A technique for controlling the relative humidity of a cathode airflow to a fuel cell stack that includes compensating for valve non-linearities. The cathode input air flows through a water vapor transfer unit where it is humidified. The humidified cathode exhaust from the fuel cell stack is output to the water vapor transfer unit to provide the water vapor for humidifying the cathode input airflow. A first control valve controls the flow of the cathode exhaust through the water vapor transfer unit and a second control valve controls the flow of the cathode exhaust that by-passes the water vapor transfer unit to control both the relative humidity of the cathode input airflow and the pressure within the stack. By compensating for the non-linearity, the first and second valves control the relative humidity of the cathode airflow without changing the cathode output resistance.