The floating wind turbines equipped with permanent magnet synchronous generators are complex nonlinear physical systems with multiple degrees of freedom. However, the complexity of these systems, the presence of unmodeled dynamics, and external disturbances pose challenges in maximizing power extraction during low-wind periods. This paper focuses on addressing this challenge for a grid-connected spar-buoy type floating offshore wind turbine (FOWT) operating in Region II. We evaluate the performance of the adaptive sliding mode control and the twisting algorithm to maximize power extraction in the low-wind region and deliver generated electricity to the grid considering the dynamic models of these systems. The controllers' performance is compared against the existing simplified adaptive super-twisting algorithm under identical operating conditions of the FOWT. The co-simulation of the National Renewable Energy Laboratory (NREL) FAST software and the MATLAB/Simulink demonstrate the robustness of the proposed controllers across different conditions regardless of disturbance inputs.