This work arises from the need to solve the problem of tracking the signal from a capacitive sensor and was promoted by Prima Industrie, a leader in the production of laser cutting machines for sheet metal. The quality of laser cutting significantly depends on the distance between the cutting head and the sheet. An algorithm controls this distance in real time by tracking the capacitive sensor signal to ensure the correct standoff. To compensate for system delays and optimize cutting performance, the system, particularly the Z-axis, was modeled using a data-driven approach based on experimental tests, exciting the system with white noise added to the different control loops.