In one aspect, a method for automatically controlling a height of an implement of an agricultural work vehicle relative to a ground surface may include monitoring, with one or more computing devices, the height of the implement relative to the ground surface. The method may also include determining, with the one or more computing devices, an implement height error by comparing the height of the implement with a predetermined target height. The method may also include calculating, with the one or more computing devices, a proportional signal based on the implement height error raised to a power greater than one. The method may also include adjusting, with the one or more computing devices, the height of the implement relative to the ground surface based on the proportional signal.
