Qual é o atraso máximo aceitável entre a entrada do piloto e a atuação da superfície de controle de vôo?

Excessive phase lag is a direct contributor to Type I Pilot-Induced Oscillation (PIO). Phase lag comes from:

• Rigid body dynamics of the aircraft (e.g. delay between elevator surface and pitch rate response)
• Actuators (finite acceleration time between input and desired surface angle)
• Structural compliance (e.g. cable friction)
• Transport delay in signals
• Finite computational bandwidth (e.g. loop closure bandwidth)

A partir de NASA Report 4683, PIO susceptibility can be expressed assuming the pilot is compensatory; that is, the pilot input and the aircraft response would be exactly in phase, except for a constant time delay (across frequencies). This model is expressed as:

$$G(s)=\frac{K}{s}e^{-\tau_e s}$$

onde $\tau_e$ is the effective time delay, or equivalently, phase rate as a function of frequency

From its research, it found that an effective time delay larger than 0.3 sec leads to PIO issues. Given a typical pilot time delay of 0.2 sec, this would imply an upper bound aircraft effective time delay of 0.1 sec at higher frequency (around 5 rad/s), end to end.

This is a classic problem in control system theory. The condition to be avoided at all costs is the case where the pilot's control actions get out of phase with the movements of the plane, so the sidestick-action makes the oscillations worse instead of damping them out.

The two ways that could happen are 1) if there are significant processing time delays in the control system connected to the sidestick and 2) if there are significant delays in the pilot's reactions.

As pointed out above, the control system time lags are tiny compared to the time constants of the plane's responses to aileron movement, etc. and the significant time lag in the overall system consisting of plane + pilot + computer control system is in the PILOT, not the control system.

This gives rise to something called PIO or pilot-induced oscillation, where the response time lag of the pilot pushes the whole system into divergent oscillation- as for example in the case of a pilot porpoising a plane down the runway after bouncing off the runway on his or her initial touchdown.

I do not know if computerized flight control systems contain subroutines that prevent PIO but perhaps Peter Kaempf knows!

Is there a maximal delay between pilot's input and flight control surface deflection to certify an aircraft?

Literally, no. The FAA's only pronouncements about latency are about ADS-B.

To measure what you're asking about, a temporal delay is too simplistic. You need something like the system's band-limited impulse response, or its temporal equivalent of a modulation transfer function. And not just from stick deflection to surface deflection, but all the way to rate of change of (say) roll rate. FAA doesn't even try to enforce numbers on the output of that process, never mind the intricacies leading up to it.

If an aircraft's control latency in some respect was dangerously large, the test pilots (or the flight simulators!) would notice it well before certification forms were sent to the FAA.

There is quite some experience in this in Level D simulators, which have computer generated responses that must match those of the original aircraft, within tight tolerances.

A couple of decades ago, the gold standard for Unix real time host computers was 30 Hz. So 30 times per second, all of the following was computed:

• Surface deflection from stick input, including cable stretch, oil flow simulation etc.
• Aerodynamic hinge moments on the surface.
• Hydraulic hinge moments exerted by the actuators.
• Aerodynamic forces amd moments on the aeroplane.
• Inertial response of the aeroplane.
• Visual system response.
• Motion system response.
• All other system states and responses.

With an update rate of 30 Hz the standard was deemed acceptable for Level D zero flight time training, which implies a time delay of 1 frame = 0.0333 sec. So we know that this is fast enough: frequency rate 30 Hz, time delay 0.0333 sec.

As an aside, for present day computers this iteration rate is something to smile at, the code that ran @ 30Hz on a state of the art realtime unix machine runs @ 3000Hz on a Macbook Pro now.

For civilian certification there are no specific requirements for certification in the FAA Part 23/25 or in the EASA CS 23/25. But obviously they require aircraft not to be prone to PIOs, even though there is no specific section addressing the issue. As @Jimmy mentioned above time delays in the control system are the main reason for type I PIOs. So designers’ objective should be minimize those time delays as much as possible.

On the other hand military requirements goes a little bit more in detail in terms of certification requirements. Aircrafts are rated as Level 1, 2, and 3 based on the time delays of 0.1, 0.2, and 0.25 seconds in the control system. Obviously, Level 1 being the best.

There is also a requirement in the same manual (Flying Qualities of Piloted Aircrafts) to define time delay in terms of phase lag. And it classifies it according to flight phases, such as takeoff and landing, cruise etc. It starts from 15 degrees and goes up to 60 degrees of phase lag for Level 1, 2, and 3 requirements.

The technical term used is latency i.e. the propagation (or transport) delay between the input (pilot control) and the output (control surface movement). The aircraft designer (or Original Equipment Manufacturer) determines the acceptable latency.

The acceptable latency depends on the type of aircraft i.e. Airlines, General Aviation, or Hobby aircraft, flight control dynamics of the particular aircraft, the systems through which the resultant signal is produced (Pilot Control Sensors -> Flight Control Computer/Mechanical Linkages -> Actuation Unit -> Surface movement), and the critically of the signal (ex: control surface actuation).

For airlines like Airbus (A330), or Boeing (B787), the latency between the pilot control inputs and the flight control surface actuation usually ranges between 50 to 100 msec.