An agricultural work vehicle comprising: an implement connected with the agricultural work vehicle; and a height control system for the implement; the height control system comprising: a implement height sensor (116, 118, 119) configured to detect a height of the implement relative to a ground surface; and a controller communicatively coupled to the implement height sensor (116, 118, 119), the controller including a processor and associated memory, the memory storing instructions that, when executed by the processor, configure the implement controller to: monitor the height of the implement relative to the ground surface based on signals received from the implement height sensor (116, 118, 119); and determine an implement height error (e(t)) by comparing the height of the implement with a predetermined target height; characterized in that the memory storing instructions further configure the implement controller to: calculate a proportional signal based on the implement height error (e(t)) raised to a power (n) greater than one; and adjust the height of the implement based on the proportional signal. an implement connected with the agricultural work vehicle; and a height control system for the implement; the height control system comprising: a implement height sensor (116, 118, 119) configured to detect a height of the implement relative to a ground surface; and a controller communicatively coupled to the implement height sensor (116, 118, 119), the controller including a processor and associated memory, the memory storing instructions that, when executed by the processor, configure the implement controller to: monitor the height of the implement relative to the ground surface based on signals received from the implement height sensor (116, 118, 119); and determine an implement height error (e(t)) by comparing the height of the implement with a predetermined target height; a implement height sensor (116, 118, 119) configured to detect a height of the implement relative to a ground surface; and a controller communicatively coupled to the implement height sensor (116, 118, 119), the controller including a processor and associated memory, the memory storing instructions that, when executed by the processor, configure the implement controller to: monitor the height of the implement relative to the ground surface based on signals received from the implement height sensor (116, 118, 119); and determine an implement height error (e(t)) by comparing the height of the implement with a predetermined target height; monitor the height of the implement relative to the ground surface based on signals received from the implement height sensor (116, 118, 119); and determine an implement height error (e(t)) by comparing the height of the implement with a predetermined target height; characterized in that the memory storing instructions further configure the implement controller to: calculate a proportional signal based on the implement height error (e(t)) raised to a power (n) greater than one; and adjust the height of the implement based on the proportional signal. calculate a proportional signal based on the implement height error (e(t)) raised to a power (n) greater than one; and adjust the height of the implement based on the proportional signal.