# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 4 Results and Discussion
### Kinematic and Dynamic Characteristics
The system's response is delayed, followed by a compensating spike. The behavior may be unstable during sharp wind changes. Figure 15 shows a mode similar to the graph in \[G_{red}(s)=\frac{1}{i_{red}}=\frac{1}{14} \tag{39}\]7 There is a fast and stable response, but the damping of oscillations occurs more slowly due to the lower D-component value. It is a good option, but lags in terms of dynamics. Figure 16 Transient response of the aerodynamic flap control system under different wind conditions and controller configurations. The top graph shows the flap angular displacement, and the bottom graph shows the corresponding angular velocity over time. The blue solid line corresponds to a wind speed of 10 m/s with fixed PID parameters. The orange dashed line shows the response at 25 m/s with the same fixed parameters, demonstrating higher overshoot and oscillations. The green dash-dotted line represents the adaptive PID control at 25 m/s, showing improved damping, reduced overshoot, and enhanced stability under strong wind conditions (coefficients: \(\alpha_{p}\) = 0.8, \(\alpha_{i}\) = 0.6, \(\alpha_{d}\) = 1.0). Based on the comparative analysis, the optimal coefficients were found to be \(\alpha_{p}\) = 0.8, \(\alpha_{i}\) = 0.6, \(\alpha_{d}\) = 1.2 (as seen in Figure 8), at which the system demonstrates the following:  
* Minimum settling time;
* Fast damping of oscillations;
* No significant overshoot;
* High stability under external disturbances. To further illustrate the performance of the compensation mechanisms under challenging conditions, two additional simulation scenarios were considered. Figure 16 presents the flap angle response under strong wind conditions (\(v\) = 35 m/s), where a 3\({}^{\circ}\) mechanical backlash introduces a short delay in actuation. Once the dead zone is overcome, the system reaches the setpoint smoothly and remains stable, confirming the effectiveness of the adaptive PID controller in suppressing dynamic overshoot. In contrast, Figure 18 shows the flap behavior under low wind conditions (\(v\) = 3 m/s), where the control torque becomes comparable to the opposing dry friction and backlash. As a result, the flap exhibits minimal movement, with only small oscillations around the initial position. This highlightsa known limitation of conventional control in low-input regimes and underscores the potential need for enhanced compensation, such as dead-zone inverse control or nonlinear gain scheduling. An especially important factor in choosing the adaptive coefficients is the quality of the response when operating in gusty wind conditions (\(v\) = 25 m/s). A comparison of the graphs shows that when using base coefficients (orange line), the system reaches the target value faster, but is accompanied by significant angular velocity oscillations and high overshoot. Such modes can lead to rapid wear of the actuators, reduced reliability, and increased load on the system. In contrast, adaptive coefficients (green line) provide a smoother and more stable response with fewer oscillations in both the angle of rotation and angular velocity. Despite a longer settling time, the system's behavior remains controllable, stable, and less susceptible to mechanical overloads. Although various advanced control techniques--including fuzzy logic, sliding mode control, and neural network-based adaptation--are widely explored in the field of wind turbine control, they were not included in this work. The primary objective of the present study was to develop a strategy that ensures physical interpretability, real-time feasibility, and ease of implementation on embedded hardware. In this context, the adaptive PID controller offers a favorable compromise. It enables dynamic adjustment of gains based on real-time estimates of wind torque while maintaining analytical transparency and low computational complexity.