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More precisely, I am wondering if there is any kind of data on how long it takes between moving the sidestick and observing a reaction on the ailerons or elevator. I know that the physical control surfaces take time to move and, thus, I am only wondering about the actual latency added by the fly-by-wire (FBW) system.

My naive assumption is that the A320 runs a fixed control loop with precise timings. So, every $n$ milliseconds it samples the sidestick, calculates the necessary control surface deflections and then sends that via some bus which runs at $m$ Hertz. So, on average there is an expected delay of $x$ milliseconds between input and the control surfaces starting to respond to the input.

Also, is the delay noticeable by pilots?

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    $\begingroup$ I know you are asking about FBW, but note that conventional cables also have lag due to stretching, as do hydraulic circuits. So you may want to turn it into a comparison question, if you wish. $\endgroup$ – ymb1 Jan 17 '18 at 11:24
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    $\begingroup$ @mins That comparison is irrelevant: there is a lot more between mouse and screen than just the display refresh rate! $\endgroup$ – kebs Jan 17 '18 at 14:04
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    $\begingroup$ Note that human reaction times are of the order of 100ms. While not directly what we need here (and hence not an answer) it's indicative. In a completely different field (aligning lasers) a 10Hz feedback rate feels like things are happening with no delay, slightly slower and it really doesn't feel like a realtime response. $\endgroup$ – Chris H Jan 17 '18 at 14:13
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    $\begingroup$ @kebs: It is relevant, I'm not talking about the monitor refresh rate, but the GUI refresh rate (rendering rate). $\endgroup$ – mins Jan 17 '18 at 14:32
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    $\begingroup$ @mins as a gamer I can definitely state that there is a clear, noticeable difference between 30hz and 60hz. Friends with 120hz monitors say that step is almost as noticeable. $\endgroup$ – Baldrickk Jan 18 '18 at 9:47
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Yes there will be a delay, but the delay caused by the control loop is really tiny. I've seen position control loops run successfully and stable at a couple of hundred Hz for simulator motion systems, and the time delay is just one iteration frame = less than 10 msec.

And as @ymb1 correctly points out, if we deflect any control surface the end position is subject to actuation forces, aerodynamic pushback forces, inertia of the surface, cable stretch and -friction, aero damping, maximum flow velocity through the servo valve etc etc. The total transfer function of stick input => surface position is such that an extra time delay of 10 msec in the total loop is not really noticeable. And control position is only the input of the aircraft response, with aircraft inertia playing a large role.

So my answer would be: a tiny time delay that can be totally disregarded.

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    $\begingroup$ @mins Most industrial control systems run on PLCs and PLCs, at the very bottom, run a loop. Conceptually, and for most practical purposes, they are programmed as, and model, a massively parallel state machine, but the state itself, by nature of the limitations of the underlying hardware, is discretized into time slices of duration required to fully evaluate the state of the system (ie: the "scan time", "frame time", or loop time). One loop consists of reading inputs, evaluating the control logic, and updating the outputs. $\endgroup$ – J... Jan 17 '18 at 13:39
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    $\begingroup$ @mins That said, for extreme circumstances most such control systems do allow for interrupts to initiate an immediate read of an input (or write to an output) during logic evaluation (ie: outside the loop) but this can actually break the otherwise guaranteed and regular maximum scan time and introduce more side-effects than it's usually worth. Typically when one is tempted to resort to such an interrupt it's a sign that the control system needs to be subdivided instead, with the more time-critical subsystem given its own controller (and that's what's usually done). $\endgroup$ – J... Jan 17 '18 at 13:43
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    $\begingroup$ @mins To be clear, a flight computer is completely specialized, of course, and won't work exactly like an industrial PLC, but any "digital fly-by-wire" systems will have something like this at the bare-metal layer. $\endgroup$ – J... Jan 17 '18 at 14:41
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    $\begingroup$ @J... Hmmm... I'm not so sure. I'd be a little surprised if they used PLCs rather than CPUs running an RTOS (or bare-metal application.) They would almost certainly use a control loop in any case, though. $\endgroup$ – reirab Jan 18 '18 at 0:45
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    $\begingroup$ The A320 uses late 80s era microprocessors for the control loops, Motorola 68020 and similar. $\endgroup$ – Koyovis Jan 18 '18 at 0:50
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I don't have an answer for the timings (I personally don't think that's publicly available information), but I can answer this

is the delay noticeable by pilots?

as I have some direct experience, and I can affirm that no, the pilot does not perceive a delay between a stick deflection and the aircraft reaction.

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  • $\begingroup$ I'd assume that the delay is approximately that of the power-steering you get in most cars. To give people a comparison to something they may have experience with. $\endgroup$ – Baldrickk Jan 18 '18 at 9:49
  • $\begingroup$ @Baldrickk you train so much and so long, that by the time you have to actually pilot, you don't need to compare it to driving anything else. $\endgroup$ – Federico Jan 18 '18 at 9:51
  • $\begingroup$ not everyone reading this will be a pilot ;) $\endgroup$ – Baldrickk Jan 18 '18 at 9:54
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    $\begingroup$ @Baldrickk ah, I thought that by "people" in your first comment you were referring to "those who pilots", not readers here, sorry. $\endgroup$ – Federico Jan 18 '18 at 9:56
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No, no, you can move a side stick much, much more quickly than moving the conventional controls.

Side stick inputs to the computers are updated every 10 ms which is extremely fast, this corresponds to 100hz update; compared to most television pictures update, FBW is twice as fast.

for very small displacement of conventional flight control, you have no flight control effect because of the system Backlash

For very fast and large inputs in FBW, the order is voluntarily dampened to protect the aircraft structure, in conventional flight controls there is no protection, you may damage the structure, mainly when the rudder is concerned even though the range is mechanically limited while in full FBW RUDDER, pedals EFFECT is voluntarily dampened when it gets dangerous to the structure

As a summary no ADDITIONAL delay with FBW

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