<p>The present study examines the utilization of a permanent magnet synchronous generator (PMSG) for the battery-stored power supply of a pump driven by a squirrel-cage induction machine (SCIM). The aim of this work is to propose a third-order sliding mode control (TOSMC) algorithm for the online estimation of wind speed and PMSG rotational speed, in order to optimize the operation of a wind turbine induction machine pumping system. The main contribution of this paper is the reduction of the cost of the wind energy chain while achieving enhanced performance. <b>The novelty of this work lies in the combination of third-order sliding mode control with a Lyapunov-based observer for sensorless estimation of both wind speed and generator rotational speed, leading to reduced total harmonic distortion (THD), faster convergence, and improved robustness to parameter variations compared with conventional sliding mode control (SMC) approaches.</b> The proposed control strategy has been subjected to numerical validation in MATLAB/Simulink, and the results have been compared with those of a sliding mode control system that incorporates sensors for wind speed and PMSG rotational speed. Simulation results for the wind turbine system under study are presented, and the analysis demonstrates that the proposed control approach exhibits superior performance in terms of error evolution and current THD compared with conventional SMC.</p>