# Investigation into the Yaw Control of a Twin-Rotor 10 MW Wind Turbine
## 5 Conclusions  
This paper presents a detailed mathematical model for the mechanical system of a WT, with equations applied in Simulink to calculate the mechanical outputs, such as the mechanical power and thrust force, and study the system's performance. The MATLAB Simulink(r) tool was used to model and simulate the overall mechanical system, and the NREL 5 MW WT was used as a reference to verify the system's behavior. This model is the core contribution of this work and was used to show the results of the proposed yaw control mechanism configuration.  
Figure 16: Chattering signals before and after applying SMC control.  
Figure 15: Sliding mode surface control.  
A twin-rotor model was adopted as a case study to design and simulate the yaw control mechanism, which is one of the main challenges of MRS turbines. The mechanical power of the simulated model was verified, and the thrust force was calculated and verified, as this is a crucial factor affecting the yaw action of MRS turbines. The proposed yaw mechanism considers the side booms carrying the two rotors as one singular moving part. Two different vectors for the wind speed were used as inputs to the model for each of the two rotors, with random values for the wind speed and direction. The thrust force was calculated for each rotor, and the twisting moment on the tower top resulting from the difference in thrust force was used as a determination factor for the yaw mechanism's action.  
A DC motor was used as an actuator for the yaw control action. The controller parameters were determined through fine-tuning until the desired torque was achieved. The SMC algorithm was used to slide over the transfer function of the system. The response curve of the controller state was very smooth, and the settling time was as little as 0.6 s. The sliding mode controller also improved the chattering in the signal significantly along the sliding surface. The yaw control mechanism played a major role in compensating for the torque induced by the difference in the thrust force between the two rotors.  
Although SMC resulted in a good response, the proposed control in its current form was unable to optimize the yaw misalignment in relation to the torque induced on the main tower. In the current configuration, where the side booms move as one part, it seems impossible to compromise between the wind flow direction and the thrust difference between the rotors.  
It is recommended that future work should also consider rotating the rotors around a vertical axis to be able to include the advantages of both yaw mechanisms--the rotors and the side booms. It is also suggested that different control algorithms should be used and optimized to obtain better results for the yaw mechanism of multi-rotor wind turbines.  
Conceptualization, A.I., A.A., S.Y. and S.S.; methodology, A.E., A.I., S.Y. and A.A.; software, A.E., A.I., A.A. and M.A.R.; validation, A.A., M.A.R. and A.I.; resources, A.A. and M.A.R.; writing--original draft preparation, A.E.; writing--review and editing, A.A., S.S., S.Y. and A.I.; visualization, A.E. and M.A.R.; supervision, A.A., S.S., S.Y. and A.I. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data are contained within the article.  
The authors declare no conflicts of interest.  
List of Abbreviations  
\begin{tabular}{l l} _Symbol_ & **Definition** \\ \(A\) & Swept area of the rotor (m\({}^{2}\)) \\ _a\({}_{Axial}\)_ & Axial induction factor (-) \\ \(B\) & Viscous damping constant (N.m/rad/s) \\ _C\({}_{P}\)_ & Power coefficient (-) \\ _C\({}_{t}\)_ & Thrust force coefficient (-) \\ _F\({}_{T}\)_ & Thrust force (kN) \\ \(J\) & Inertia constant (kg.m\({}^{2}\)) \\ _K\({}_{t}\)_ & Torque constant (-) \\ _K\({}_{p}\)_ & Back EMF constant (-) \\ \(L\) & Armature inductance (H) \\ _P\({}_{m}\)_ & Mechanical power (kW) \\ \(R\) & Armature resistance (\(\Omega\)) \\ _RR_ & Rotor's radius (m) \\ \(T\) & Torque (kN.m) \\ \end{tabular}