# Nonlinear Model Predictive Control for Doubly Fed Induction Generator with Uncertainties
## 3 Simulation Results
This reduction can be attributed to the accurate filtering of the wind speed noise signal used as the input to the system. In order to thoroughly assess the performance of the nonlinear MPC based on the designed Lyapunov function, an arbitrary variable input signal is applied to the system, and the resulting outcomes are depicted in the following Figures 7-10. Evaluation of Figures 7-10 indicates that the nonlinear MPC strategy based on the designed Lyapunov function, intended for variable inputs, has also yielded satisfactory results. Although the stabilization of reactive power fluctuations is not optimal, considering the nonlinear nature of the wind turbine system and the variable characteristic of the wind speed parameter, it can be concluded that overall acceptable results have been achieved. Figure 6: Stabilization of the generator reactive power by applying a fixed input. Figure 7: Stabilization of the generator’s rotor angular speed by applying a variable input. To validate the proposed method outlined in this paper, we conducted a performance comparison with a control mechanism based on the PID controller. The responses in Figures 11 and 12 demonstrate the active and reactive power of the generator, respectively, when using the nonlinear MPC and PID control structure. The study acknowledges the importance of performing a robustness analysis to evaluate the performance of the proposed control strategy under diverse operational conditions, disturbances. A thorough examination has been conducted, offering insights into the system's resilience and pinpointing potential areas for further improvement. After recognizing system instability in open-loop mode, the initial deployment of a conventional Model Predictive Controller (MPC) results in suboptimal performance. Consequently, a robust methodology is introduced, incorporating a Kalman filter to mitigate wind input noise, coupled with a nonlinear MPC and Lyapunov function. Rooted in the genuine and nonlinear system model, this approach guarantees controller stability under varying conditions. Implemented within the MATLAB 2021b environment, widely utilized in scientific and engineering applications, the robustness analysis unveils the stability of the controlled doubly fed induction generator (DFIG) system across diverse scenarios. Figure 8: Stabilization of the generator’s pitch angle by applying a variable input. Figure 2.0 Stabilization of the generator’s active power by applying a variable input. The viability of implementing the proposed control strategy for doubly fed induction generators (DFIGs) in real-time systems is a crucial aspect for its practical application in wind turbines. A detailed assessment of computational requirements is imperative to ensure alignment with the processing power, memory, and communication bandwidth constraints inherent in real-time environments. Examining the strategy's practical deployment entails evaluating its adaptability to hardware limitations, communication protocols, and integration with existing control systems in operational wind turbines. Real-world implementation serves as a vital validation step, enabling a comprehensive evaluation of the strategy's performance under dynamic and unpredictable conditions. Successfully address  
Figure 2.1 Comparison of the response obtained from the proposed mechanism and the PID controller for the active power. Figure 2.2 Stabilization of the generator’s reactive power by applying a variable input. ing these considerations not only validates the proposed control strategy but also positions it as a reliable and efficient solution for enhancing wind turbine control in real-world scenarios.