# Performance Evaluation of a Quadcopter by an Optimized Proportional-Integral-Derivative Controller
## 1 Introduction
The work in [14] proposed an NLPID (nonlinear PID) controller to stabilize the translational and rotational motion of a 6-DOF (degree of freedom) UAV quadrotor system and force it to track a given trajectory with minimum energy and error, except in the previous discussion of the PID controller which has the three parameters that can be adjusted according to the MPU6050 return angular speed and rate [15]. Generally, the motor speed is controlled by the PID controller in order to ensure that the quadcopter UAV PID is stably controlled. In [16], where the use of Ziegler-Nichols oscillation tuning rules is described, the use of closed-loop testing to obtain critical point information that is needed to determine the PID controller is detailed. The work presented in [17] illustrates a quadcopter equipped with PID controllers for stabilization requirements and that are used to regulate its four basic motions: roll, pitch, yaw angles, and altitude. The quadcopter was originally equipped with sensors and software to estimate and control the orientation of the quadcopter. In addition, an APE (adaptive perturbation estimator) was based on a DSC (dynamic sliding control) applying the PID for a UAV, as demonstrated in [18]. The presented controller is used to significantly remove the negative effects of uncertainties/perturbations to improve the stabilization control performance of a UAV. In general, the basis of the PID controller is ultimately defined by a feedback system. However, due to the non-linear and physical parameters of multi-rotor UAVs, the attitude control system of the UAV will be designed as a cascade structure of PID control. In general, the controller consists of three attitude angles; these are Yaw (YAW), Pitch (PITCH), Roll (ROLL), which are arranged on the \(X\), \(Y\), and \(Z\) axis, respectively. The \(Z\)-axis of the fuselage is surrounded, and the attitude control is the basis of the quadrotor UAV PID control  
Figure 1: Basic Optimized PID architecture proposed in the article simulated with Matlab®Simulink. method. The basic knowledge of cascade PID is supplemented to facilitate future design. A multi-rotor UAV simulation model created in Matlab(r)Simulink that presented the results of the first stage is discussed in [19]. In the previous report, a quadcopter mechanical model was developed based on Simscape Multibody library elements. In addition, an angular position and flight altitude control model based on PID controllers was designed using the standard Simulink libraries. It is assumed that stability, controllability, and even causality are normally the critical conditions of a control system. On the other hand, based on the constrains that motivated the investigation of the quadcopter and the data readings of the sensor analyzed by the IMU, the overall results obtained follow the methodologies proposed in this article. Recently, the PID is not efficient as mentioned by many other studies, such as in the discussion articles [20; 21; 22], when the environment faces external disturbances and parametric variations. However, the scenario considered in the current article points out that the use of PID was focused on the practice experiment without too much mathematical analysis. That is, the motivation for the proposed \"optimized PID\" is to try to give contributions on the following points:  
1. Try to obtain the most stable conditions of the UAV by adjusting the four parameters, \(k_{p}\), \(k_{i}\), \(k_{d}\), of a PID controller. 2. Trying to obtain the best results from a PID controller that can implicitly control the roll, pitch, and the yaw of a quadrotor. 3. Attempt to implement the proposed \"optimized PID\" with some experimental tools (Proteus(r), Matlab/Simulink(r), and MCU IDE) for validating the obtained results. It is believed that these results from the experimental simulation will be of interest to beginners (even senior scientists) in terms of stability and control for a PID controller. 4.