This paper presents a computationally efficient aeroservoelastic modeling approach for dynamic load alleviation in large wind turbines with trailing-edge aerodynamic control surfaces. The aeroelastic model is expressed directly in a state-space formulation and trailing-edge flaps are modeled directly in the unsteady aerodynamics. The linear model of a single rotating blade is used to design a Linear-Quadratic-Gaussian regulator for minimizing the root-bending moments, which is shown to provide load reductions of about 20% in closed-loop on the full wind turbine non-linear aeroelastic model.