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Optimal controllers, namely Model Predictive Control (MPC), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> Control (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula>), and Linear Quadratic Gaussian control (LQG), are designed for a 5 MW horizontal-axis variable-speed wind turbine. The control design models required as part of the optimal control design are obtained by using a high fidelity aeroelastic model (i.e., DNV Bladed). The optimal controllers are eventually designed in three operating modes: below-rated, just below-rated, and above rated-wind speeds, based on linearized control design models. The linearized models are reduced by using a model reduction technique to facilitate the design of optimal controllers. The controllers are analyzed not only in the time domain but also in the frequency domain and on the torque/speed plane. Simulation results demonstrated that optimal controllers perform better than the standard proportional-integral-derivative (PID) controller, particularly for removing oscillation due to the drive-train mode without incorporating a drive-train damper.