A Robust Fractional-Order Nonsingular Terminal Sliding Mode Control With Deep Learning-Based Lie Derivative Estimation for Maximum Power Point Tracking in Wind Turbine

This paper presents a Robust Fractional-Order Sliding Mode Control (FOSMC) with Nonsingular Integral Terminal Dynamics, integrated with Densely Connected Convolutional Networks (DenseNet) for Lie Derivatives Estimation, to achieve Maximum Power Point Tracking (MPPT) in Wind Energy Conversion Systems (WECS) based on Permanent Magnet Synchronous Generators (PMSG). The proposed method effectively addresses the challenges of nonlinear dynamics, uncertain wind conditions, and chattering effects, which are common in traditional control approaches. The core innovation lies in fractional-order sliding mode control, which enhances convergence speed and robustness while ensuring finite-time stability. Unlike classical Sliding Mode Control (SMC), the proposed Nonsingular Terminal Sliding Mode (NTSM) formulation eliminates singularities and improves tracking accuracy. Additionally, to overcome inaccuracies in numerical differentiation, a Densely Connected Convolutional Neural Network (DenseNet) is employed to estimate higher-order Lie derivatives, providing real-time system state approximation and improving control precision. A rigorous Lyapunov stability theorem guarantees the finite-time convergence of the considered system. Extensive MATLAB/Simulink simulations validate the effectiveness of the proposed control law by comparing it with the existing classical controllers. The results demonstrate superior MPPT efficiency, faster transient response, reduced chattering, and enhanced robustness under varying wind conditions.