# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 4 Results and Discussion  
### Kinematic and Dynamic Characteristics  
The analysis of the kinematic and dynamic characteristics of the aerodynamic flap control mechanism revealed the system's high sensitivity to external disturbances, including sudden wind speed changes, the presence of backlash, and inertial loads. It was established that the behavior of the flap is governed by a combination of factors--from the characteristics of the servo motor to the properties of the transmission links--and requires precise coordination of control actions. Classical control approaches with fixed parameters do not provide sufficient stability and accuracy under variable operating conditions. This highlights the need for the development of an intelligent control system capable of adapting to current external influences, ensuring fast and stable flap positioning, and compensating for the negative effects of mechanical nonlinearities. The main goal of this section is to construct a mathematical model of the control system, select a regulator structure, and define the parameters that ensure efficient mechanism performance under various wind load scenarios. The MG996R servo motor can be approximated as a second-order linear dynamic system, represented by the following transfer function [39]:  
\[G(s)=\frac{K}{s(Ts+1)} \tag{37}\]  
where \(K\) is the gain coefficient, depending on the characteristics of the motor and the gearbox. For this servo model, \(K\) = 6.28 rad/s is assumed, which corresponds to the conversion from frequency response to angular output; \(T\) is the time constant, characterizing the inertial properties of the system. The value \(T\) = 0.12 \(s\) is based on datasheet specifications and experimental measurements; \(s\) is Laplace operator, used for analyzing dynamic systems in the frequency domain. The transfer function reflects the inertial-amplifying nature of the servo control system, where the output signal (shaft rotation angle) is the integral of the control input, attenuated by a time delay. Substituting the numerical parameter values into Equation (37), we obtain the specific form of the transfer function for the MG996R model:  
\[G(s)=\frac{6.28}{s(0.12s+1)} \tag{38}\]This model allows for describing the servo's dynamic response to control input and can be further used for stability analysis, PID controller tuning, and numerical simulation of the system's response to various input signals. In particular, it is applicable when calculating the angular accelerations of the flap and constructing the complete controllable model of the mechanism. For more accurate modeling of the control system, it is necessary to consider not only the dynamics of the servo itself but also the characteristics of the transmission components--the gearbox and the aerodynamic flap drive mechanism. These elements introduce additional inertial and scaling effects, determining the final kinematic transmission from the control input to the output element--the aerodynamic flap. The gearbox integrated into the MG996R servo reduces speed and increases torque delivered to the output shaft. Its gear ratio is \(i_{red}\) = 14. Accordingly, the gearbox's transfer function in the system's transmission chain can be represented as a scaling coefficient [40]:  
\[G_{red}(s)=\frac{1}{i_{red}}=\frac{1}{14} \tag{39}\]  
The next element in the kinematic chain is the lever mechanism, which connects the gearbox output shaft to the rotation axis of the aerodynamic flap. This mechanism also has its own transmission ratio, which defines the relationship between the rotation angle of the lever and the rotation angle of the flap. For the given configuration, \(i_{mech}\) = 1.875.