# A Comparative Study of Control Methods for X3D Quadrotor Feedback Trajectory Control
###### Abstract
For the quadrotor's flip operation, [PERSON] compares the performance of three distinct types of attitude control systems [6]; PID, sliding mode and open-loop controllers are all used in his article to develop quadrotor attitude controllers. PID control is one of the most often used control strategies [1], [7] along with back-stepping [8; 9], nonlinear Hoo control [10], Kalman filter [11], and so on. Other control methodologies, such as fuzzy control systems, are also investigated and applied to a quadrotor, as discussed in [12; 13]. In the research in [14; 15], the implementation, testation, validation, authentication, and comparison of LQR, PID, and state feedback controllers have been performed on an X3D Quadrotor in NI LabVIEW simulation. The application of sub-super-stochastic matrices to bipartite tracking control in sign networks is presented in [16]. The research [17] represented an innovative decentralized control strategy for the Cucker-Smale model to analyze the leader-follower flocking behavior on networks that encompass both cooperative and rival relationships between agents. The research [18] addressed the PID and LQR controller implementation for the Qball X4 trajectory tracking. Simulations and experiments were conducted to compare the performance of the developed control strategies. A mathematical model was developed in the research paper [18] to simulate the behavior of a quadrotor with four motors driven by PID using a simple approach. In the study [19], feedback linearization and the LQR controller were proposed to stabilize the quadrotor attitude in the trajectory. A gain-scheduling fuzzy controller for quadrotor position and height control was proposed in the research [19]. The study [20] compared and implemented three controllers into an actual quadrotor in real-time, including PID, LQR, and backstepping. The research [21] offered three robust procedures for controlling a quadrotor in a predetermined trajectory based on the MIT rule and sliding-mode methods. A variety of commonly used quadrotor controllers were described in the previous study. With their algorithms, many control techniques have their strengths and limitations. As a result, the quadrotor's applications and performance determine the appropriate controller. The strengths and limitations of several controllers for controlling quadrotor systems are presented in Table 1.  
The primary motivation of this research is to show the experimental results of well-known and recently developed theoretical studies in the field of modern control system design and analysis for the quadrotor system. One of the most significant properties of control systems analysis is stability. Control systems must meet specified criteria for the system under investigation to operate as desired in both transient and steady-state response values that are as close to the desired value as possible. Therefore, the research presents the development and comparison of the quadrotor control system. The quadrotor plant is initially linearized for hover flight before the linear control approaches are implemented. This research compares the performance of linear and nonlinear control techniques, taking into consideration the restricted onboard computer resources. Because of the constraints imposed by nonlinearity factors and external disturbances, the primary goal is to maintain the translation position's stability, attitude, and altitude of an x3D quadrotor. The key contribution of the proposed research is to develop control systems for x3D quadrotors that will allow them to control the translation position \((x,y,z)\) while stabilizing its attitude angles (_roll_\(\phi\), _pitch_\(\theta\) _and yaw_\(\psi\)) by forcing the position \((x,y,z)\) and yaw (\(\psi\)) to track their respect to reference inputs while keeping the roll (\(\phi\)) and pitch (\(\theta\)) angles negligible [21]. The desired parameters, such as rise time, settling time, peak time, and maximum percent overshoot, and steady-state errors are analyzed in the MATLAB Simulink environment for the x3D quadrotor.