The impact of surge motion on aerodynamic unsteadiness in modern floating offshore wind turbines (FOWT) is a well-recognized phenomenon. When coupled with advanced controllers integrated into these turbines, it can lead to fluctuations in power output. This paper introduces a state-space model that incorporates dynamic inflow effects resulting from surge motion and a PID pitch controller. Additionally, an observation equation is formulated to predict the system power output. Through time series validations, the proposed state-space model demonstrates its ability to accurately capture power responses influenced by surge motions. The developed model serves as a valuable tool for the comprehensive analysis of FOWT, allowing for the exploration of the intricate interplay between unsteady aerodynamics, advanced control mechanisms, and power output.