This Article is motivated by identification of sticky control valves under oscillatory or general types of input signals in feedback control loops. A novel Hammerstein system with Preisach model as the input nonlinearity is proposed to capture the behavior of sticky control valves followed by linear dynamic subsystems. Preisach model is flexible for capturing complicated signatures of sticky control valves, and encloses the data-driven stiction models, which describe the behaviors of sticky control valves in oscillations, as special cases. A regularized iterative method is proposed to identify the Hammerstein systems. The persistently exciting (PE) condition for identification of Preisach model is established for oscillatory input signals, after showing that a known sufficient PE condition established for general input signals is not satisfied by oscillatory signals. Simulated, experimental, and industrial examples are provided to support the obtained results.