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Gusts change the dynamic pressure of the airflow over the wing. Vertical gusts even change the angle of attack. Both will change the lift the wing creates, and especially vertical gusts add stresses for the structure and discomfort for the passengers.

By changing aileron deflection, the wing's lift can also be manipulated. If the aileron deflection is just enough to compensate the added aerodynamic load due to a gust, both the wing and the passengers will benefit. By coupling the readings of accelerometers near the wing tip, the FCS can adjust the aileron deflection and ideally keep the wing bending constant.

Since the ailerons are at the outer 30% of span, they have a big influence on the root bending moment, but affect only a small part of the lift the wing can create. Therefore, while the bending moment can be nicely held constant, the lift will still vary, but less than without gust alleviation.

The part referring to the stick in the quoted patent refers to a mechanical control system with a naturally stable aircraft. If an aircraft with such a control system flies into a vertical gust, it will pitch up or down, which in turn will shift the equilibrium stick position. However, this will happen with some delay (the fuselage tip will "see" the gust first, and the tail will be affected by it some tenths of a second later), so the stick movement is a poor source for a feedback loop. I wonder why the patent mentions it - maybe the patentee wanted to cover all input sources.