# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 3 Dynamic Analysis of the System
For a three-link system, the numerical values are presented in \[\delta_{r}=\frac{F_{s}L_{r}^{3}}{3 EI} \tag{22}\]5  
According to (36) and the data in Table 2, \(X_{cm}\) = 0.058 m. Thus, the center of mass is shifted toward the flap, which increases inertial loads. The values of link masses and geometrical parameters were selected based on realistic proportions typical for compact vertical-axis wind turbine mechanisms. The moment of inertia, mass distribution, and lever arm dimensions were derived analytically using fundamental dynamic principles to reflect a physically plausible system layout. This ensures that the modeled behavior of the control mechanism--including angular acceleration, torque demand, and susceptibility to oscillations--corresponds to configurations that can be realized in practice. Such an approach makes the control system analysis directly applicable to real-world implementations, rather than based on abstract or arbitrarily simplified structures. The dynamic analysis of the flap control mechanism in a two-tier Savonius wind turbine demonstrated the system's high sensitivity to external disturbances, particularly to changes in wind load. The primary external torque acting on a single flap depends on the square of wind speed: when the speed increases from 10 m/s to 25 m/s, the torque rises from 1.76 N\(\cdot\)m to 10.16 N\(\cdot\)m--nearly 5.8 times. Such a sharp increase in external load requires an immediate and precisely coordinated response from the actuator. At the same time, the flap's moment of inertia, equal to 0.0096 kg\(\cdot\)m\({}^{2}\), creates substantial resistance to changes in angular velocity, especially during sudden disturbances. In the event of a wind speed jump from 15 to 25 m/s, the system experiences an impact torque of approximately 1.76 N\(\cdot\)m, which, when transmitted through a gearbox with a gear ratio of 14, is converted into a reactive torque of 0.126 N\(\cdot\)m on the gear transmission. This torque can induce parasitic oscillations and overload the mechanism. It was also established that a backlash of about 3\({}^{\circ}\) (0.052 rad) causes a phase delay in the flap's response to control actions, which is especially critical under low wind conditions and must be compensated either mechanically or algorithm \begin{table}
\begin{tabular}{c c c} \hline
**Link** & **Mass (kg)** & **Coordinates** \\ \hline Flap & 0.3 & (0.15, 0) \\ Lever & 0.1 & (0.075, 0) \\ Gearbox & 0.5 & (0, 0) \\ \hline \end{tabular}
\end{table} 
Table 2: Numerical values of the link parameters. cally. The dry friction model, with a coefficient of 0.05 and a lever arm of \(R_{s}\) = 0.08 m, generates a constant braking torque that, at low speeds, is comparable to the control torque and can completely block flap movement. Even when using a high-torque servo such as the MG996R, resistance and inertial effects must be taken into account. Mass distribution analysis showed that the system's center of mass is offset toward the flap by 0.0525 m from the rotor center, which increases inertial loads and contributes to vibrations. Calculations revealed that under a sharp rise in wind load, the flap's angular acceleration can reach 183 rad/s\({}^{2}\), confirming the need for damping and response speed limitation. Taking into account all these factors--high external loads, inertia, friction, backlash, and vibrations--it becomes evident that an active control system with adaptability to changing conditions is necessary. Classical control schemes with fixed coefficients are insufficient: they either fail to compensate for external influences in time or induce oscillations and overloads. To ensure stable, reliable, and resource-efficient operation of the mechanism, an adaptive control system is required. It must be capable of adjusting its parameters based on wind conditions, accounting for system dynamics, compensating for backlash and friction, and preventing resonance and impact phenomena.