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In an answer about the F-117 Peter Kämpf writes

F-117 (...) is unstable and uncontrollable without artificial stabilization.

I wonder how such an aircraft comes to existence, specifically how one develops the program without which the aircraft can't be flown.

How one establishes (presumably in a wind tunnel using a scaled model) that the plane will not be stable or controllable, but it can be helped by an artificial stabilization system well enough to be flyable? How does one develop the system itself? How it is determined that the stabilization system has became mature and reliable enough to permit test flights?

Sorry about the question being somewhat blurred, I realize I don't even know what exactly to ask about. Any suggestions or reasonable edits welcome (in worst case I can roll the edit back).

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    $\begingroup$ This would probably take a college degree to understand. Short answer is, as long as things can be modeled mathematically, like being represented by differential equations, you can develop control rules for it, things like three wood sticks stacked vertically and balanced by a robotic hand. Modeling, controlling, simulation, and validation each has an entire science for it. $\endgroup$ – user3528438 Jan 18 '18 at 19:44
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    $\begingroup$ Except the "determine that.....mature and reliable" part. For instance take a look at how many test pilot have died during early testing of each fly-by-wire equipped airplane. $\endgroup$ – user3528438 Jan 18 '18 at 19:46
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Most modern high agility ariplanes (such as fighter jets) are unstable in the sense that (among other things) their center of gravity (nearly) coinsides with their center of lift (i.e. they are wildly out of balance). The benefits include the ability of the airplane to react to control inputs nearly instantaneously. That the design will be unstable can be determined at a very early stage in the process (during the 'sketch' phase, really). Given a fast enough control system, nearly anything can be controlled (and modeled) so to answer your second question, to design a control system, all one needs to know is how complicated the system is (the order of the system) and how fast it should be. The first question can be answered based on very general principles (most aircraft can be modeled by a fourth order system). The second question is also easy to estimate (100 Hz is usually enough, don't ask me how I know this).

Of course, tricky regimes (supersonic, transonic, supercritical angle of attack, etc.) might require some time in the tunnel but these are to determine some parameters of the general model that has been decided on at the design stage.

That the system works is usually not in question before the plane is tested. Whether a human pilot will find it controllable is another matter. This is why the design of a modern high agility aircraft is done in parallel with a simulator design to see how the pilot would react. The simulator of course, is based on the same model that the actual design is (and is constantly modified as more experimental data becomes known).

Finally, even if the airplane is well designed, and everything works, the certification stage is where most accidents happen. For example, to test the single engine performance of a twin engine airplane the tests must be carried out at near sea level pressure, quite low to the ground. Not much time to react when the plane gets too slow.

A good book to read about these issues is Aircraft design: a conceptual approach by D. Raymer. You will quickly discover that one can practically calculate the look of the plane (controls location, high-wing, low-wing, where the engines go, etc.) based on its mission.

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    $\begingroup$ I'd give you another upvode if I could for the book reference alone! $\endgroup$ – Pavel Jan 19 '18 at 9:20
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There seems to be some kind of stubborn myth that unstable systems are impossible to control by humans, and you need some high tech computer magic to do it. This is not true.

I invite you to take a broomstick, tennis racket or baseball bat, and balance it on one end. If you succeeded: congratulations! You just stabilized an unstable system! Now continue doing this while reading an after-takeoff checklist. You will likely drop the broomstick in the process. Alternatively, try and balance a pencil instead of a broomstick. You will find this much more difficult or indeed impossible.

There are two things to take away from this. Unstable systems are simply any system that 'falls over' when you do nothing to correct for it, and secondly, unstable systems can be stabilized using a feedback controller. This controller (whether it is you or a computer) looks at the error (difference between the actual position and the desired position), and calculates a suitable actuator output.

