Adaptive Robust Nonlinear Optimal Sliding Mode Control for Wind Turbines: A Hybrid OHAM‐Based Approach to Maximize Power Capture

ABSTRACT In this article, we propose an adaptive robust nonlinear optimal sliding mode control (SMC) using the optimal homotopy asymptotic method (RNOSC‐OHAM) for maximizing wind power capture. Because of the unstable nature of the wind and the presence of uncertainties and disturbances in the structure of the wind turbine, the optimal controller cannot provide robustness against uncertainties. Hence, we integrated this approach with a proportional–integral–derivative SMC (PID‐SMC) scheme to ensure the robustness of the system. The presented hybrid control input signal involves two components: a nonlinear optimal control law that provides the optimal performance of the nominal system and an adaptive PID‐SMC law. The adaptive PID‐SMC law employs a PID sliding surface along with adaptive mechanisms to create the robustness of the nonlinear wind turbine system. The nonlinear optimal control policy is designed by addressing the partial differential Hamilton–Jacobi–Bellman (HJB) equation. This equation is approximated using the OHAM. This combination strategy reduces the final time of the optimal control problems, provides desired responses and improves performance. Additionally, the RNOSC‐OHAM controller facilitates the safe performance of the wind turbine under uncertainties and maximizes the wind power captured. To evaluate the performance of RNOSC‐OHAM, the results of the presented algorithm are compared with some existing control schemes. The results indicate that the designed RNOSC‐OHAM controller is very rapid and needs few iterations and computational costs. Indeed, the present control scheme exhibits the best characteristics and has the fastest transient response. The RNOSC‐OHAM controller offers a proper balance between enhancing aerodynamic power capture and minimizing low‐speed shaft fluctuations using a small control input.