_applied sciences_  
_Article_  
Comparison of Optimal Control Designs for a 5 MW Wind Turbine  
[PERSON] 1 and [PERSON] 2,*()  
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with controllers that stem from the PID control, over the past decade, optimal controllers have been gaining enough attention in the literature due to their flexibility and ability to incorporate wind speed estimation/prediction into the objective functions that are only present in optimal controllers. Optimal controller are becoming even more relevant because more wind turbines are being equipped with a LiDAR (light detection and ranging) system, which measures the upcoming wind before it impacts the turbine. In this paper, wind turbine controllers are designed using three of the most popular optimal controllers, i.e., model predictive control (MPC), linear quadratic Gaussian (LQG), and \(H_{\infty}\) control. Thus, there is some work in the literature that reports on the design of wind turbine controllers based on optimal controllers. For example, the design of an SISO LQG controller to alleviate the fatigue loads on the blades, drive-train, and tower is reported in [4; 5; 6]. The design of a multi-input multi-output (MIMO) LQG controller that attempts to strike a good balance between the maximization of power output and minimization of fatigue loading is introduced in [5; 6; 7]. Similar work but based on MPC [8; 9; 10] and \(H_{\infty}\) controller [11; 12] instead of LQG [4; 5; 6] is available in the literature. However, to the best of the authors' knowledge, there is no paper that provides a comparison between these optimal controllers. In this paper, MPC, LQG, and \(H_{\infty}\) controllers are compared not only with each other but also with the standard PID controller most frequently used in industry. In this study, optimal controllers require linear models, and the DNV Bladed models of the Supergen Wind Energy Consortium (Supergen) 5 MW exemplar turbine, which has been used for various EU and UK projects over the past 12 years, are linearised in each mode. Each linear model is attained in the state space form. Since the resulting linearized models are extremely complex, realization and tuning of optimal controllers are more difficult. Thus, these linearized models must be reduced. Therefore, a Match-DC-gain model reduction algorithm [13] is employed. This algorithm eliminates the weakly coupled states, i.e., the states with the smallest Hankel singular values. In addition, MPC, LQG, and \(H_{\infty}\) controllers are developed based on these linear models, and their performances are compared not only with each other but also with the standard proportional-integral-derivative (PID) controller [14]. Therefore, the main contribution of this paper is not to introduce a new control algorithm but to apply existing optimal control algorithms, i.e., MPC, LQG, and \(H_{\infty}\) and to compare their performances. The optimal controllers are compared not only with each other but also with the controller mostly used in industry, i.e., PID.