# Height Control System for Wind Turbines Based on Critical Wind Speed Calculation
## 5 Experimental Tuning of PI Controller Parameters  
In this study, a detailed selection of PI controller coefficients was conducted for the rotor-lowering system of the Onipko wind turbine in strong wind conditions. The primary goal of the experiment was to determine the optimal values of the proportional (\(K_{p}\)), integral (\(T_{i}\)), and differential (\(T_{d}\)) coefficients to ensure reliable and stable system operation under high wind speeds. The PID controller cont_c in the TIA PORTAL software environment served as the object of the study. In the initial experiment, only the integral component was included, with an integration time of 20 s, a polling cycle time of 1 s, and a proportionality coefficient of 1. The response of the control signal LMN to the change in integration time was analyzed with SP_INT = 40 and GAIN = 1. The results of the investigation are presented in Table 2.  
In Figures 3-8 the red line (LMN_I) is the value of the integral component of the regulator (I-component), the white line (LMN) indicates the overall control signal of the system (LMN), the yellow line (ER) is a regulation error (Error, ER) and the green line is the desired value. Figure 5: Integral regulator at \(T_{i}\) = 100 ms.  
Figure 6: Integral regulator at \(T_{i}\) = 300 ms.  
Figure 7: Integral regulator at \(T_{i}\) = 500 ms. The first integration time value was chosen to be 10 ms, during which the control signal entered self-oscillation and did not recover (Figure 3). At the minimum integration time \(T_{i}\) = 10 ms, persistent self-oscillations can be observed. Increasing \(T_{i}\) to 50 ms provides an excellent control signal graph with damped oscillations (Figure 4), and the signal tends toward the desired value. The lines are the same as in Figure 3.  
Gradually increasing the integration time led to a reduction in oscillations and an acceleration of the transition process (Figures 5 and 6). At \(T_{i}\) = 300 and 500 ms, the oscillations were so minimal that calculating the damping coefficient became impossible (Figures 7 and 8). It should be noted that at \(T_{i}\) = 1000 ms, oscillations do not occur at all, and the control signal gradually approaches SP_INT exponentially. However, while previously the transition time gradually decreased with an increase in \(T_{i}\), it has now doubled. During the investigation of the \(P\) component, it was noted that as \(K_{p}\) increases, the value of the control signal gradually increases both at the beginning and the end of the transition process (Figures 9 and 10). Additionally, there is a trend of decreasing transition time. However, with very high values of \(K_{p}\), for example, 10, the transition process destabilizes. The results are presented in Table 3.  
Figure 8: Integral regulator at \(T_{i}\) = 1000 ms.  
Figure 9: Proportional regulator at \(K_{p}\) = 0.5. In Figure 9 to Figure 10, the green line (SP_INT) represents the setpoint, the desired value the system aims to reach; the red line (PV_IN) is the current value of the controlled parameter (Process Variable); the yellow line (LMN_OBJECT) is the control signal generated by the PID regulator to reach the setpoint (SP_INT); and white line (LMN) the overall control signal of the system. The next step involves combining the P and I components. The proportional gain was chosen to be 2.5 because at this value, the P component does not exceed the desired setpoint (SP_INT). The following results were obtained when varying the integration time, as shown in Table 4.  
At small values of \(T_{i}\), the control signal at the beginning of the transition process exhibits a distinctly oscillatory nature (Figure 11). The \(I\) component completely overshadows the \(P\) component due to its significantly larger magnitude. As the integration time increases further, the initial oscillations decrease (Figure 12), and subsequently, the transition process takes on an exponential form from the moment the influence of the \(P\) component ceases, but it takes significantly more time (Figure 13).