# Event-Triggered Fault-Tolerant ADRC for Variable-Load Quadrotor with Prescribed Performance
## 5 Simulation Experiments  
This study employed \(MATLAB\) for simulation implementation, with the total simulation duration set to 20 s and a fixed step size of 0.01 s. The parameter settings for the quadrotor, PSO, and event-triggered mechanism are shown in Table 1.  
The parameters related to the prescribed performance function of the position controller were \(p_{x0}=p_{y0}=p_{z0}=3.5\), \(p_{x\infty}=p_{y\infty}=p_{z\infty}=0.3\), \(\mu_{x}=\mu_{y}=\mu_{z}=1\), \(\underline{\gamma}_{x}=\underline{\gamma}_{y}=\underline{\gamma}_{z}= \overline{\gamma}_{x}=\overline{\gamma}_{y}=0.5\), \(\overline{\gamma}_{z}=1\). The parameters related to the prescribed performance function of the attitude controller were \(p_{\phi 0}=p_{\theta 0}=p_{\psi 0}=3\), \(p_{\phi\infty}=p_{\theta\infty}=0.1\), \(\mu_{\phi}=\mu_{\theta}=\mu_{\phi}=0.5\), \(\underline{\gamma}_{\phi}=\underline{\gamma}_{\theta}=\underline{\gamma}_{ \psi}=\overline{\gamma}_{\phi}=\overline{\gamma}_{\theta}=\overline{\gamma}_{ \psi}=0.9\).  
Let the initial position and attitude of the quadrotor be \(\begin{bmatrix}x&y&z&\phi&\theta&\psi\end{bmatrix}^{T}=\begin{bmatrix}0&0&0&0&0&0 \end{bmatrix}^{T}\). The desired trajectory was set as an expanding arcing path ascending from the origin, expressed by  
\[\begin{cases}x_{d}(t)=0.5t\sin(0.8t)\\ y_{d}(t)=0.5t\cos(0.8t)\\ z_{d}(t)=3+0.1t\end{cases}.\]  
Let yaw angle \(\psi_{d}=0^{\circ}\). Let the load \(\mathcal{L}=\begin{bmatrix}m,l_{x},l_{y},l_{z}\end{bmatrix}^{T}\) vary on the flight as  
\[\mathcal{L}(t)=\begin{bmatrix}1.5,0.1\cos(1t)+0.2\sin(2t),0.2\cos(2t)+0.1\sin (2t),0.3\end{bmatrix}^{T}.\]  
Consider a quadrotor maintaining connection with a payload that continuously oscillates within the \(x-y\) plane, resulting in dynamic changes to the center of gravity. Both the attitude and position channels are subject to zero-mean Gaussian noise disturbances with a standard deviation of \(1\). By constructing two typical failure modes, loss of effectiveness and bias fault, the system verifies the fault-tolerant control performance and robust stability of the designed controller under different fault conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Parameters of Quadrotor**} & \multicolumn{2}{c}{**Parameters of PSO**} & \multicolumn{2}{c}{**Parameters of ETM**} \\ \multicolumn{1}{c}{**Symbol**} & **Value** & **Symbol** & **Value** & **Symbol** & **Value** \\ \hline \(M\) & 2.5 (kg) & \(n\) & 50 & \(\gamma_{1}\) & 0.01 \\ \(l\) & 0.6 (m) & \(d\) & 4 & \(\gamma_{2}\) & 0.03 \\ \(g\) & 9.8 (m/s\({}^{2}\)) & \(w_{ini}\) & 0.8 & \(M_{1}^{1}\) & 5 \\ \(k_{c}\) & 0.06 (N\(\cdot\)m/m\({}^{2}\)) & \(w_{fin}\) & 0.2 & \(M_{1}^{2}/M_{1}^{3}\) & 1000 \\ \(k_{a}\) & 0.02 (N\(\cdot\)s\({}^{2}\)/rad\({}^{2}\)) & \(c_{1}/c_{2}\) & 2 & \(M_{1}^{4}\) & 10 \\ \(J_{x}\) & 1.4 (kg\(\cdot\)m\({}^{2}\)) & \(max\_iter\) & 15 & \(M_{2}\) & 10 \\ \(J_{y}\) & 1.4 (kg\(\cdot\)m\({}^{2}\)) & \(\gamma_{p}\) & 0.15 & & \\ \(j_{z}\) & 2.8 (kg\(\cdot\)m\({}^{2}\)) & \(\underline{t}\) & 2 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of quadrotor, PSO, and event-triggered mechanism.