# Adaptive Recursive Sliding Mode Control (ARSMC)-Based UAV Control for Future Smart Cities
## 5 Discussion: Simulation Response of Control Strategies  
The novel ARSMC strategy effectively addresses key issues, such as finite-time convergence, robustness for parametric perturbations, and singularity. To verify its effectiveness, we conducted a comparison study and evaluated the performance of the controller in terms of the vertical stability (pitch angle) and horizontal stability (yaw angle). Additionally, the controller was tested in the presence of disturbances, such as external disturbances, parametric uncertainties, coupling effects, and noise signals. The simulation response of TRMS under different control strategies provides key ideas on how the augmentation of a recursive strategy in SMC with adaptive laws performs better. The convergence time of pitch and yaw angles in Figures 7 and 8 represents the brief response with their convergence time in subplots. The figure that shows the square input for both the pitch angle and yaw angle of the TRMS illustrates that the pitch angle has a faster convergence time than the yaw angle. This delay is because the main rotor must be stabilized first in order to counteract the disturbance generated by the tail rotor, such as the gyroscopic torque effect and the coupling effect. As a result, the convergence time of the tail rotor cannot be faster than that of the main rotor. Figure 8: Yaw angle of UAV for ARSMC. Figure 7: Pitch angle of UAV for ARSMC. The step input tracking response in the simulation confirms that the control theory regarding the convergence time of the angles, specifically the pitch and yaw angles, is logical and results in a sharp stability response. According to the effectiveness of the proposed controller, the control actions response for both angles can be characterized on the basis of minimum voltage variations. A subplot also shows the attenuation due to the applied noise signal and the range of disturbance being tackled by an efficient controller. Other subplots verify how the controller can manage the considered disturbance over time. The system response becomes more stable over time, which represents a remarkable difference with respect to other applied control methods to date. The convergence time and effect of attenuation are greater in the yaw angle. The reason behind this change is that the coupling effect due to the disturbance torque is greater due to the weighted rotor as well as the blades of the main rotor. A slight sharp variation in yaw angle is generated by different factors created by the main rotor. The time constant values are also provided in the subplots of both figures, which refer to the characteristic timescales associated with the system's response to changes or disturbances. The specific time constants depend on the nature and complexity of the mechanical system under consideration. The control actions of both angles are elaborated via Figures 9 and 10. The control action for the pitch angle shows slightly more variations compared to the control input of the yaw angle. There are several reasons for this. As we know, the pitch angle and yaw angle are both important angles that need to be controlled in a twin-rotor MIMO (multiple-input multiple-output) system. However, the response of the pitch angle control input may show more variations compared to the yaw angle control input due to several factors. The first reason is that the twin-rotor MIMO system is inherently unstable and highly nonlinear. This means that even small changes in the input or the system's parameters can result in significant variations in the output. The pitch angle control input may be more sensitive to changes in the system's dynamics, leading to more variations in the response. The second reason is that the pitch angle control input may require more precise control than the yaw angle control input. Pitch angle control is essential for maintaining the altitude and stability of the system, which requires very precise control.