Is stick input considered “desired turn rate” “desired angle of attack” or something else?
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It entirely depends on the design of the system. “Fly-by-wire” just means that the surfaces are controlled electronically, not by physical cables. What the electronics are actually doing varies wildly by airplane.
The simplest/oldest versions just command control surface position, exactly the same as non-fly-by-wire. This doesn’t give you any new functionality but may result in lighter, higher performing, easier to maintain system.
You can write the software to command whatever you want. In pitch that can be angle of attack, pitch rate, g-force, elevator position, etc. A fairly common pitch law is called “C*”, a blend of pitch rate (at low speed) and g-force (at high speed).
In roll it could be aileron position, roll rate, bank angle, etc. The one that most closely imitates a well behaved conventional airplane is roll rate.
For rudder it can be rudder angle, sideslip angle, yaw rate, etc.
Which is the “right” choice depends, a lot, on what the airplane is for and how you want it to feel to the pilots.
There are no physical connections from the flight stick/yoke to the control surfaces on the aircraft.
Old school aircraft had actual wires that would push/pull the flight surfaces… This evolved into hydraulics…
Fly-by-wire replaces those physical connections with electronic ones .. so the input provided by the pilot goes through a computer and is output to the electrically controlled control surface…
The F-16 and F-117 were some of the best examples… Both were aerodynamically unstable and needed a flight computer to translate the pilots’ input to reliability control the plane(s)…
A lot of modern fly by wire is a pilot input saying “I want to do this (Roll/Bank/Yaw)” and the plane then decides how much it will do. The force used by the pilot is interpreted as an “urgency” input more than anything else.
If a pilot jams the controls over the plane will consider it’s current configuration and give the pilot the maximum allowed effect. This can vary wildly depending on phase of flight, weight, power, speed, and if wheels/flaps are up or down. If you’re low and slow with all your gear down the effect will be different to a high speed level flight response. You may get 10° angle of bank or you may get 45°. It’s up to the pilot to know what to expect.
Aircraft originally used steel cables connecting every control surface to the stick or pedals. Even the engine throttle was controlled by a physical connection. However, much like your car, slowly we started to allow an electrical circuit to control the airplane. Though for a few years the planes with fly by wire also had a physical back up in case of failure. After a few years of safe flight records we trusted the electronics and computers enough to make places that operated solely on the electronics without any physical back up.
It was also a necessary advancement with jet engines. The air speed over a control surface that a modern jet produces would be incredibly difficult to manipulate without hydraulics. Which disconnects the physics cable from the control surface anyway.
Though as an added bonus, the computer could take an unstable plane and force it to be stable. For instance, the first stealth aircraft, the F117 would’ve been impossible to fly without a computer. It was unstable in pitch (up and down), roll (tilting side to side) and yaw (twisting side to side with the rudder). Under normal flight conditions the plane would actively be out of balance. The computer would read what the plane was doing, add or subtract the pilots control input, and then send that to the control surfaces multiple times a second. So even in straight and level flight the computer was making small adjustments to the control surfaces to keep the plane flying as intended.
It took a while for them to get the computer dialed in, so in testing it was nicknamed the “wobblin’ goblin” because the computer either over or undershot corrections and then had to catch up on the subsequent correction thus making the ride a little well, wobbly.
There is actually a code of federal regulations that dictate how the control surfaces should feel and react;
[https://www.law.cornell.edu/cfr/text/14/25.143](https://www.law.cornell.edu/cfr/text/14/25.143)
So, it is really bank angle and pitch angle the computer is interpreting based on the position of the stick in approximation of how the plane would handle if it was actuated directly by cabled or hydraulics.
Many of us have drive by wire cars, my brakes are drive by wire, so the resistance is totally arbitrary to the computer. Fortunately, modeling things like steering, braking, and throttle resistance is fairly simple.
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