# Optimal Control Strategy for Floating Offshore Wind Turbines Based on Grey Wolf Optimizer
## 1 Introduction
Comparing the OOSPI with the classical GSPI, the calculation method of the control gains of the GSPI involves some simplifications and assumptions, which can decrease its efficiency. This can be avoided by the optimization process when finding the optimal control gains that satisfy the objective function. The design of the control parameters of the ROSCO controller is similar to those used for the GSPI, so it has the same problems that can be solved  
Figure 1: Different floating platforms for FOWTs. when using the OOSPI. On the other hand, the LPV, LQR, and FFC controllers are mainly designed based on the linearized model generated by the OpenFAST software. Therefore, the controller performance is based on the chosen linearization points. Hence, these models provide good performance close to a linearization point and weak performance further away from it. The key contributions of this work are:  
* Proposed a self-tuning improved version of the GSPI that reduces platform movement by more than 50%. * Using the grey wolf optimizer (GWO) [17] algorithm intelligence, the OOSPI parameters are obtained with low effort. According to the principles of the \"no-free lunch\" hypothesis, the success of a metaheuristic optimizer cannot be anticipated [17]. As a result, various metaheuristic optimizers are used in this study to compare their performance to that of the GWO. The used algorithms for the comparison are Harris hawks optimization (HHO) [18], African vultures optimization algorithm (AVOA) [19], COOT optimization algorithm [20], sine cosine algorithm (SCA) [21], and whale optimization algorithm (WOA) [21]. Compared with GWO, which uses the best three solutions to drive the optimization process, each of the previously mentioned algorithms has several characteristics. AVOA uses the two best algorithm solutions to represent the two groups of eagles stronger than the others. This makes a balance between diversity and resonance. This AVOA is more flexible and has less computational complexity, but it was not able to perform well when dealing with more complex problems. Regarding the COOT algorithm, the optimization process is carried out by a lead group. Multiple leading points will enhance the exploration ability with low computational efforts. However, the accuracy of the guiding mechanism is relatively weak compared to other algorithms. The SCA algorithm updates the candidate solutions based on the best-obtained solution as the target point. The SCA algorithm's search agents are able to diverge and converge thanks to several random and adaptive factors. This can enhance its accuracy but needs more calculation time. The HHO is a more advanced optimization algorithm that controls the exploitation and exploration phases based on a transition factor. The authors focused on enhancing exploration ability to converge to the optimal solution with the lowest possible iterations. However, this requires more elapsed time per iteration, which increases the total calculation time. The remainder of this work is structured as follows: The system models employed in this investigation, including the aerodynamic, mechanical, and electrical components, are presented in Section 2. Section 3 depicts the suggested control system's technique. Section 4 shows the results of the co-simulation between MATLAB/Simulink and OpenFAST. Section 5 of this study presents the conclusions.