The above example however demonstrates that humans do not make great feedback controllers. They can't multitask well, which is detrimental for unstable systems: when you let go of the controls for just a second, any disturbance will exacerbate itself; and secondly, for systems with a very short time constant (like a small pencil), the reaction time (in control terms: phase lag) of humans is too large to stabilize the system.

This is where the computer comes in. Based on a model of the aircraft dynamics, a controller is designed which stabilizes the system (and while this is perhaps not very easy, it is perfectly possible to design a controller 'offline', i.e., without the actual aircraft, only with a mathematical model). Depending on the model accuracy and the control design, this stabilizing controller may have some limitations. In control engineering, you can generally choose between either a quick reaction time to a (pilot) input, or a very stable system, but there is always a bit of a trade-off in 'agility' versus 'twitchiness'. See @alexh's answer for how they solve this: they put pilots in a simulator (sometimes, this is an actual aircraft modified to behave like the target aircraft), and determine the best controller. A key point here is that the pilot is also part of the whole control loop; minor deficiencies in the computer controller can be corrected by the test pilot.

Secondly, there is a concept called 'region of attraction': for unstable systems, your controller may only work in normal conditions. If your broomstick were upside-down (hanging from your hand), it's a non-trivial task to upright it again. Similarly, if your aircraft is in a flat spin, you may need to revert to another controller to regain control. Note that pilots also revert to this kind of feed-forward control in a spin: kick down the rudder, and don't let go until you're out of the spin again. For unstable aircraft, there may not always be a way to regain control (for example, if the aircraft is very stable flying in reverse), which is why bailing out is an important ability for test pilots in unstable aircraft.

Finally, there is the point of mechanical linkage. In a simple aircraft, the controls are directly linked to the control surfaces. In an unstable aircraft, this is undesirable as the pilot may cause pilot induced oscillations (which they are prone to do even in stable aircraft!). Instead, the pilot's input are fed into the flight computer, which makes the aircraft feel stable as far as the pilot is concerned. This means that these aircraft cannot be flown without a computer, not necessarily because it is difficult, but simply because the pilot does not directly control the aircraft. Test flights are still possible if the computer is programmed with a marginally stable controller (whether they are successful, history will tell...)

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  • $\begingroup$ Agree w.r.t. control of unstable systems is possible by humans, after all the original Wright flyer is an unstable design. It is only the high levels of instability on modern aircraft has been made possible with the introduction of flight control systems. The time to double amplitude of the system such that a pilot would be unable to control it. However a modern FCS will mix a blend of a quick system and a stable system. You need a quick system to avoid PIO but you can wash this out and feed in the stable system for a trimmed condition. $\endgroup$ – Adrian Jan 19 '18 at 10:09
  • $\begingroup$ also just to point out it is possible to have a mathematical model of the pilot as well so the system modelling does include pilot in the loop analysis. $\endgroup$ – Adrian Jan 19 '18 at 10:11
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The entire system is mathematically modelled and tested prior to first flight.

You use empirical methods (ESDU), wind tunnel data and CFD to build an aerodynamic model that includes variations in Mach No., Alpha, Sideslip and control surfaces. You build models of the airdata system, engines, hydraulics, actuators and FCS. You include sensor models, analogue to digitial interfaces. Also have a set of equations of motion and an atmospheric model.

You then combine all the models together and analyse them as a complete system. Check the linear stability, gain and phase margins etc. Build a flight simulator to assess the handling qualities. The modelling allows you to test the system robustness by throwing lots of extreme tolerances at the system and making sure it's still safe.

You can then perform rig testing so for example replace the actuator model with real hardware and check the real hardware performs as predicted by the model.

Once you have tested everything and you have evidence of your work to convince the authorities that your design is safe you can go and fly.

It's not finished yet because you record all your flight data and match the data to your models, correcting and fine tuning the models when you see any discrepancies.

The best part is when you are involved in a first flight and the first comment from the test pilot when he landed was "that flies just like the simulator", it gives you confidence that your modelling is pretty good.

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