Pneumatic diaphragm valves with high friction index have the potential to decrease the control loop performance and induce limit cycles. Usually, the friction models used to model diaphragm valves are the simplest ones, mainly because there are not precise sensors available to benefit from friction models with higher complexity, as the dynamics that are modeled by more complex friction models can not be observed experimentally. In this thesis, algorithms and guidelines are designed to estimate, in open and closed loop, the valve model with simpler friction models, such as the Kano and Karnopp, as well as more complex friction models, such as the LuGre and GMS. The experimental tests, performed with two industrial valves with stem position and diaphragm pressure sensors, one with higher and the other with lower friction index, show that the GMS model has the most consistent prediction precision, with slightly better accuracy than the Karnopp model. The automatic friction compensation is developed using the Adaptive Inverse Control framework, where an offline process tunes a given controller using the previously estimated valve model. Experimental tests were performed, with several different control structures, using the Kano, Karnopp and GMS friction models to tune the controller. The results indicates that when the GMS friction model is used in the Adaptive Inverse Control framework, it is more likely to obtain optimal controller tunings, even though the Kano and Karnopp models provide pretty good tunings, as well.