Three different control design methods have been investigated, and will be discussed regarding their advantages and disadvantages: (1) Classical linear PID (Proportional Integral Derivative) control design; (2) Linear H8 control design based on LMI (Linear Matrix Inequalities) criteria; (3) Nonlinear LPV (Linear Parameter Variant) control design based on convex optimization. Controller input signals in all cases are rotor speed and axial tower top acceleration. Because of the nonlinear aerodynamics of a wind turbine, for each design some type of gain scheduling is required. The basic practical aspects, e.g. anti-windup and gain scheduling have been verified in non-linear simulations.