Most of the controller tuning methods in process control are based on linear models. Through the development of a detail model of the actuator-pneumatic valve dynamics, we show that even if the static characteristic of the valve is linear (including possible linearity of the flow dependence on the valve opening) the actuator-valve dynamics are strongly nonlinear. Therefore, tuning of the flow loop will be affected by the selection of the operating point and the amplitude of the relay in the relay feedback test (RFT) or modifications of this test. It is shown that Lyapunov linearisation around an equilibrium point fails to provide a local linear model of the system, and modified RFT probing is used for investigation of the system dynamics. The same test is used for the proportional-integral controller tuning in various operating points. It is recommended that the difference in the dynamic response of the loop for different relay amplitudes and operating points should be accounted for by larger stability margins.