Finite-frequency Control and Energy Optimization of Nonlinear Wind Turbines Using T–s Fuzzy Models

This paper proposes an integrated fuzzy control and energy management strategy for nonlinear wind energy systems by combining the generalized Kalman–Yakubovich–Popov (gKYP) lemma with Takagi–Sugeno (T–S) fuzzy modeling. The nonlinear dynamics of the wind turbine are represented by a T–S fuzzy model, which enables the design of a finite-frequency Linear Matrix Inequality (LMI)-based controller. An observer-based structure incorporating a fuzzy Sliding Mode Observer (SMO) is developed to estimate unmeasured states and improve robustness against disturbances and modeling uncertainties. The control law is designed according to a Parallel Distributed Compensation (PDC) structure, while finite-frequency analysis is employed to enhance stability and disturbance attenuation over specified frequency ranges. In addition, a Stateflow-based energy management strategy is developed to regulate power flow, supply the load, and protect the battery by maintaining its state of charge within predefined limits. Simulation results demonstrate the effectiveness of the proposed approach in maintaining stable generator operation, improving disturbance rejection, and ensuring efficient power management under varying operating conditions.