# Investigation into the Yaw Control of a Twin-Rotor 10 MW Wind Turbine
## 4 Results and Discussion
### Application of Position Control on the System Model  
As stated in the previous section, yaw position control can be applied to the system as planned. To rotate the WT's boom carrying the two rotor-nacelle assemblies toward the wind flow direction, the separately excited DC motor parameters were fine-tuned to obtain a high torque, and a gearbox with a gear ratio of 1:60 was used. In order to reach the total torque required for rotating the WT's boom to a specific angular position, four DC motors with specifications designed for angular position control were simulated. The system's TF and parameters were first tested for a step input signal to verify its output response and torque as an open-loop system before applying any control techniques. The system did not reach the required input, which meant that a control method was required for the system. PID and SMC controllers were applied to the motors' transfer function. A comparison of the SMC and PID controllers with fine-tuned parameters is shown in Table 3. The simulation results of the step reference input signals for SMC and PID, respectively, are illustrated in Figure 12 and show that the system response with the SMC technique had very low overshoot compared with that of the PID controller. Additionally, the rise and settling times of SMC were much better and faster than those of PID. Figure 11: Twin-rotor mechanical outputs. The detailed system response results are shown in Table 4. Compared with the PID controller, the SMC controller had a better and faster response, which was more suitable for the purpose of this work. SMC was applied to the TF of this designed system by changing the SMC parameters to construct a sliding surface. The system's dynamic state on this sliding surface was restricted due to the changes in the random input angle signals. SMC has three different parameters. \"C\" is the bandwidth constant of the system, which is multiplied by the input angle and added to the differentiation of this input angle signal in order to obtain the sliding surface that the dynamic variables will follow; \"u\" is a control law based on the sliding surface obtained and tuned through the parameter \"\(\delta\)\", which forces the controlled signal to smoothly chatter around the reference signal. The parameter values were fine-tuned until the response was accepted at C = 10, K = 300, and \(\delta\) = 50. The SMC signal with respect to the reference input signal is shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Controller**} & \multicolumn{4}{c}{**System Response Parameters**} \\  & **Rise Time (ms)** & **Settling Time (s)** & **Overshoot \%** & **Undershoot \%** \\ \hline PID & 46.438 & 0.867 & 30.921 & 1.990 \\ SMC & 35.465 & 0.170 & 0.802 & 1.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SMC vs. PID response results. Figure 12: Response of SMC vs. PID. It can be observed that the SMC forced the system's signal to slide over the sliding surface, following the desired output angular position. This action led to a reduction in yaw misalignment; hence, the rotors faced upwind while counteracting the induced twisting moment on the tower top. Accordingly, the power of the turbine was maximized for the different flow conditions at each rotor. Figure 14 shows the significant chattering of the input signal on the sliding surface due to its sudden variation. This chattering represents the deviation of the system's dynamic state from the desired state before applying the SMC. Figure 15 shows the enhancement in the chattering signals after applying the SMC control law, which significantly reduced it to follow the sliding surface with fewer fluctuations. However, SMC showed better responses in tracking the dynamic state of the angular position control of the system. Figure 14: System’s chattering signal before applying SMC. Figure 13: SMC response. Figure 16 shows the chattering in the signals before and after applying SMC. The SMC-controlled system showed very low chattering compared with the signal chattering.