to what I am trying to say. I am not a flight control engineer, so the professionals can likely find some (hopefully) small problems with my analysis.
The case of the autopilot flying the aircraft is actually not as complex as that of a human flying the aircraft. A human can adopt any one of several thousand different control strategies. The autopilot can only adopt the strategy it is programmed for. As a result, from a design standpoint, it is much easier to identify control demands for autopilot flight than for direct human controlled flight. The possiblity of exceeding the hydraulic supply capability of the aircraft was undoubtedly addressed since the engineers could go through all their worst case situations and tradeoffs and have a reasonable assurance of proper control behavior.
For small control inputs at a low rate of change, a hydraulic actuator can keep up with the changing demand and position its control surface very accurately. This is linear behavior in that control response is directly proportional to control input and achieves the commanded position with minimal delay.
As the rate (frequency) and amplitude of control inputs increase, the control actuator has increasing difficulty in accurately achieving the commanded position and it takes longer for the actuator to achieve the new position until finally, it cannot since the signal has already reversed. This happens because at some point, the actuator is moving at its maximum possible speed as determined by its hydraulic control valve opening or by control rate limits built into the control system (to achieve predictable control performance).
Electrical engineers use a tool called a Bode Plot to graph out control system response to a constant amplitude sinusoidal input of varying frequency.
Below is a Bode Plot of a Low Pass electronic filter, an item with response characteristics similar to a hydraulic cylinder.
File:Bode Low-Pass.PNG - Wikipedia, the free encyclopedia
From the graph you can see that system response amplitude declines past some critical frequency (in this instance 100 Hz, but on an aircraft control probably more like 1 Hz).
At some higher frequency, there no useable control response available-the control just sits there and buzzes.
Meanwhile the phase lag of the response grows as frequency gets higher. If you consider the case of 95 degree phase lag, the response could be considered to consist of two components, one 90 degrees out of phase and one (albeit small) 180 degrees out of phase!
Flight control engineers can design adaptive features into their control designs for known features through clever use of integrators and differentiators and by filtering out critical undesirable frequencies from the feedback path, but they need a predictable basis for hydraulic cylinder performance. That basis is that normal hydraulic pressure is available. If hydraulic pressure surges up and down as various elements of the flight control system are actuated, the predictability of all the engineer’s control studies goes down the toilet. The controls will move in unpredictable non-linear ways and induce additional time lags. That is the thesis of the second pathway to loss of control.
This thesis cannot be proved with the presently available information. We will need the flight recorders to understand what happened. My intent is to merely point out another way that AF447 could have been lost.
It should be noted that control rate limiting is inherent in all mechanical actuators and can cause PIO under proper circumstances. Almost every Fly-By-Wire aircraft has had some PIO instances during its development and operational history.
Both pilots and autopilots do their job through closing the aircraft control feedback loop. Dynamic loss of control while on autopilot could be considered as a special case under the heading of PIO. Many of the principles are the same.