# A Comparative Study of Control Methods for X3D Quadrotor Feedback Trajectory Control
## 4 Simulation Results  
All linear and nonlinear controllers can provide system stability and optimum performance under their nominal conditions. It is indeed challenging to obtain equivalent results from both the simulation and the real-time experiment due to highly precise parameter adjustment and nonlinear parameters and dynamics. Researchers generally use modelled linear controllers because of their simplicity of design and implementation, as well as their ability to produce high-quality experimental data. On the other hand, robustness, noise and disturbance elimination, limitation control at the endpoints, and more precise trajectory tracking are all advantages of nonlinear controllers [34; 35; 36]. Therefore, theoretical studies reveal that linear controllers such as LQR and PID are good at maintaining stability under nominal conditions but not so good at ensuring robustness. The fuzzy controller, on the other hand, cannot guarantee nominal stability but can offer adequate and excellent maneuvering performance. Furthermore, hybrid and adaptive controllers are created as units in which many controllers can work together to provide the finest balance of robustness, nominal stability, flexibility, optimality, simplicity, tracking ability, rapid response, and disturbance rejection to a system, among other features. High computation, a large amount of training data, estimation error, and the existence of uncertainty are the issues that these controllers must confront to achieve satisfying performance, even though they are capable of ensuring remarkable outcomes when the system is disturbed by uncertainty. For example, LQR becomes LQG when the Kalman filter is used to generate a state observer and eliminate signal noise. Secondly, to achieve excellent maneuvering performance, a model reference adaptive controller is used to update the PID controller gain. Figure 12 shows the proposed control structure, which includes a control unit, an X3D Quadrotor, an inertial measurement unit (IMU), and a Kalman filter. The reference input will be received first by the quadrotor system. It measures the translational position and rotational position, velocities, and accelerations of the X3D Quadrotor at a specified time. The output of the quadrotor is then sent to the IMU sensor, which includes a three-axis accelerometer and a gyroscope. The Kalman filter is used to rectify and filter the output of an IMU sensor before it is fed back to the control unit. The control unit then generates an output that is equivalent to the thrust that all motors must provide in order to maintain the well-defined requirements of the X3D quadrotor. The proposed control structure mentioned above is implemented in the MATLAB Simulink environment. To evaluate the performance of all control systems for the specified reference position, unit step tests are performed in all the three axes, x, y, and z. Desired references for step input at the xyz positions are set to 1. The simulation period of an X3D Quadrotor system is defined as 30, 50, and 400 s, correspondingly, for positional testing (x, y, and z) among suggested controllers. Figure 12: Quadrotor closed-loop control system. Figures 13-18 illustrate the output response of the closed-loop control system for the longitudinal position (\(x\)-axis), lateral position (\(y\)-axis), altitude (\(z\)-axis), and attitude (roll, pitch, and yaw angle) for each of the four controllers. All controllers work well in keeping the quadrotor in the proper reference position, as can be seen in these figures. Tables 6-8 provides the comparison of step test results in terms of rising time, settling time, peak time, and overshoot for all three dimensions (\(x,y,\) and \(z\)). Figures 13 and 14 show the X and Y position responses, whereas Figure 15 shows the height (\(z\)-axis) response.