Control of a drilling system drilling a wellbore is improved using a hydraulic model corrected for pressure losses. A surface backpressure of the outlet and a standpipe pressure of the inlet are measured with sensors in the system. An estimate of the standpipe pressure is calculated based integrating from the measured surface backpressure back to the inlet in the hydraulics model. The pressure loss increment in the hydraulics model is calculated based on a difference between the measured and estimated standpipe pressures. Meanwhile, a parameter in the drilling system is monitored during drilling so the parameter can be adjusted at least partially based on the hydraulics model corrected for the pressure loss.