This article proposes a comparative study of three high order sliding mode control (HOSMCs) algorithms for the 5MW tensioned-leg platform (TLP) based floating offshore wind turbines (FOWT). The control objectives are to regulate the rotor speed to its nominal value and to reduce the fluctuations of the platform pitch angle. A nonlinear control-oriented model of the 5 MW TLP-based FOWT has been selected from the literature and adapted for nonlinear controller design. Then, a continuous-twisting algorithm (CTA), a quasi-continuous homogeneous algorithm (QCA) and a super-twisting algorithm (STA) have been designed to meet the control objectives in turbulent and high wind speed conditions. Finally, these robust nonlinear controllers have been validated in simulations and compared with each other using OpenFAST code in MATLAB/Simulink.