The pitch control law
In a conventional aircraft the stick commands elevator deflection, and the pilot must translate: how much deflection gives the pitch change I want, at this speed, at this CG? The FBW pitch law removes the translation by commanding the outcome directly. In level flight under the normal pitch law, the stick commands load factor, and, blended with it at lower speeds, pitch rate: stick back a little asks for a little more than 1 g (or a gentle pitch rate); the computers deflect whatever elevator that requires today. Stick neutral commands exactly 1 g, and with it the current flight path held: release the stick and the aircraft keeps its trajectory, the system trimming continuously by itself, undisturbed by gusts, thrust changes or configuration changes it can counter. The same input gives the same response at any speed, weight or CG: the law absorbs the differences the pilot once had to judge.
Why the system wants the CG
Feed the flight control system the CG position and two families of advantage follow:
handling — knowing the CG, the computers scale their commands so the aircraft responds identically at any loading, and the certified limits are guarded accurately rather than conservatively.
economics — the larger advantage. A conventional aircraft must carry its CG comfortably ahead of the neutral point, paying for the stability with a tail download and its trim drag: the extra drag the whole balancing arrangement costs. An FBW aircraft can safely fly with the CG further aft, because the computers supply artificial stability where the airframe's own margin has been relaxed: less download to carry, less trim drag, lower fuel burn.
Some types even pump fuel into a tail trim tank in cruise to move the CG aft deliberately, and on an FBW aircraft the flight control system is the safety net that lets that position sit further aft still.
Degraded control laws
The control law is software running on sensors and computers, so its sophistication degrades with its inputs. Lose enough sensors, computers or hydraulics, and the system steps down a ladder the syllabus wants by name:
Normal law — full functionality, full protections.
Alternate law — the load-factor demand survives, but protections are reduced or lost: most of the envelope's hard walls become warnings (typically the load-factor limit is the one protection that survives), and the aircraft can now be stalled.
Direct law — the computers stop interpreting, and stick position commands surface deflection, proportionally, like a conventional aeroplane, with no protections and manual trim.
mechanical backup — beneath the software entirely: on the classic FBW airliners, pitch trim and rudder retain a mechanical or dedicated-electric path, enough to keep wings level and pitch controllable while the crew restores computers, a last resort, not a flying mode.