# A Comparative Study of Control Methods for X3D Quadrotor Feedback Trajectory Control
###### Abstract  
Unmanned aerial vehicles (UAVs), particularly quadrotor, have seen steady growth in use over the last several decades. The quadrotor is an under-actuated nonlinear system with few actuators in comparison to the degree of freedom (DOF); hence, stabilizing its attitude and positions is a significant challenge. Furthermore, the inclusion of nonlinear dynamic factors and uncertainties makes controlling its maneuverability more challenging. The purpose of this research is to design, implement, and evaluate the effectiveness of linear and nonlinear control methods for controlling an X3D quadrotor's intended translation position and rotation angles while hovering. The dynamics of the X3D quadrotor model were implemented in Simulink. Two linear controllers, linear quadratic regulator (LQR) and proportional integral derivate (PID), and two nonlinear controllers, fuzzy controller (FC) and model reference adaptive PID Controller (MRAPC) employing the MIT rule, were devised and implemented for the response analysis. In the MATLAB Simulink Environment, the transient performance of nonlinear and linear controllers for an X3D quadrotor is examined in terms of settling time, rising time, peak time, delay time, and overshoot. Simulation results suggest that the LQR control approach is better because of its robustness and comparatively superior performance characteristics to other controllers, particularly nonlinear controllers, listed at the same operating point, as overshoot is 0.0% and other factors are minimal for the x3D quadrotor. In addition, the LQR controller is intuitive and simple to implement. In this research, all control approaches were verified to provide adequate feedback for quadrotor stability. X3D quadrotor; closed-loop system; PID; LQR; fuzzy control; model reference adaptive PID +
Footnote †: journal: Applied Sciences  
nature, it offers a great maneuverability advantage. It has a good hovering ability and a quick response for tracking [2]. It is widely used in both outdoor and indoor situations for research and monitoring. High-performance quadrotor control in intense and maneuverable flight is a challenging problem due to the complex nature of the dynamic model, severe coupling, and nonlinear characteristics. Scientists may use the control of quadrotors for testing and evaluating novel concepts in a range of disciplines, including flight control theory, navigation, and real-time systems. Many researchers from all around the globe have detailed various methods for operating quadrotor UAVs, to the extent of developing an effective stabilizing and navigation system based on the standard control input. A PID controller is extensively used in many industrial applications because of its simplicity and ease of implementation, on the other hand, the LQR controller provides better performance concerning certain measures of performance; fuzzy controller and adaptive PID controller are also extensively implemented for nonlinear systems. Many investigations have been performed on the application of PID, LQR, fuzzy, state feedback, and other control methods to quadrotor UAVs as a plant, but there has been relatively little study on the comparison of linear and nonlinear control methods. The study in [3] proposed a method for simulating and establishing parameters for a quadcopter to analyze and improve the performance of this system and its stability. The system was mounted on a structure that could be freely moved along a vertical axis. The computer received real-time data from sensors and measuring devices. The paper [4] proposed a comparison of nonlinear and linear control methods for quadrotor systems. In this paper [5], a comparison of PID and LQR control techniques is provided. Both controllers provide appropriate feedback for quadrotor stability, according to this study.