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"The radio"... ATC? I've added some points of interest to a screen capture of the location. They were well within the normal TDZ, but that is their choice, up until they have selected reverse thrust at least. There is no magic about doing a GA, the aircraft follows the SSC input intros case, AS IT DID AT LHR, and neither of those events has indication of a PIO, or APIO or anything similar, BEFORE the tail strike. Have another look at the SSC trace for the LHR event that you have linked to, the tail strike occurs before the pilot reverses the SSC pitch command, and that is a high amplitude input as a consequence of the attitude achieving ANU sufficient to achieve the tail strike. During these events, by memory and assumption of Airbus architecture, the pitch is in a direct law, the pilot is not commanding a g load, he/she/it is commanding a deflection of the elevator.
No indeed. There is no PIO before the tail strike. But the triangle shape in the elevator deflections is a very clear indication of PIO.
The PIO appeared because the aircraft was slow to react, which prompted the pilot flying to maintain too big of an order, leading the aircraft to overreact, and himself to overcorrect. This puts too much demand in elevator deflection
speed, which is the slope of the curve. When the curve is a steadily descending and ascending line, in a triangle shape, it means you reached the elevator maximum deflection speed, which is a very clear indication of PIO. It didn't last for long as only a few triangles are visible. But it's a very clear sign. You won't find anything similar on the curves for a normal go around.
Reaching maximum elevator speed means the elevators are chasing a target that they can't reach. It means that the aircraft cannot respond timely to the pilot's orders.
As for the long landing, you can find the recordings on the youtube video just below your post... I'm not going to write the exact same thing that I already wrote. Just wait for the final report if you don't believe me. Or look for another similar incident report if you're impatient.
The thrust line is providing a considerable ANU moment, and what is interesting is the sequence of the pilot input; When increasing the pitch up moment from the engines, adding full aft SSC at the same time is going to always result in a wild ride until the gain of the input and the direction of the input is resolved by the pitch moment attained by the engines. For a normal takeoff, the thrust moment is nominally stable (nominal, as the ATR iis commanding an EPR or RPM, which is gross thrust, but net thrust reduces as TAS increases, (the -mdot.V0 component)). In the GA case pulling back while thrust is increasing will hive a total ANU pitch rate that is undesired. stabilising the engine at GA and then putting in the SSC command would avoid the excessive pitch rate that occurs, and there is nothing novel in that, it is what we have done for 75 years with underwing pylon mounted engines.
If you look at the curves, it's not what happens. The engines are still almost at idle when the tail strikes the runway.
So the elevators are responsible for the pitch up. If you use an image processing software to put the two curves, pilot input and elevator response, in relation to each other, you will see that there is a delayed response from the elevators, of almost one second. Then, while the elevators are not following the order they're given, the pilot waits for them while maintaining his input... If the elevators had responded, surely the pilot, who is not incompetent, would have given a smaller overall input. and he might not have stricken the tail.
During these events, by memory and assumption of Airbus architecture, the pitch is in a direct law, the pilot is not commanding a g load, he/she/it is commanding a deflection of the elevator.
Yes. It should be. But if you look at the curves, again by superposing both, you will see that if most of the time the elevators follow closely the input, in what is believably a direct law, they do not follow properly between 2 and 4 seconds before the tailstrike.
Having an excessive resultant pitch rate is not a "PIO", it is the wrong applied control deflection given the total moments that are being generated. LHR was not caused by a PIO, nor is YYZ.
LHR is not caused by PIO. (in all I'm writing I'm not talking about YYZ because I don't have any curves obviously)
However, the fact that PIO occurred shows that the aircraft wasn't responding as expected by the pilot. And if you look closely in this 2-4 seconds before event timeframe, you will see that the elevators indeed responded with a delay.
the crew react and potentially overreact in a state of anxiety.
Before saying things like this, you should at least go in a simulator, perform a go around. Then, when the curve analysis will have shown that you successfully performed a go around in spite of a one second delay in elevator response, you will be in a better position to criticise... If the elevator delay does not occur, you've proven nothing, and you're left with looking for why the elevators responded nicely in one case and late in another case.
The pilot-induced oscillation (PIO) can be defined as sustained oscillations or instabilities resulting from the pilot being in the control loop. These oscillations would not occur if the pilot had not closed the loop, since with few exceptions the airplane alone is dynamically stable. It follows that control system dynamics as well as airframe and pilot dynamics enter into this phenomenon. In other words, it is the total system that must be considered when evaluating PIO.
PIO occurs easily when the aircraft response is approximately one second. Because it is also the human response time.
Have you ever flown a delta wing microlight ? Like this one :
https://images.virginexperiencedays....ompress,format
Especially in roll, these things are a bit difficult to control, at least at first. Inducing a roll requires a large force in your arms, so it takes time to move it. Then it's not ailerons that you're moving but the entire fuselage under the wing. So it's even longer to get a roll angle and a turn. Since there is a delay, it's easy especially if you over correct to get into PIO.
Indeed, the aircraft will not enter oscillations by itself, because it's dynamically stable. Dynamically unstable aircraft would be very difficult to fly and not certified.
What I'm saying since the beginning is contained here :
It follows that control system dynamics as well as airframe and pilot dynamics enter into this phenomenon
Elevator maximum speed is part of control system dynamics 
If you'd like to go into more details you can send me a PM