## 4 Simulations and Experimental Test
### Comparisons with Other Methods  
In order to show the performance improvement of the proposed control scheme, simulations are conducted by comparing the proposed control scheme with PID control [17] and SMC with radical basic function neural network (SMC-RBFNN) [25]. Among the two control schemes, PID control is the most widely used method in practice, while SMC-RBFNN is also an advanced nonlinear control approach which can alleviate the chattering and improve robustness without sacrificing control performance. The parameters of the three control schemes are given in the Appendix A. The process of the simulations is described as follows.  
The whole simulation is completed within 90 s. At first, the UAV spirals up to 80 m in the first 40 s. In the next 10 s, the UAV flights forward the \(X\) direction, and a lateral sinusoidal disturbance force with amplitude of 4N is introduced in 45-49 s. Then, the UAV turns right at 50 s and flights forward the \(Y\) direction. In 55-59 s, the sinusoidal disturbance of the rolling moment with magnitude of 1.5 N\(\cdot\)m is introduced. At 60 s, the UAV turns right and flights forward the opposite direction of the \(x\)-axis. In 65-69 s, the sinusoidal disturbance of the pitching moment with magnitude 1.5 N\(\cdot\)m is introduced. Finally, the UAV reduces the altitude and lands in the last 20 s. The desired and actual trajectories of the tilt tri-rotor UAV are shown in Figure 8.  
Figure 8: Path following.  
Figure 7: Attitude variations under the disturbances when parameters change \((\phi,\theta,\psi)\).  
The curves of the position, attitude, and the thrust \(T\) are depicted in Figures 9-11. In Figure 9, compared with the other methods, the position errors of the proposed SMC-AD control method in this paper always keep a smaller value in the simulation process when the external force or moment disturbances are added. Besides, in the stage of taking off and landing, the proposed control scheme shows better tracking performance. In the aspect of attitude control, Figure 10 show that roll, pitch, and yaw motion can quickly suppress the influence of torque disturbance and track the desired attitude signal by using the proposed method. In the whole simulation process, the PID control show greater attitude vibrations, and the curves of the proposed method are close to that of the SMC-RBFNN control scheme. Figure 11 shows the virtual thrust which is computed by the flight controller. It can be seen that the proposed SMC-AD method successfully restricts the virtual control thrust and the thrust is smaller and smoother than the other two methods. This kind of restriction is very useful in practical applications. Once actuator saturation occurs, the UAV without thrust constraint may be unexpectedly unstable.  
Besides, the integral of absolute value of error (IAE) \(IAE_{x}=\int_{0}^{T}|x|dt\) performance index is also used to compare the control performance of these three control schemes. The less value of the IAE index means faster convergence rate and better control performance. The IAE indexes acquired from the simulations are presented in Table 3. It can be observed that the indexes of the proposed SMC-AD control scheme in the position control are much smaller than the two other methods. As for the attitude control, the gap between the indexes of the proposed method and the other two methods are shorten. However, the performance of the SMC-AD control scheme is also better than the PID control and the  
Figure 11: Virtual control thrust \(T\).  
Figure 10: Attitude variations \((\phi,\theta,\psi)\).  
SMC-RBFNN control scheme. According to the results given above, it illustrates that the proposed method significantly improves the control performance of the tilt tri-rotor UAV in the hover mode.