# Simulation of a Quadrotor under Linear Active Disturbance Rejection
## 4 System Simulation
At the same time, adaptive control also solves the parameter deviations caused by external disturbances and greatly improves the accuracy of the position control channel of the quadrotor UAV. Analysis of in Figure 6a-c shows that AP\(-\)ADRC has almost the same control effect as classical LADRC, and AP\(-\)ADRC requires fewer parameters to be optimized. Figure 6: Response curves of position control under three disturbances. (**a–c**) are the tracking curves for each of the three position control channels. **Example 3**. : _Simulation case 3 is to verify the stability, accuracy and rapidity of the RBF \(-\)ADRC robust control system for the full \(-\)attitude take \(-\)off of the quadrotor UAV. Three mathematical models of uncertain disturbances are given first._  
**Uncertain disturbance 1: strong wind disturbance**  
The mathematical model of the wind disturbance is designed with reference to the literature [30]. Wind disturbance will provide uncertain acceleration and the simulation is performed under time\(-\)varying disturbances. The mathematical model of the disturbance is shown in Equation (38), where \(\[PERSON]_{x}(t)\), \(\[PERSON]_{y}(t)\), \(\[PERSON]_{z}(t)\), \(\[PERSON]_{\theta}(t)\), \(\[PERSON]_{\varphi}(t)\), \(\[PERSON]_{\psi}(t)\) gives the external wind disturbance on the position and attitude channels, respectively. On the basis of this wind disturbance model, we randomly select a higher gain to offer the wind disturbance model a stronger disturbance to test the immunity of the proposed control scheme. \[\left\{ \begin{array}{l}\Xi_{x}(t)=10\sin(0.1013t-3.0403)+7\sin \left(0.5t+\frac{\pi}{2}\right)\\ \[PERSON]_{y}(t)=8\sin(0.5t-1)+6\cos(0.8t)\\ \Xi_{z}(t)=8\cos(0.6t)\\ \Xi_{\theta}(t)=5\cos(0.6t)\\ \Xi_{\varphi}(t)=9\sin(0.5t)\\ \Xi_{\psi}(t)=8\sin(0.6t)\end{array} \right. \tag{38}\]  
**Uncertain perturbation 2: step perturbation**  
Step disturbance is the most severe working state for the system and it can test the performance of the system in a wide range. Therefore, the introduction of step disturbance is of great significance to study the robustness of quadrotor. **Uncertain Perturbation 3: White Noise Perturbation**  
The resistance and wind force of the quadrotor in flight are unknown, with complexity and variability. White noise can simulate these uncertain disturbances well. Therefore, white noise is introduced to detect the robustness of the control system. This is extremely important. The three disturbances are placed in one graph for comparison at different times. The simulation graph is shown in Figure 7.  
Simulation case 3 is designed to test the immunity of the proposed REF\(-\)ADRC controller. Simulation case 2 shows that the AP\(-\)ADRC control scheme is more robust and has better control performance than the classical LADRC, therefore, in this simulation we compare the REF\(-\)ADRC with the AP\(-\)ADRC. To test the immunity of REF\(-\)ADRC to disturbances, we have designed three different strong disturbance models. To facilitate the comparison of the two controllers' performance, the above three uncertain disturbances are now designed in one simulation. This simulation produces a sparing disturbance with a final value of 5 at the 5 th second, a white noise disturbance from 10 to 15 s and a gust disturbance from 20 to 30 s, the mathematical model is shown in Equation (38). (a), (b) and (c) in Figure 7 show that the pitch angle reaches equilibrium at 1 s, the roll and yaw angles both reach equilibrium at 0.3 s and the response rate of the proposed control scheme is essentially the same as that of AP\(-\)ADRC, after which it reaches a steady state. At the 5 th second, after the saving disturbance is added, both control schemes overshoot, but the overshoot of AP\(-\)ADRC is greater.