# Research on Amphibious Multi-Rotor UAV Out-of-Water Control Based on ADRC
## 4 Controller Design
In addition, to reduce the high-frequency jitter of the control signal, the \(sat(s)\) function is used instead of \(\text{sgn}(s)\), in the form shown in Equation (23). When the jitter condition of the output control signal is weak, it can be used as the final control quantity. \[sat(s)= \begin{cases}1&,s>\Delta\\ ks&,-\Delta\leq s\leq\Delta\\ -1&,s<-\Delta\end{cases}  \tag{23}\]  
Equation (24) is used to simulate the disturbing external force during the motion across the medium. Additionally, considering the position offset generated by the amphibious multi-rotor UAV due to wave surge during underwater waves, this paper uses the random signal as shown in Figure 5 to represent the position offset and add it to the simulation position control loop. Figure 5: Random offset. \[\left\{ \begin{array}{l}d_{fX}+d_{kX}+d_{lX}=0\\ d_{fY}+d_{kY}+d_{lY}=0\\ d_{fZ}+d_{kZ}+d_{lZ}=2\sin(0.2\pi t)\\ d_{fK}+d_{kK}+d_{lK}=\sin(t)\\ d_{fM}+d_{kM}+d_{lM}=\sin(t)\\ d_{fN}+d_{kN}+d_{lN}=\sin(t)\end{array} \right. \tag{24}\]  
The physical parameters of the amphibious multi-rotor UAV and the parameters designed for the simulation experiments are shown in Table 4.  
A simulation experiment using MATLAB with a simulation time of 15 s; given the initial position \(Z=-1m\) and the desired position \(Z=1m\); initial positions of \(\phi=0.5 rad\), \(\theta=0.4 rad\), and \(\psi=0.3 rad\), and desired positions of \(\phi=0\), \(\theta=0\) and \(\psi=0\). The parameters of the PID controller and SMC controller are also adjusted to show better control performance, and the parameters of the ADRC controller are adjusted to meet the control requirements. The final simulation results are shown in Figures 6 and 7. From the simulation results of the attitude angle control in Figure 6, it can be found that PID, SMC, and ADRC can all bring the attitude of the UAV to the set desired attitude in about 3-4 s and keep the attitude in the vicinity of the desired attitude. It can also be found that after 4 s, the PID control curve has an obvious fluctuation compared with SMC and ADRC, and the fluctuation range is \([-1.5^{\circ},1.5^{\circ}]\); the SMC and ADRC control curve is relatively flat, and the fluctuation range is \([-0.7^{\circ},0.7^{\circ}]\); for the attitude control of the water exit process, PID and SMC and ADRC can all complete the effective control of the UAV attitude, but the anti-interference ability of the PID algorithm is weaker than SMC and ADRC. \begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Numerical Value** & **Name** & **Numerical Value** \\ \hline \(m(kg)\) & 5 & \(H(m)\) & 0.31 \\ \hline \(B(N)\) & 42.5 & \(Z_{B}(m)\) & 0.06 \\ \hline \(g(m\cdot s^{-2})\) & 9.8 & \(K_{Fau}\) & \(3.5\times 10^{-2}\) \\ \hline \(l_{x}(kg\cdot m^{-2})\) & 0.1146 & \(K_{Fau}\) & \(4.97\times 10^{-6}\) \\ \hline \(l_{y}(kg\cdot m^{-2})\) & 0.1408 & \(K_{Tau}\) & \(1.126\times 10^{-4}\) \\ \hline \(l_{z}(kg\cdot m^{-2})\) & 0.1793 & \(K_{Tau}\) & \(2.012\times 10^{-5}\) \\ \hline \(R(m)\) & 0.065 & \(\rho_{a}(kg\,\cdot\,m^{-3})\) & 1.293 \\ \hline \(l(m)\) & 0.42 & \(\rho_{w}(kg\,\cdot\,m^{-3})\) & 1000 \\ \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figure 6: Simulation results of PID, SMC and ADRC out-of-water motion attitude angle control: (a) roll angle, (b) pitch angle, (c) yaw angle. From the simulation results of the altitude control in Figure 7, we can find that PID, SMC, and ADRC can all complete the altitude control of UAV. The time for the PID to reach the desired height for the first time is 3 s, which has better rapidity compared with SMC and ADRC, but the control curve of the PID is more fluctuating, with a fluctuation range of \([0.8m,1.2m]\) and an obvious amount of overshoot. The time for SMC and ADRC to reach the desired height for the first time is 6 s. Although there is a small reduction in rapidity, the fluctuation of the SMC control curve is smaller, and the fluctuation range is \([0.9m,1.1m]\), and there is a reduction in overshoot, which also reflects better anti-interference performance.