The aim of this paper is to present a linear quadratic Gaussian (LQG) controller designed with two main objectives: to allow the contribution of wind turbines (WTs) to the primary frequency regulation of an island power system, and to reduce the WTs drive-train mechanical stresses. The designed LQG1_CPC_Track controller is compared, in terms of the mentioned objectives, to a more classical controller containing two uncoupled control loops. The comparison is carried out in a simulation model of the Guadeloupian island power system taken as a case study. The model is implemented in Eurostag software. Simulation results show that the contribution of both controllers to the primary frequency regulation is satisfactory, and that the LQG1_CPC_Track allows reducing drive-train mechanical stresses significantly. Thus, thanks to the LQG1_Track, on top of allowing the integration of more wind energy in the grid with the contribution to primary frequency regulation, WTs would have less maintenance costs and could be manufactured with cheaper material.