# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 1 Introduction
These works provide valuable data on structural response to external loads; however, they do not incorporate control algorithms that account for real mechanical nonlinearities such as backlash and viscous friction. In [10], researchers proposed a backlash compensation algorithm for control mechanisms in vertical-axis wind turbines. Nevertheless, the study did not include adaptive tuning of control parameters under sudden changes in wind load, which may reduce the system's stability in real-world conditions. In [11], researchers examined the impact of friction on the quality of blade control in wind turbines. Although the authors provided a detailed analysis of the negative effects of friction, they did not offer adequate methods for compensating for this effect under dynamically changing loads. In [12; 13; 14], researchers focused on optimizing PID controllers for VAWT control. These studies present interesting approaches to regulator coefficient selection, but the proposed solutions were not tested for robustness under sustained and abrupt wind loads, leaving questions about the reliability and effectiveness of the methods unresolved. Predictive approaches described in [15; 16] and Ref. [17] offer promising techniques for wind turbine control, particularly under variable wind conditions. However, these studies primarily focus on controller tuning and wind adaptation, without explicitly modeling the mechanical nonlinearities present in actuator-flap systems. Key effects such as backlash, dry friction, and impulsive torque disturbances are either neglected or highly simplified, which limits the applicability of the proposed methods in real mechanical configurations. In contrast, Ref. [18] provides a detailed kinematic and dynamic analysis of vertical-axis wind turbine (VAWT) structures, addressing the physical behavior of the system components. Yet, it lacks the integration of adaptive or predictive control methods, which are essential for enhancing system responsiveness and energy efficiency. The present work combines both perspectives by introducing an adaptive control strategy grounded in a high-fidelity dynamic model that incorporates mechanical nonlinearities. This integration ensures that the control algorithm remains robust under real-world conditions, where actuator imperfections and structural dynamics significantly affect system performance. This combined modeling-and-control approach constitutes the main novelty of the proposed study. This study addresses these challenges through a comprehensive approach that includes detailed kinematic and dynamic modeling of the aerodynamic flap control system for a two-tier Savonius rotor. Special attention is given to the integration of mechanical components, actuators (in particular, servos), and the development of mathematical models that fully consider nonlinear factors such as backlash, friction, and dynamic loads. A key aspect of this research is the optimization of adaptive PID controller parameters and the integration of predictive control elements to ensure high efficiency and reliability of the system under real operating conditions.