# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 5 Conclusions  
The conducted research aimed at the development and analysis of an adaptive control system for the aerodynamic flaps of a two-tier Savonius rotor, operating under variable wind loads. During the study, a detailed kinematic model of the control mechanism was built, taking into account the drive structure, transmission links, and the rotation geometry. The simulation showed that at a motor angular speed of 50 rad/s, the linear velocity at the end of the lever reaches 0.536 m/s, while the linear velocity at the edge of the flap is 0.114 m/s. In the presence of backlash of 3\({}^{\circ}\) (0.052 rad), a phase delay in the mechanism's response of up to 0.15 s was observed, which is especially critical under low wind conditions. Sensitivity analysis demonstrated that even a small change in lever length or transmission ratio affects the movement amplitude, inertial characteristics, and positioning accuracy of the flap. The dynamic analysis confirmed the system's high sensitivity to external disturbances. It was shown that the wind torque increases with the square of the wind speed, from 1.76 N\(\cdot\)m at 10 m/s to 10.16 N\(\cdot\)m at 25 m/s, which is equivalent to an almost sixfold increase in load. In such conditions, inertial characteristics play a critical role--the moment of inertia of the flap (0.0096 kg\(\cdot\)m\({}^{2}\)) significantly limits the system's response speed and requires precise tuning of the control inputs. During a wind gust from 15 to 25 m/s, the simulation showed an impact angular acceleration of up to 183 rad/s\({}^{2}\), which can induce oscillations that transition into resonance modes, especially when there is insufficient damping or backlash in the transmission. Strength and deformation analysis of the key structural elements--the lever, flap, and gear connections--showed that deflections under maximum loads do not exceed 0.04 mm, and the elastic deformation of the teeth is around 7.18 \(\times\) 10\({}^{-6}\) mm, which confirms the high stiffness and durability of the design. Special attention was paid to the design and tuning of the control system. The use of a classical PID controller with coefficients \(K_{p}=2.1\), \(K_{i}=5.25\), \(K_{d}=0.21\) (based on the Ziegler-Nichols method) demonstrated unstable system behavior under strong winds: overshoot reached 25%, high-frequency oscillations in angular velocity up to 2 rad/s were observed, and actuator overloads occurred. The introduction of an adaptive control scheme with variable coefficients depending on the current wind speed (gain scheduling) significantly improved the stability and quality of the response. The optimal parameters were found to be \(\alpha_{p}=0.8\), \(\alpha_{i}=0.6\), \(\alpha_{d}=1.2\), at which the transient process lasted less than 2.5 s, overshoot did not exceed 5%, and the angular velocity remained within safe limits (<0.9 rad/s). The simulation also showed that including a predictive filter further smooths the transient processes and prevents oscillations during strong wind gusts. Thus, the adaptive control system presented in this work has proven its effectiveness and applicability for real operating conditions of vertical-axis wind turbines of the Savonius type. Given the mechanical nonlinearities accounted for in the model--friction, backlash, impacts, and inertial effects--it can be stated that the developed solution not only ensures high accuracy of aerodynamic flap positioning but also reduces dynamic overloads, thereby extending the lifespan of mechanical components. The numerical results, calculation methods, and conclusions can be used for the development of intelligent control systems for next-generation wind turbines operating in unstable climatic conditions, including urban and coastal areas. To further support the presented results, future work will include laboratory-scale experimental validation of the proposed control system. A physical prototype of the two-tier Savonius rotor with adaptive aerodynamic flaps will be developed and tested under controlled wind conditions.