# Optimal Control Strategy for Floating Offshore Wind Turbines Based on Grey Wolf Optimizer
## 1 Introduction  
Offshore wind turbines (OWTs) are a profitable way to generate clean and sustainable electricity. The availability of strong, steady, and low-turbulence offshore wind conditions is one of the most significant advantages of OWTs [1]. Taking advantage of these advantageous circumstances and overcoming the constraints associated with onshore installations has piqued the curiosity of many, making the development of offshore wind farms an enticing proposition. This insight is reflected in the increasing use of OWTs [2]. Currently, most OWTs in operation are supported by fixed-bottom foundations such as monopiles, jackets, and tripods. These structures normally suit shallow to intermediate water depths (50 m). Their economic rewards, however, are low [3]. Using floating platforms, on the other hand, enables the deployment of floating offshore wind turbines (FONTs) to locations further out at water. FONTs positioned adequately in deep water benefit from a multitude of advantages. These include utilizing more consistent wind conditions, minimizing acoustic noise levels, and diminishing visual impact. In addition, FOWTs outperform their onshore and fixed-bottom offshore equivalents. As a result, selective offshore wind turbine deployment can minimize many of the issues associated with onshore wind turbines [4, 5]. In addition, the economic returns are considerably better compared to the fixed bottom types [6]. Several governments, including the European Union and the United Kingdom,have committed to decarbonizing their economy by 2050 [7]. Germany, France, the United Kingdom, Denmark, and the Netherlands have all carried out a substantial amount of research on deploying FOWTs inside their respective national seas [3]. These efforts contributed to the creation and advancement of several FOWT projects. Some of them are now in various stages of development or have already been commissioned. Numerous FOWT designs have been put out, examined, and optimized in recent years [8]. Each design has special mooring lines and supporting platform settings [9]. These platforms are modeled after well-known floating support structures in the offshore oil and gas sector, such as semi-submersibles, tension leg platforms (TLPs), and spar buoys. Figure 1 depicts these platforms. However, the FOWT structure is exposed to several factors associated with the floating platform that may affect its performance or damage its structure [10; 11]. For these reasons, a control system is required. The control system should maximize produced power when wind speeds are between the cut-in and rated thresholds and maintain power at the rated value when wind speeds exceed the rated threshold. However, a floating platform's additional degrees of freedom might cause undesired structural vibrations. These vibrations, notably platform pitching, enhance the swings in generator power output and exhaust the entire structure. To regulate the WTs while attempting to limit these movements, linear control techniques such as the GSPI controller [12], linear parameter varying (LPV), linear quadratic regulator (LQR) [13], and feedforward control (FFC) [14] have been used. The National Renewable Energy Laboratory (NREL) has suggested a reference open-source controller (ROSCO) for a 15 MW IEA FOWT [15]. This controller regulates both torque and collective pitch angles. Conversely, these controllers are based on linear models created by the OpenFAST (Fatigue, Aerodynamics, Structures, and Turbulence) around an operational point reflecting specific wind and wave conditions [16]. As a result, their performance is determined via the linearization points chosen. The problems caused by model nonlinearity and uncertainty are handled in this study by using metaheuristic optimization algorithms. These algorithms benefit from considering the system as a \"black box\", which implies that the system's increased complexity does not inhibit its performance while calculating the appropriate GSPI controller parameters.